From 4ff3650b441a25245bc343b0de37289e63ab221e Mon Sep 17 00:00:00 2001
From: Sophie Lee <sophie.a.lee10@gmail.com>
Date: Thu, 4 Jul 2024 17:11:21 +0100
Subject: [PATCH] Convert RMarkdown files to quarto, host as book, add
 appendices

---
 .gitignore                                    |    2 +
 _book/Introduction-to-R-with-Tidyverse.pdf    |  Bin 0 -> 1204732 bytes
 _book/data_description.qmd                    |   45 +
 _book/images/arrow_shortcut.png               |  Bin 0 -> 1122 bytes
 _book/images/code_chunk_icon.png              |  Bin 0 -> 1208 bytes
 _book/images/export_shortcut.png              |  Bin 0 -> 1760 bytes
 _book/images/knit_icon.png                    |  Bin 0 -> 1585 bytes
 _book/images/new_file_shortcut.png            |  Bin 0 -> 854 bytes
 _book/images/open_shortcut.png                |  Bin 0 -> 995 bytes
 _book/images/project_icon.png                 |  Bin 0 -> 2176 bytes
 _book/images/r_meme.png                       |  Bin 0 -> 270681 bytes
 _book/images/rmarkdown_new.png                |  Bin 0 -> 41009 bytes
 _book/images/rmarkdown_pipe.png               |  Bin 0 -> 17045 bytes
 _book/images/rstudio_ide.png                  |  Bin 0 -> 190685 bytes
 _book/images/run_shortcut.png                 |  Bin 0 -> 1135 bytes
 _book/images/save_shortcut.png                |  Bin 0 -> 419 bytes
 _book/images/visualisation_table.png          |  Bin 0 -> 115508 bytes
 _book/images/zoom_shortcut.png                |  Bin 0 -> 1495 bytes
 _book/index.html                              |  678 ++++++
 _book/search.json                             |  162 ++
 _book/session1_notes.html                     | 1013 ++++++++
 _book/session2_notes.html                     | 1174 ++++++++++
 _book/session3_notes.html                     |  887 +++++++
 _book/session4_notes.html                     | 1113 +++++++++
 .../figure-html/Add custom theme-1.png        |  Bin 0 -> 19894 bytes
 .../figure-html/Facet by region-1.png         |  Bin 0 -> 32889 bytes
 .../figure-html/Factor region-1.png           |  Bin 0 -> 31249 bytes
 .../Manually setting aesthetics-1.png         |  Bin 0 -> 19971 bytes
 .../figure-html/Scatter without London-1.png  |  Bin 0 -> 20017 bytes
 .../Scatterplot SFA and CT total 2020-1.png   |  Bin 0 -> 20145 bytes
 ...rplot, SFA and council tax by region-1.png |  Bin 0 -> 31731 bytes
 .../figure-html/log1p transformation-1.png    |  Bin 0 -> 26405 bytes
 .../figure-html/region colour palette-1.png   |  Bin 0 -> 26353 bytes
 .../figure-html/scale_x and scale_y-1.png     |  Bin 0 -> 27440 bytes
 .../figure-html/theme void-1.png              |  Bin 0 -> 14857 bytes
 _book/session5_notes.html                     | 1107 +++++++++
 ...sfa_2020 and ct_total_2020 by region-1.png |  Bin 0 -> 25556 bytes
 _book/site_libs/bootstrap/bootstrap-icons.css | 2078 +++++++++++++++++
 .../site_libs/bootstrap/bootstrap-icons.woff  |  Bin 0 -> 176200 bytes
 _book/site_libs/bootstrap/bootstrap.min.css   |   12 +
 _book/site_libs/bootstrap/bootstrap.min.js    |    7 +
 _book/site_libs/clipboard/clipboard.min.js    |    7 +
 _book/site_libs/quarto-html/anchor.min.js     |    9 +
 _book/site_libs/quarto-html/popper.min.js     |    6 +
 .../quarto-syntax-highlighting.css            |  203 ++
 _book/site_libs/quarto-html/quarto.js         |  899 +++++++
 _book/site_libs/quarto-html/tippy.css         |    1 +
 _book/site_libs/quarto-html/tippy.umd.min.js  |    2 +
 _book/site_libs/quarto-nav/headroom.min.js    |    7 +
 _book/site_libs/quarto-nav/quarto-nav.js      |  289 +++
 .../quarto-search/autocomplete.umd.js         |    3 +
 _book/site_libs/quarto-search/fuse.min.js     |    9 +
 .../site_libs/quarto-search/quarto-search.js  | 1286 ++++++++++
 _quarto.yml                                   |   40 +
 data_description.qmd                          |   45 +
 exercise solutions.qmd                        |  353 +++
 index.qmd                                     |   23 +
 session1_notes.Rmd => session1_notes.qmd      |  136 +-
 session2_notes.Rmd => session2_notes.qmd      |   83 +-
 session3_notes.Rmd => session3_notes.qmd      |   41 +-
 session4_notes.Rmd => session4_notes.qmd      |   84 +-
 session5_notes.qmd                            |  304 +++
 62 files changed, 11950 insertions(+), 158 deletions(-)
 create mode 100644 _book/Introduction-to-R-with-Tidyverse.pdf
 create mode 100644 _book/data_description.qmd
 create mode 100644 _book/images/arrow_shortcut.png
 create mode 100644 _book/images/code_chunk_icon.png
 create mode 100644 _book/images/export_shortcut.png
 create mode 100644 _book/images/knit_icon.png
 create mode 100644 _book/images/new_file_shortcut.png
 create mode 100644 _book/images/open_shortcut.png
 create mode 100644 _book/images/project_icon.png
 create mode 100644 _book/images/r_meme.png
 create mode 100644 _book/images/rmarkdown_new.png
 create mode 100644 _book/images/rmarkdown_pipe.png
 create mode 100644 _book/images/rstudio_ide.png
 create mode 100644 _book/images/run_shortcut.png
 create mode 100644 _book/images/save_shortcut.png
 create mode 100644 _book/images/visualisation_table.png
 create mode 100644 _book/images/zoom_shortcut.png
 create mode 100644 _book/index.html
 create mode 100644 _book/search.json
 create mode 100644 _book/session1_notes.html
 create mode 100644 _book/session2_notes.html
 create mode 100644 _book/session3_notes.html
 create mode 100644 _book/session4_notes.html
 create mode 100644 _book/session4_notes_files/figure-html/Add custom theme-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Facet by region-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Factor region-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Manually setting aesthetics-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Scatter without London-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Scatterplot SFA and CT total 2020-1.png
 create mode 100644 _book/session4_notes_files/figure-html/Scatterplot, SFA and council tax by region-1.png
 create mode 100644 _book/session4_notes_files/figure-html/log1p transformation-1.png
 create mode 100644 _book/session4_notes_files/figure-html/region colour palette-1.png
 create mode 100644 _book/session4_notes_files/figure-html/scale_x and scale_y-1.png
 create mode 100644 _book/session4_notes_files/figure-html/theme void-1.png
 create mode 100644 _book/session5_notes.html
 create mode 100644 _book/session5_notes_files/figure-html/scatterplot sfa_2020 and ct_total_2020 by region-1.png
 create mode 100644 _book/site_libs/bootstrap/bootstrap-icons.css
 create mode 100644 _book/site_libs/bootstrap/bootstrap-icons.woff
 create mode 100644 _book/site_libs/bootstrap/bootstrap.min.css
 create mode 100644 _book/site_libs/bootstrap/bootstrap.min.js
 create mode 100644 _book/site_libs/clipboard/clipboard.min.js
 create mode 100644 _book/site_libs/quarto-html/anchor.min.js
 create mode 100644 _book/site_libs/quarto-html/popper.min.js
 create mode 100644 _book/site_libs/quarto-html/quarto-syntax-highlighting.css
 create mode 100644 _book/site_libs/quarto-html/quarto.js
 create mode 100644 _book/site_libs/quarto-html/tippy.css
 create mode 100644 _book/site_libs/quarto-html/tippy.umd.min.js
 create mode 100644 _book/site_libs/quarto-nav/headroom.min.js
 create mode 100644 _book/site_libs/quarto-nav/quarto-nav.js
 create mode 100644 _book/site_libs/quarto-search/autocomplete.umd.js
 create mode 100644 _book/site_libs/quarto-search/fuse.min.js
 create mode 100644 _book/site_libs/quarto-search/quarto-search.js
 create mode 100644 _quarto.yml
 create mode 100644 data_description.qmd
 create mode 100644 exercise solutions.qmd
 create mode 100644 index.qmd
 rename session1_notes.Rmd => session1_notes.qmd (80%)
 rename session2_notes.Rmd => session2_notes.qmd (88%)
 rename session3_notes.Rmd => session3_notes.qmd (92%)
 rename session4_notes.Rmd => session4_notes.qmd (91%)
 create mode 100644 session5_notes.qmd

diff --git a/.gitignore b/.gitignore
index f309394..ee091e7 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,3 +5,5 @@
 
 **.Rmd
 
+
+/.quarto/
diff --git a/_book/Introduction-to-R-with-Tidyverse.pdf b/_book/Introduction-to-R-with-Tidyverse.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..29835f1b01feb27b495cc91f927b80706f3b8ada
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diff --git a/_book/data_description.qmd b/_book/data_description.qmd
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--- /dev/null
+++ b/_book/data_description.qmd
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+# Data description {.unnumbered}
+
+## What is 'CSP'?
+The data we will be using throughout this course relates to the Core Spending Power (CSP) of English local authorities between 2015 and 2020. This is a measure of the resources available to local authorities in England to fund service delivery. The CSP is broken down into several components, presented as variables in the data. These components include:
+
+- Settlement Funding Assessment (`sfa`)
+- Compensation for under-indexing the business rates multipler (`under_index`)
+- Income from council tax (`ct_total`)
+- New Homes Bonus (`nhb`)
+- Rural Services Delivery Grant (`rsdg`)
+
+Spending power is given in millions of pounds (£). The data were provided by the UK government's Department for Levelling Up, Housing and Communities. Full guidance on the data can be found on the [Department's website](https://www.gov.uk/government/publications/explanatory-note-on-core-spending-power-provisional-local-government-finance-settlement-2024-to-2025/explanatory-note-on-core-spending-power-provisional-local-government-finance-settlement-2024-to-2025). A brief description of the variables included in the data are given below.
+
+## Descriptions of variables
+
+### Identifier variables
+Each dataset contains a unique identifier code variable, `ons_code`. This is a code given by the Government's Office for National Statistics (ONS), and is used to join different datasets. There is also an `authority` variable which contains the local authority name (to see where each local authority lies on a map, you can visit the [Government's geoportal website](https://geoportal.statistics.gov.uk/documents/cb64eeb1b0a74e5ca277f9fac58500f4/explore)).
+
+### Regions of England
+In addition to each local authority's unique code and name, we are given the region that they lie within. England is separated into 9 regions (shown on [this map](https://geoportal.statistics.gov.uk/documents/bfe6f7099f9e4cc59f8064962959bfb5/explore)) which are given as acronyms in the data. These are:
+
+- `L` = London
+- `NW` = North West
+- `NE` = North East
+- `YH` = Yorkshire and the Humber
+- `WM` = West Midlands
+- `EM` = East Midlands
+- `EE` = East England
+- `SW` = South West
+- `SE` = South East
+
+### Settlement Funding Assessment (SFA)
+The Settlement Funding Assessment (`sfa` in the data) is the baseline funding level of local authorities, and includes the Revenue Support Grant (a central government grant given to local authorities).
+
+### Under-indexing business rate multipliers
+The `under_index` variable is given to compensate local authorities that under-indexed business rate multipliers in previous years (i.e. those that used a measure of inflation that was lower than that should have been used).
+
+### Council tax
+Council tax (`ct_total`) is the income made by each local authority from council tax. In England, the amount of council tax charged to residents is set by each local authority to make up additional revenue needed to cover planned spending.
+
+### New Homes Bonus
+The `nhb` variables is the funding received as part of the New Homes Bonus, a government inncentive to encourage local authorities to promote new housing delevopment.
+
+### Rural Services Delivery Grant 
+The `rsdg` variable is funding received as part of the Rural Services Delivery Grant, provided to rural councils to recognise additional costs in these areas.
diff --git a/_book/images/arrow_shortcut.png b/_book/images/arrow_shortcut.png
new file mode 100644
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new file mode 100644
index 0000000000000000000000000000000000000000..5b590a6954332935961793d58adadc78beb21c09
GIT binary patch
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index 0000000000000000000000000000000000000000..f1b97e964b4480c7445a58f33a56a99da90050bb
GIT binary patch
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diff --git a/_book/images/knit_icon.png b/_book/images/knit_icon.png
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GIT binary patch
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GIT binary patch
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diff --git a/_book/images/open_shortcut.png b/_book/images/open_shortcut.png
new file mode 100644
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GIT binary patch
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+<meta name="dcterms.date" content="2024-06-15">
+
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+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session1_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">2</span>&nbsp; <span class="chapter-title">Session 1: Introduction to R and RStudio</span></span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session2_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Session 2: Introduction to tidyverse and data wrangling</span></span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session3_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">4</span>&nbsp; <span class="chapter-title">Session 3: Data preparation and manipulation</span></span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session4_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">5</span>&nbsp; <span class="chapter-title">Session 4: Data visualisation with ggplot2</span></span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session5_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">6</span>&nbsp; <span class="chapter-title">Reproducible research with RMarkdown</span></span></a>
+  </div>
+</li>
+    </ul>
+    </div>
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+<div id="quarto-sidebar-glass" class="quarto-sidebar-collapse-item" data-bs-toggle="collapse" data-bs-target=".quarto-sidebar-collapse-item"></div>
+<!-- margin-sidebar -->
+    <div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
+        <nav id="TOC" role="doc-toc" class="toc-active">
+    <h2 id="toc-title">Table of contents</h2>
+   
+  <ul>
+  <li><a href="#welcome" id="toc-welcome" class="nav-link active" data-scroll-target="#welcome"><span class="header-section-number">1</span> Welcome!</a>
+  <ul class="collapse">
+  <li><a href="#data-used-for-the-course" id="toc-data-used-for-the-course" class="nav-link" data-scroll-target="#data-used-for-the-course"><span class="header-section-number">1.1</span> Data used for the course</a></li>
+  <li><a href="#license" id="toc-license" class="nav-link" data-scroll-target="#license"><span class="header-section-number">1.2</span> License</a></li>
+  </ul></li>
+  </ul>
+</nav>
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+<!-- main -->
+<main class="content" id="quarto-document-content">
+
+<header id="title-block-header" class="quarto-title-block default">
+<div class="quarto-title">
+<h1 class="title">Introduction to R with Tidyverse</h1>
+</div>
+
+
+
+<div class="quarto-title-meta">
+
+    <div>
+    <div class="quarto-title-meta-heading">Author</div>
+    <div class="quarto-title-meta-contents">
+             <p>Sophie Lee </p>
+          </div>
+  </div>
+    
+    <div>
+    <div class="quarto-title-meta-heading">Published</div>
+    <div class="quarto-title-meta-contents">
+      <p class="date">June 15, 2024</p>
+    </div>
+  </div>
+  
+    
+  </div>
+  
+
+
+</header>
+
+
+<section id="welcome" class="level1" data-number="1">
+<h1 data-number="1"><span class="header-section-number">1</span> Welcome!</h1>
+<p>Welcome to the course materials for the <strong>Introduction to R with Tidyverse</strong> course.</p>
+<p>This course is designed to equip you with the essential skills to leverage the power of R and Tidyverse for their work. The course begins with a gentle introduction to the user-friendly RStudio interface and the basics of the R coding language, or syntax. This makes it ideal for anyone with little or no prior coding experience, or those looking for a refresher of the basics.</p>
+<p>Through this course, you will learn how to manipulate, transform, and clean data efficiently, and how to create compelling visualisations to communicate your findings effectively. Throughout the course, we will discuss best practices for reproducible coding.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Throughout these notes, you will also see boxes like this containing ‘style tips’. These ensure that your code follows the <a href="https://style.tidyverse.org/">Tidyverse style guide</a>, making it as consistent and readable as possible.</p>
+</div>
+</div>
+<section id="data-used-for-the-course" class="level2" data-number="1.1">
+<h2 data-number="1.1" class="anchored" data-anchor-id="data-used-for-the-course"><span class="header-section-number">1.1</span> Data used for the course</h2>
+<p>The examples and exercises in these materials are based on real world data. This data relates to the Core Spending Power (CSP) of English local authorities between 2015 and 2020.</p>
+<p>Data for this course can be downloaded from the <code>data</code> folder of this course’s <a href="https://github.com/sophie-a-lee/Introduction_R_Tidyverse_course">repository</a>.</p>
+<p>For more information about this data, including variable descriptions and sources, see <a href="data_description.qmd">the appendix</a>.</p>
+</section>
+<section id="license" class="level2" data-number="1.2">
+<h2 data-number="1.2" class="anchored" data-anchor-id="license"><span class="header-section-number">1.2</span> License</h2>
+<p>I believe that science should not be behind a paywall, that is why these materials are available for free online, licensed under a <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA licence</a>.</p>
+
+
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+    "text": "2.1 The RStudio interface\nThere are a number of software packages based on the R programming language aimed at making writing and running analyses easier for users. They all run R in the background but look different and contain different features.\nRStudio has been chosen for this course as it allows users to create script files, allowing code to be re-run, edited, and shared easily. RStudio also provides tools to help easily identify errors in R code, integrates help documentation into the main console and uses colour-coding to help read code at a glance.\nBefore installing RStudio, we must ensure that R is downloaded onto the machine. R is available to download for free for Windows, Mac, or Linux via the CRAN website.\nRstudio is also free to download from the Posit website.",
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+    "text": "2.1.0.1 The RStudio console window\nThe screenshot below shows the RStudio interface which comprises of four windows:\n\n\n\nRStudio interface\n\n\nWindow A: R script files\nAll analysis and actions in R are carried out using the R syntax language. R script files allow you to write and edit code before running it in the console window.\n\n\n\n\n\n\nStyle tip\n\n\n\nLimit script files to 80 characters per line to ensure it is readable.\nRStudio has an option to add a margin that makes this easier to adhere to. Under the Tools drop-down menu, select Global options. Select Code from the list on the right, then under the Display tab, tick the Show margin box.\n\n\nIf this window is not visible, create a new script file using File -&gt; New File -&gt; R Script from the drop-down menus or clicking the  icon above the console and selecting R Script. This will open a new, blank script file. More than one script file can be open at the same time.\nCode entered into the script file does not run automatically. To run commands from the script, highlight the code and click the  icon above the top right corner of the script window (this can be carried out by pressing Ctrl + Enter in Windows or Command + Enter on a Mac computer). More than one command can be run at the same time by highlighting all of them.\nThe main advantage of using the script file rather than entering the code directly into the console is that it can be saved, edited and shared. To save a script file, use File -&gt; Save As… from the drop down menu, or click the  icon at the top of the window. It is important to save the script files at regular intervals to avoid losing work. Once the script file has been saved, we can also use the keyboard shortcuts Ctrl + s on Windows and Command + s on Mac to save the latest script file.\n\n\n\n\n\n\nStyle tip\n\n\n\nScript file names should be meaningful, lower case, and end in .R. Avoid using special characters in file names, including spaces. Use _ instead of spaces.\nWhere files should be run in a specific order, prefix the file name with numbers.\n\n\nPast script files can be opened using File -&gt; Open File… from the drop-down menu or by clicking the  icon and selecting a .R file. The keyboard shortcut to open an existing script file is Ctrl + o on Windows, and Command + o on Macs.\nWindow B: The R console\nThe R console window is where all commands run from the script file, results (other than plots), and messages, such as errors, are displayed. Commands can be written directly into the R console after the &gt; symbol and executed using Enter on the keyboard. It is not recommended to write code directly into the console as it is cannot be saved or replicated.\nEvery time a new R session is opened, details about version and citations of R will be given by default. To clear text from the console window, use the keyboard shortcut control + l (this is the same for both Windows and Mac users). Be aware that this clears all text from the console, including any results. Before running this command, check that any results can be replicated within the script file.\nWindow C: Environment and history\nThis window lists all data and objects currently loaded into R. More details on the types of objects and how to use the Environment window are given in later sections.\nWindow D: Files, plots, packages and help\nThis window has many potential uses: graphics are displayed and can be saved from here, and R help files will appear here. This window is only available in the RStudio interface and not in the basic R package.\n\n\nExercise 1\n\nOpen a new script file if you have not already done so.\nSave this script file into an appropriate location.",
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+    "text": "2.2 R syntax\nAll analyses within R are carried out using syntax, the R programming language. It is important to note that R is case-sensitive, so always ensure that you use the correct combination of upper and lower case letters when running functions or calling objects.\nAny text written in the R console or script file can be treated the same as text from other documents or programmes: text can be highlighted, copied and pasted to make coding more efficient.\nWhen creating script files, it is important to ensure they are clear and easy to read. Comments can be added to script files using the # symbol. R will ignore any text following the # on the same line.\n\n\n\n\n\n\nStyle tip\n\n\n\nCombining # and - creates sections within a script file, making them easier to navigate and organise.\nFor example:\n\n# Load data ----------\n\n# Tidy data ----------\n\n\n\n\n\n\n\n\n\nHelpful hint\n\n\n\nTo comment out chunks of code, highlight the rows and use the keyboard shortcut ctrl + shift + c on Windows, and Command + shift + c on Mac\n\n\nThe choice of brackets in R coding is particularly important as they all have different functions:\n\nRound brackets ( ) are the most commonly used as they define arguments of functions. Any text followed by round brackets is assumed to be a function and R will attempt to run it. If the name of a function is not followed by round brackets, R will return the algorithm used to create the function within the console.\nSquare brackets [ ] are used to set criteria or conditions within a function or object.\nCurly brackets { } are used within loops, when creating a new function, and within for and if functions.\n\nAll standard notation for mathematical calculations (+, -, *, /, ^, etc.) are compatible with R. At its simplest level, R is just a very powerful calculator!\n\n\n\n\n\n\nStyle tip\n\n\n\nAlthough R will work whether a space is added before/after a mathematical operator, the style guide recommends to add them surrounding most mathematical operations (+, -, *, /), but not around ^.\nFor example:\n\n# Stylish code\n1959 - 683\n(351 + 457)^2 - (213 + 169)^2\n\n# Un-stylish code\n1959-683\n(351+457)^2 - (213 + 169) ^ 2\n\n\n\n\nExercise 2\n\nAdd your name and the date to the top of your script file (hint: comment this out so R does not try to run it)\nUse R to calculate the following calculations. Add the result to the same line of the script file in a way that ensures there are no errors in the code.\n\n\n\\(64^2\\)\n\\(3432 \\div 8\\)\n\\(96 \\times 72\\)\n\nWhen you have finished this exercise, select the entire script file (using ctrl + a on windows or Command + a on Mac) and run it to ensure there are no errors in the code.",
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+    "text": "2.3 R objects and functions\n\n2.3.1 Objects\nOne of the main advantages to using R over other software packages such as SPSS is that more than one dataset can be accessed at the same time. A collection of data stored in any format within the R session is known as an object. Objects can include single numbers, single variables, entire datasets, lists of datasets, or even tables and graphs.\n\n\n\n\n\n\nStyle tip\n\n\n\nObject names should only contain lower case letters, numbers and _ (instead of a space to separate words). The should be meaningful and concise.\n\n\nObjects are defined in R using the &lt;- or = symbols. For example,\n\nobject_1 &lt;- 81\n\nCreates an object in the environment named object_1, which takes the value 81. This will appear in the environment window of the console (window C from the interface shown earlier).\n\n\n\n\n\n\nStyle tip\n\n\n\nAlthough both work, use &lt;- for assignment, not =.\n\n\nTo retrieve an object, type its name into the script or console and run it. This object can then be included in functions or operations in place of the value assigned to it:\n\nobject_1\n## [1] 81\n\nobject_1 * 2\n## [1] 162\n\nR has some mathematical objects stored by default such as pi that can be used in calculations.\n\npi\n## [1] 3.141593\n\nThe [1] that appears at the beginning of each output line indicates that this is the first element in the object. If there were two lines then the second line would start with the number of that element in square brackets.\nFor example, if we had an object with 6 elements and when called the first line contained the first 5 elements, each line would begin with [1] and [6] respectively.\n\n\n2.3.2 Functions\nFunctions are built-in commands that allow R users to run analyses. All functions require the definition of arguments within round brackets (). Each function requires different information and has different arguments that can be used to customise the analysis. A detailed list of these arguments and a description of the function can be found in the function’s associated help file.\n\n\n2.3.3 Help files\nEach function that exists within R has an associated help file. RStudio does not require an internet connection to access these help files if the function is available in the current session of R.\nTo retrieve help files, enter ? followed by the function name into the console window, e.g ?mean. The help file will appear in window D of the interface shown in the introduction.\nHelp files contain the following information:\n\nDescription: what the function is used for\nUsage: how the function is used\nArguments: required and optional arguments entered into round brackets necessary for the function to work\nDetails: relevant details about the function in question\nReferences\nSee also: links to other relevant functions\nExamples: example code with applications of the function\n\n\n\n2.3.4 Error and warning messages\nWhere a function or object has not been correctly specified, or their is some mistake in the syntax that has been sent to the console, R will return an error message. These messages are generally informative and include the location of the error.\nThe most common errors include misspelling functions or objects:\n\nsqrt(ojbect_1)\n## Error in eval(expr, envir, enclos): object 'ojbect_1' not found\n\nSqrt(object_1)\n## Error in Sqrt(object_1): could not find function \"Sqrt\"\n\nOr where an object has not yet been specified:\n\nplot(x, y)\n## Error in eval(expr, envir, enclos): object 'x' not found\n\nWhen R returns an error message, this means that the operation has been completely halted. R may also return warning messages which look similar to errors but does not necessarily mean the operation has been stopped.\nWarnings are included to indicate that R suspects something in the operation may be wrong and should be checked. There are occasions where warnings can be ignored but this is only after the operation has been checked.\nWhen working within the R console, if an incomplete command is run, a + symbol will appear in the console, rather than the usual &gt;. This indicates that R expects you to keep writing the previous code. To overcome this issue, either finish the command on the next line of the console, or press the esc button on your keyboard to start from scratch.\nOne of the benefits of using RStudio rather than the basic R package is that it will suggest object or function names after typing the first few letters. This avoids spelling mistakes and accidental errors when running code. To accept the suggestion, either click the correct choice with your mouse or use the tab button on your keyboard.\n\n\n2.3.5 Cleaning the environment\nTo remove objects from the RStudio environment, we can use the rm function. This can be combined with the ls() function, which lists all objects in the environment, to remove all objects currently loaded:\n\nrm(list = ls())\n\n\n\n\n\n\n\nWarning\n\n\n\nThere are no undo and redo buttons for R syntax. The rm function will permanently delete objects from the environment. The only way to reverse this is to re-run the code that created the objects originally from the script file.\n\n\n\n\n2.3.6 R packages\nR packages are a collection of functions and datasets developed by R users that expand existing R capabilities or add completely new ones. Packages allow users to apply the most up-to-date methods shortly after they are developed, unlike other statistical software packages that require an entirely new version.\n\n2.3.6.1 Installing packages from CRAN\nThe quickest way to install a package in R is by using the install.packages function. This sends RStudio to the online repository of tested and verified R packages (known as CRAN) and downloads the package files onto the machine you are currently working from in temporary files. Ensure that the package you wish to install is spelled correctly and surrounded by ''.\n\n\n\n\n\n\nWarning\n\n\n\nThe install.packages function requires an internet connection, and can take a long time if the package has a lot of dependent packages that also need downloading.\nThis process should only be carried out the first time a package is used on a machine, or when a substantial update has taken place, to download the latest version of the package.\n\n\n\n\n2.3.6.2 Loading packages to an R session\nEvery time a new session of RStudio is opened, packages must be reloaded. To load a package into R (and gain access to the associated functions and data), use the library function.\nLoading a package does not require an internet connection, but will only work if the package has already been installed and saved onto the computer you are working from. If you are unsure, use the function installed.packages to return a list of all packages that are loaded onto the machine you are working from.\n\n\n\n\n\n\nStyle tip\n\n\n\nAdd your library function at the beginning of your script file. This reminds you to re-load packages when opening a new R session, and reduces the chance of error messages from functions requiring these packages.",
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+    "text": "3.1.1 Styles of R coding\nUp to this point, we have not thought about the style of R coding we will be using. There are different approaches to R coding that we can use, they can be thought of as different dialects of the R programming language.\nThe choice of R ‘dialect’ depends on personal preference. Some prefer to use the ‘base R’ approach that does not rely on any packages that may need updating, making it a more stable approach. However, base R can be difficult to read for those not comfortable with coding.\n\n\n\n\n\n\n\n\n\nThe alternative approach that we will be adopting in this course is the ‘tidyverse’ approach. Tidyverse is a set of packages that have been designed to make R coding more readable and efficient. They have been designed with reproducibility in mind, which means there is a wealth of online (mostly free), well-written resources available to help use these packages.\nIf you have not done so already, install the tidyverse packages to your machine using the following code:\n\ninstall.packages('tidyverse')\n\n\n\n\n\n\n\nWarning\n\n\n\nThis can take a long time if you have never downloaded the tidyverse packages before as there are many dependencies that are required. Do not stress if you get a lot of text in the console! This is normal, but watch out for any error messages.\n\n\nOnce the tidyverse package is installed, we must load it into the current working session. At the beginning of your script file add the following syntax:\n\nlibrary(tidyverse)\n\n\n\n\n\n\n\nStyle tip\n\n\n\nBegin every script file with the library command, loading packages in before any data. This avoids any potential errors arising where functions are called before the necessary package has been loaded into the current session.\n\n\n\n\n3.1.2 The working directory\nThe working directory is a file path on your computer that R sets as the default location when opening, saving, or exporting documents, files, and graphics. This file path can be specified manually but setting the working directory saves time and makes code more efficient.\nThe working directory can be set manually by using the Session -&gt; Set Working Directory -&gt; Change Directory… option from the drop-down menu, or the setwd function. Both options require the directory to be specified each time R is restarted, are sensitive to changes in folders within the file path, and cannot be used when script files are shared between colleagues.\nAn alternative approach that overcomes these issues is to create an R project.\n\n3.1.2.1 R projects\nR projects are files (saved with the .Rproj extension) that keep associated files (including scripts, data, and outputs) grouped together. An R project automatically sets the working directory relative to its current location, which makes collaborative work easier, and avoids issues when a file path is changed.\nProjects are created by using the File -&gt; New project option from the drop-down menu, or using the  icon from the top-right corner of the RStudio interface. Existing projects can be opened under the File -&gt; Open project… drop-down menu or using the project icon.\nWhen creating a new project, we must choose whether we want to create a new directory or use an existing one. Usually, we will have already set up a folder containing data or other documents related to the analysis we plan to carry out. If this is the case, we are using an existing directory and selecting the analysis folder as the project directory.\n\n\n\n\n\n\nStyle tip\n\n\n\nHave a clear order to your analysis folder. Consider creating separate folders within a project for input and output data, documentation, and outputs such as graphs or tables.",
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+    "text": "3.2 4.3 Data input\nTo ensure our code is collaborative and reproducible, we should strive to store data in formats that can be used across multiple platforms. One of the best ways to do this is to store data as a comma-delimited file (.csv). CSV files can be opened by a range of different softwares (including R, SPSS, STATA and excel), and base R can be used to open these files without requiring additional packages.\nBefore loading files in R, it is essential to check that they are correctly formatted. Data files should only contain one sheet with no pictures or graphics, each row should correspond to a case or observation and each column should correspond to a variable.\nTo avoid any errors arising from spelling mistakes, we can use the list.files function to return a list of files and folders from the current working directory. The file names can be copied from the console and pasted into the script file. As the data are saved in a folder within the working directory, we must add the argument path = to specify the folder we want to list files from.\n\nlist.files(path = \"data\")\n## [1] \"CSP_2015.csv\"         \"CSP_2016.csv\"         \"CSP_2017.csv\"        \n## [4] \"CSP_2018.csv\"         \"CSP_2019.csv\"         \"CSP_2020.csv\"        \n## [7] \"CSP_long_201520.csv\"  \"data_description.pdf\"\n\nThis list should contain 6 CSV files with the core spending power in local authorities in England between 2015 and 2020. We will first load and explore the 2020 data using the read_csv function and attaching the data to an object. Remember to add the data folder to the file name.\n\ncsp_2020 &lt;- read_csv(\"data/CSP_2020.csv\")\n\nImported datasets will appear in the Environment window of the console once they are saved as objects. This Environment also displays the number of variables and observations in each object. To preview the contents of an object, click on its name in the Environment window or use the function View(data).\nOther useful functions that help explore a dataset include:\n\n# Return variable names from a dataset object\nnames(csp_2020)\n## [1] \"ons_code\"         \"authority\"        \"region\"           \"sfa_2020\"        \n## [5] \"under_index_2020\" \"ct_total_2020\"    \"nhb_2020\"         \"nhb_return_2020\" \n## [9] \"rsdg_2020\"\n\n\n\n\n\n\n\nStyle tip\n\n\n\nVariable names should follow the same style rules as object names: only contain lower case letters, numbers, and use _ to separate words. They should be meaningful and concise.\n\n\n\n# Display information about the structure of an object\nstr(csp_2020)\n## spc_tbl_ [396 × 9] (S3: spec_tbl_df/tbl_df/tbl/data.frame)\n##  $ ons_code        : chr [1:396] \"E07000223\" \"E07000026\" \"E07000032\" \"E07000224\" ...\n##  $ authority       : chr [1:396] \"Adur\" \"Allerdale\" \"Amber Valley\" \"Arun\" ...\n##  $ region          : chr [1:396] \"SE\" \"NW\" \"EM\" \"SE\" ...\n##  $ sfa_2020        : num [1:396] 1.77 3.85 3.23 3.67 4.08 ...\n##  $ under_index_2020: num [1:396] 0.0708 0.1465 0.1292 0.147 0.1557 ...\n##  $ ct_total_2020   : num [1:396] 6.53 5.4 6.85 11.61 6.42 ...\n##  $ nhb_2020        : num [1:396] 0.0881 0.6061 1.5786 2.2949 1.1547 ...\n##  $ nhb_return_2020 : num [1:396] 0 0 0 0 0 0 0 0 0 0 ...\n##  $ rsdg_2020       : num [1:396] 0 0.326 0 0 0 ...\n##  - attr(*, \"spec\")=\n##   .. cols(\n##   ..   ons_code = col_character(),\n##   ..   authority = col_character(),\n##   ..   region = col_character(),\n##   ..   sfa_2020 = col_double(),\n##   ..   under_index_2020 = col_double(),\n##   ..   ct_total_2020 = col_double(),\n##   ..   nhb_2020 = col_double(),\n##   ..   nhb_return_2020 = col_double(),\n##   ..   rsdg_2020 = col_double()\n##   .. )\n##  - attr(*, \"problems\")=&lt;externalptr&gt;\n\nOutput from the str function differs depending on the type of object it is applied to. For example, this object is a tibble (tbl, Tidyverse’s name for a dataset). The information given about tibbles includes the object dimensions (396 x 9, or 396 rows and 9 columns), variable names, and variable types.\nIt is important to check that R has correctly recognised variable type when data are loaded, before generating any visualisations or analysis. If variables are incorrectly specified, this could either lead to errors or invalid analyses. We will see how to change variables types later in this session.\n\n# Return the first 6 rows of the tibble\nhead(csp_2020)\n## # A tibble: 6 × 9\n##   ons_code  authority    region sfa_2020 under_index_2020 ct_total_2020 nhb_2020\n##   &lt;chr&gt;     &lt;chr&gt;        &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;\n## 1 E07000223 Adur         SE         1.77           0.0708          6.53   0.0881\n## 2 E07000026 Allerdale    NW         3.85           0.147           5.40   0.606 \n## 3 E07000032 Amber Valley EM         3.23           0.129           6.85   1.58  \n## 4 E07000224 Arun         SE         3.67           0.147          11.6    2.29  \n## 5 E07000170 Ashfield     EM         4.08           0.156           6.42   1.15  \n## 6 E07000105 Ashford      SE         2.88           0.115           7.92   3.05  \n## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;\n\n\n# Return the final 6 rows of the tibble.\ntail(csp_2020)\n## # A tibble: 6 × 9\n##   ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020\n##   &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;\n## 1 E07000229 Worthing    SE         2.69            0.108          9.52    0.961\n## 2 E07000238 Wychavon    WM         2.65            0.106          6.29    4.73 \n## 3 E07000007 Wycombe     SE         0               0              0       0    \n## 4 E07000128 Wyre        NW         3.41            0.137          7.64    1.28 \n## 5 E07000239 Wyre Forest WM         2.84            0.114          7.45    0.262\n## 6 E06000014 York        YH        27.1             1.06          93.8     2.68 \n## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;\n\n\n3.2.1 Selecting variables\nOften, our analysis will not require every variable in a downloaded dataset, and we may wish to create a smaller analysis tibble. We may also wish to select individual variables from the tibble to apply functions to them without including the entire dataset.\nTo select one or more variable and return them as a new tibble, we can use the select function from tidyverse’s dplyr package.\nFor example, if we wanted to return the new homes bonus (nhb) for each local authority (the seventh column of the dataset), we can either select this based on the variable name or its location in the object:\n\n# Return the nhb_2020 variable from the csp_2020 object\nselect(csp_2020, nhb_2020)\n## # A tibble: 396 × 1\n##    nhb_2020\n##       &lt;dbl&gt;\n##  1   0.0881\n##  2   0.606 \n##  3   1.58  \n##  4   2.29  \n##  5   1.15  \n##  6   3.05  \n##  7   0     \n##  8   0     \n##  9   1.05  \n## 10   1.85  \n## # ℹ 386 more rows\n\n# Return the 7th variable of the csp_2020 object\nselect(csp_2020, 7)\n## # A tibble: 396 × 1\n##    nhb_2020\n##       &lt;dbl&gt;\n##  1   0.0881\n##  2   0.606 \n##  3   1.58  \n##  4   2.29  \n##  5   1.15  \n##  6   3.05  \n##  7   0     \n##  8   0     \n##  9   1.05  \n## 10   1.85  \n## # ℹ 386 more rows\n\nWe can select multiple variables and return them as a tibble by separating the variable names or numbers with commas:\n\n# Return three variables from the csp_2020 object\nselect(csp_2020, ons_code, authority, region)\n## # A tibble: 396 × 3\n##    ons_code  authority            region\n##    &lt;chr&gt;     &lt;chr&gt;                &lt;chr&gt; \n##  1 E07000223 Adur                 SE    \n##  2 E07000026 Allerdale            NW    \n##  3 E07000032 Amber Valley         EM    \n##  4 E07000224 Arun                 SE    \n##  5 E07000170 Ashfield             EM    \n##  6 E07000105 Ashford              SE    \n##  7 E31000001 Avon Fire            SW    \n##  8 E07000004 Aylesbury Vale       SE    \n##  9 E07000200 Babergh              EE    \n## 10 E09000002 Barking And Dagenham L     \n## # ℹ 386 more rows\n\nWhen selecting consecutive variables, a shortcut can be used that gives the first and last variable in the list, separated by a colon, :. The previous example can be carried out using the following code:\n\n# Return variables from ons_code upt to and including region\nselect(csp_2020, ons_code:region)\n## # A tibble: 396 × 3\n##    ons_code  authority            region\n##    &lt;chr&gt;     &lt;chr&gt;                &lt;chr&gt; \n##  1 E07000223 Adur                 SE    \n##  2 E07000026 Allerdale            NW    \n##  3 E07000032 Amber Valley         EM    \n##  4 E07000224 Arun                 SE    \n##  5 E07000170 Ashfield             EM    \n##  6 E07000105 Ashford              SE    \n##  7 E31000001 Avon Fire            SW    \n##  8 E07000004 Aylesbury Vale       SE    \n##  9 E07000200 Babergh              EE    \n## 10 E09000002 Barking And Dagenham L     \n## # ℹ 386 more rows\n\nThe select function can also be combined with a number of ‘selection helper’ functions that help us select variables based on naming conventions:\n\nstarts_with(\"xyz\") returns all variables with names beginning xyz\nends_with(\"xyz\") returns all variables with names ending xyz\ncontains(\"xyz\") returns all variables that have xyz within their name\n\nOr based on whether they match a condition:\n\nwhere(is.numeric) returns all variables that are classed as numeric\n\nFor a full list of these selection helpers, access the helpfile using ?tidyr_tidy_select.\nThe select function can also be used to remove variables from a tibble by adding a - before the variable name or number. For example:\n\n# Remove the ons_code variable \nselect(csp_2020, -ons_code)\n## # A tibble: 396 × 8\n##    authority            region sfa_2020 under_index_2020 ct_total_2020 nhb_2020\n##    &lt;chr&gt;                &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;\n##  1 Adur                 SE         1.77           0.0708          6.53   0.0881\n##  2 Allerdale            NW         3.85           0.147           5.40   0.606 \n##  3 Amber Valley         EM         3.23           0.129           6.85   1.58  \n##  4 Arun                 SE         3.67           0.147          11.6    2.29  \n##  5 Ashfield             EM         4.08           0.156           6.42   1.15  \n##  6 Ashford              SE         2.88           0.115           7.92   3.05  \n##  7 Avon Fire            SW        16.0            0.437          27.8    0     \n##  8 Aylesbury Vale       SE         0              0               0      0     \n##  9 Babergh              EE         2.14           0.0857          5.77   1.05  \n## 10 Barking And Dagenham L         75.7            2.31           65.8    1.85  \n## # ℹ 386 more rows\n## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;\n\nThe select function returns the variable(s) in the form of a tibble (or dataset). However, some functions, such as basic summary functions, require data to be entered as a vector (a list of values). Tibbles with a single variable can be converted into a vector using the as.vector function, or we can use the base R approach to selecting a single variable. To return a single variable as a vector in base R, we can use the $ symbol between the data name and the variable to return:\n\ncsp_2020$nhb_2020\n\nIt is important to save any changes made to the existing dataset. This can be done using the write_csv function:\n\nwrite_csv(csp_2020, file = \"data/csp_2020_new.csv\")\n\n\n\n\n\n\n\nWarning\n\n\n\nWhen saving updated tibbles as files, use a different file name to the original raw data. Using the same name will overwrite the original file. We always want a copy of the raw data in case of any errors or issues.\n\n\n\n\n3.2.2 Filtering data\nThe filter function, from tidyverse’s dplyr package allows us to return subgroups of the data based on conditional statements. These conditional statements can include mathematical operators, e.g. &lt;= (less than or equal to), == (is equal to), and != (is not equal to), or can be based on conditional functions, e.g. is.na(variable) (is missing), between(a, b) (number lies between a and b).\nA more comprehensive list of conditional statements can be found in the help file using ?filter.\nFor example, to return the core spending power for local authorities in the North West region of England, we use the following:\n\n# Return rows where region is equal to NW from the csp_2020 object\nfilter(csp_2020, region == \"NW\")\n## # A tibble: 46 × 9\n##    ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020\n##    &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;\n##  1 E07000026 Allerdale   NW         3.85            0.147          5.40   0.606 \n##  2 E07000027 Barrow-in-… NW         4.40            0.125          4.74   0.0111\n##  3 E06000008 Blackburn … NW        58.1             1.79          55.9    0.999 \n##  4 E06000009 Blackpool   NW        63.3             1.94          60.1    0.266 \n##  5 E08000001 Bolton      NW        84.2             2.73         115.     0.506 \n##  6 E07000117 Burnley     NW         5.90            0.171          7.16   0.694 \n##  7 E08000002 Bury        NW        42.3             1.44          89.0    0.458 \n##  8 E07000028 Carlisle    NW         3.34            0.134          7.49   1.49  \n##  9 E06000049 Cheshire E… NW        42.5             1.70         230.    11.2   \n## 10 E31000006 Cheshire F… NW        13.5             0.380         30.1    0     \n## # ℹ 36 more rows\n## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;\n\nMultiple conditional statements can be added to the same function by separating them with a comma ,. For example, to return a subgroup of local authorities in the North West region that had a settlement funding assessment (SFA) of over £40 million, we use the following:\n\nfilter(csp_2020, region == \"NW\", sfa_2020 &gt; 40)\n## # A tibble: 23 × 9\n##    ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020\n##    &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;\n##  1 E06000008 Blackburn … NW         58.1             1.79          55.9    0.999\n##  2 E06000009 Blackpool   NW         63.3             1.94          60.1    0.266\n##  3 E08000001 Bolton      NW         84.2             2.73         115.     0.506\n##  4 E08000002 Bury        NW         42.3             1.44          89.0    0.458\n##  5 E06000049 Cheshire E… NW         42.5             1.70         230.    11.2  \n##  6 E06000050 Cheshire W… NW         56.3             2.12         196.    10.2  \n##  7 E10000006 Cumbria     NW        107.              3.56         248.     0.824\n##  8 E47000001 Greater Ma… NW         50.6             1.28          50.5    0    \n##  9 E06000006 Halton      NW         45.6             1.45          52.2    2.21 \n## 10 E08000011 Knowsley    NW         84.1             2.50          56.8    2.10 \n## # ℹ 13 more rows\n## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;\n\n\n\n3.2.3 Pipes\nWhen creating an analysis-ready dataset, we often want to combine functions such as select and filter. Previously, these would need to be carried out separately and a new object would need to be created or overwritten at each step, clogging up the environment.\nIn tidyverse, we combine multiple functions into a single process by using the ‘pipe’ symbol %&gt;%, which is read as ‘and then’ within the code.\n\n\n\n\n\n\nHelpful hint\n\n\n\nTo save time when piping, use the keyboard shortcut ctrl + shift + m for Windows, and Command + shift + m for Mac to create a pipe.\n\n\nFor example, we can return a list of local authority names from the North West region:\n\n# Using the csp_2020 object\ncsp_2020 %&gt;% \n  # Return just rows where region is equal to NW, and then\n  filter(region == \"NW\") %&gt;% \n  # Select just the authority variable\n  select(authority)\n## # A tibble: 46 × 1\n##    authority            \n##    &lt;chr&gt;                \n##  1 Allerdale            \n##  2 Barrow-in-Furness    \n##  3 Blackburn with Darwen\n##  4 Blackpool            \n##  5 Bolton               \n##  6 Burnley              \n##  7 Bury                 \n##  8 Carlisle             \n##  9 Cheshire East        \n## 10 Cheshire Fire        \n## # ℹ 36 more rows\n\n\n\n\n\n\n\nStyle tips\n\n\n\nWhen combining multiple functions within a process using pipes, it is good practice to start the code with the data and pipe that into the functions, rather than including it in the function itself.\n\n\nThe pipe can also be combined with the filter function to count the number of observations that lie within a subgroup:\n\n# Take the csp_2020 object\ncsp_2020 %&gt;% \n  # Return just rows where region is equal to NW, and then\n  filter(region == \"NW\") %&gt;% \n  # Count the number of rows\n  count()\n## # A tibble: 1 × 1\n##       n\n##   &lt;int&gt;\n## 1    46\n\n\n\n3.2.4 Creating new variables\nThe function mutate from tidyverse’s dplyr package allows us to add new variables to a dataset, either by manually specifying them or by creating them from existing variables. We can add multiple variables within the same function, separating each with a comma ,.\nFor example, we can create a new variables with the squared settlement funding assessment (sfa_2020), and another that recodes the council tax variable (ct_total_2020) into a categorical variable with three levels (low: below £5 million, medium: between £5 million and £15 million, and high: above £15 million):\n\n# Create a new object, csp_2020_new, starting with the object csp_2020\ncsp_2020_new &lt;- csp_2020 %&gt;% \n  # Add a new variable, sfa_2020_sq, by squaring the current sfa_2020 variable\n  mutate(sfa_2020_sq = sfa_2020 ^ 2,\n         # Create ct_2020-cat by cutting the ct_total_2020 object\n         ct_2020_cat = cut(ct_total_2020, \n                           # Create categories by cutting at 0, 5 and 15\n                           breaks = c(0, 5, 15, Inf),\n                           # Add labels to these new groups\n                           labels = c(\"Low\", \"Medium\", \"High\"),\n                           # Include the lowest break point in each group\n                           include_lowest = TRUE))\n\n\n\n\n\n\n\nHelpful hint\n\n\n\nThe c function takes a list of values separated by commas and returns them as a vector. This is useful when a function argument requires multiple values (and we don’t want R to move onto the next argument, which is what a comma inside functions usually means).\n\n\nThe mutate function is also useful for reclassifying variables when R did not correctly choose the variable type. In this example, the region variable is a grouping variable, but str(csp_2020) shows it is recognised by R as a character. Grouping variables in R are known as factors. To convert the region variable to a factor, we use the factor function inside mutate:\n\ncsp_2020_new &lt;- csp_2020 %&gt;% \n  # Add a new variable, sfa_2020_sq, by squaring the current sfa_2020 variable\n  mutate(sfa_2020_sq = sfa_2020 ^ 2,\n         # Create ct_2020-cat by cutting the ct_total_2020 object\n         ct_2020_cat = cut(ct_total_2020, \n                           # Create categories by cutting at 0, 5 and 15\n                           breaks = c(0, 5, 15, Inf),\n                           # Add labels to these new groups\n                           labels = c(\"Low\", \"Medium\", \"High\"),\n                           # Include the lowest break point in each group\n                           include_lowest = TRUE),\n         region_fct = factor(region, \n                             # To order the variable, use the levels argument\n                             levels = c(\"L\", \"NW\", \"NE\", \"YH\", \"WM\", \n                                        \"EM\", \"EE\", \"SW\", \"SE\")))\n\n# Check variables are correctly classified\nstr(csp_2020_new)\n## tibble [396 × 12] (S3: tbl_df/tbl/data.frame)\n##  $ ons_code        : chr [1:396] \"E07000223\" \"E07000026\" \"E07000032\" \"E07000224\" ...\n##  $ authority       : chr [1:396] \"Adur\" \"Allerdale\" \"Amber Valley\" \"Arun\" ...\n##  $ region          : chr [1:396] \"SE\" \"NW\" \"EM\" \"SE\" ...\n##  $ sfa_2020        : num [1:396] 1.77 3.85 3.23 3.67 4.08 ...\n##  $ under_index_2020: num [1:396] 0.0708 0.1465 0.1292 0.147 0.1557 ...\n##  $ ct_total_2020   : num [1:396] 6.53 5.4 6.85 11.61 6.42 ...\n##  $ nhb_2020        : num [1:396] 0.0881 0.6061 1.5786 2.2949 1.1547 ...\n##  $ nhb_return_2020 : num [1:396] 0 0 0 0 0 0 0 0 0 0 ...\n##  $ rsdg_2020       : num [1:396] 0 0.326 0 0 0 ...\n##  $ sfa_2020_sq     : num [1:396] 3.12 14.86 10.41 13.46 16.66 ...\n##  $ ct_2020_cat     : Factor w/ 3 levels \"Low\",\"Medium\",..: 2 2 2 2 2 2 3 NA 2 3 ...\n##  $ region_fct      : Factor w/ 9 levels \"L\",\"NW\",\"NE\",..: 9 2 6 9 6 9 8 9 7 1 ...\n\nAlthough there is no real ordering to the regions in England, attaching this order allows us to control how the are displayed in outputs. By default, character variables are displayed in alphabetical order. By adding the order to this variable, we will produce output where the reference region (London) will be displayed first, followed by regions from north to south.\n\n\nExercise 3\n\nHow many local authorities were included in the London region?\nGive three different ways that it would be possible to select all spend variables (sfa_2020, nhb_2020, etc.) from the CSP_2020 dataset.\nCreate a new tibble, em_2020, that just includes local authorities from the East Midlands (EM) region.\n\n\nHow many local authorities in the East Midlands had an SFA of between £5 and 10 million?\nCreate a new variable with the total overall spend in 2020 for local authorities in the East Midlands.",
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+    "text": "4.1.1 Combining two datasets\nWe may need to combine data from different files within R to perform an analysis. For example, in our case we have the core spending power for each year between 2015 and 2020. If our analysis required comparing this spending over the time period, we would need to combine these files together.\nBefore the data can be combined, it must be loaded into R. We will begin combining data from 2015 and 2016, then extend this to the entire period.\n\n# Return a list of files to copy from the working directory\nlist.files(path = \"data\")\n\n[1] \"CSP_2015.csv\"         \"CSP_2016.csv\"         \"CSP_2017.csv\"        \n[4] \"CSP_2018.csv\"         \"CSP_2019.csv\"         \"CSP_2020.csv\"        \n[7] \"CSP_long_201520.csv\"  \"data_description.pdf\"\n\n# Load the 2015 data and attach as an object\nCSP_2015 &lt;- read_csv(\"data/CSP_2015.csv\")\n\n# Load the 2016 data and attach as an object\nCSP_2016 &lt;- read_csv(\"data/CSP_2016.csv\")\n\nNext, we will combine these datasets by joining them using key variable(s) which are shared between them. In this case, each local authority has a unique identifier code (ons_code) and naming variable (authority), they also should have the same region listed across both datasets.\nIn Tidyverse, there is a family of ‘joining’ functions that combine two datasets at a time. The choice of function depends on which observations we wish to keep where the joining variables do not match between data. In this example, we expect all local authority values to be the same across years, so will use the full_join function.\nFor more information about different joining options, check the helpfile via ?full_join.\n\n# Create a new object by joining the two datasets\ncsp_201516 &lt;- full_join(CSP_2015, CSP_2016, \n                        # List the key joining variables (in speech marks)\n                        by = c(\"ons_code\", \"authority\", \"region\"))\n\n\n\n4.1.2 Joining multiple datasets\nR’s joining functions can only be applied to two datasets at a time. To combine all 6 core spending power datasets from 2015 to 2020 in this way would require a lot of repetitive coding (which we want to avoid where necessary).\nAn alternative approach would be to automate this process by using functional programming, implemented using tidyverse’s purrr package.\nThe first step of this process requires loading all csv files into R by repeatedly applying read_csv. This requires a list of file names from the working directory. The function list.files introduced earlier contains an optional argument, pattern which can be used to return files and folders that match a naming pattern. In this case, all csv files begin “CSP_20”, so to return this list of names from the data folder, we use the function:\n\ncsp_201520 &lt;- list.files(path = \"data\", pattern = \"CSP_20\")\n\nNext, we apply read_csv to each element of the list of file names. The function map allows us to do this and return a list of tibbles. As the data lies in a folder in the working directory, we must add this file path to the file names:\n\n# Return a list of files in the data folder containing CSP_20\ncsp_201520 &lt;- list.files(path = \"data\", pattern = \"CSP_20\") %&gt;% \n  # Add \"data/\" to each of these file names\n  paste0(\"data/\", .) %&gt;% \n  # Apply read_csv to every element of the list (of file names)\n  map(read_csv)\n\nFinally, we require a function that apply full_join iteratively to the list of tibbles and reduce it to a single tibble containing core spending powers for all years. The function that does this is reduce:\n\n# Return a list of files in the data folder containing CSP_20\ncsp_201520 &lt;- list.files(path = \"data\", pattern = \"CSP_20\") %&gt;% \n  # Add \"data/\" to each of these file names\n  paste0(\"data/\", .) %&gt;% \n  # Apply read_csv to every element of the list (of file names)\n  map(read_csv) %&gt;% \n  # Reduce the list of tibbles to a single object by iteratively joining\n  reduce(full_join, by = c(\"ons_code\", \"authority\", \"region\"))\n\n\n\n4.1.3 Transforming data\nThe dataset containing core spending power in England between 2015 and 2020 is currently in what is known as wide format. This means there is a variable per measure per year, making the object very wide.\nSome analyses and visualisations, particularly those used for temporal data, require a time variable in the dataset (for example, year). This requires the data to be in a different format, known as long format. Long format is where each row contains an observation per year (making the data much longer and narrower).\nTo convert data between wide and long formats, we can use the tidyverse functions pivot_longer and pivot_wider.\nThe first argument required by pivot_longer is the data we wish to transform. This is followed by the columns we wish to pivot (in this case, all variable other than the local authority codes, names, and regions). The next steps will depend on the format of data we wish to transform, format of the data we would like to generate, the values we need to include in the long dataset, and where this information will be extracted from.\nFor worked examples and a detailed explanation of different approaches that can be used to pivot data, access the vignette for these function by entering vignette(\"pivot\") into the R console.\nIn the core spending power example, the new dataset will contain a row per local authority per year. A new year variable will be created using the suffix of the original variable names, and the prefix of the original names (e.g. sfa) will be retained for the new variable names.\nUsing a combination of the helpfile (?pivot_longer) and vignette, the arguments required to convert this data are names_to, to specify the old variable names will be used in the new data, and names_pattern to define how the old variable names will be separated.\n\n# Create an object csp_long by pivotting csp_201520\ncsp_long &lt;- pivot_longer(csp_201520, \n                         # Pivot columns sfa_2015 up to and including rsdg_2020\n                         cols = sfa_2015:rsdg_2020,\n                         # Separate the old variable names in two, \n                         # keep the prefix as it was, and put the suffix \n                         # into a new variable, year\n                         names_to = c(\".value\", \"year\"),\n                         # The name prefix and suffix were separated by an _,\n                         # the prefix can take different lengths, the suffix \n                         # is always the final 4 characters\n                         names_pattern = \"(.*)_(....)\")\n\n# Check the new, long dataset's structure\nstr(csp_long)\n\ntibble [2,376 × 10] (S3: tbl_df/tbl/data.frame)\n $ ons_code   : chr [1:2376] \"E07000223\" \"E07000223\" \"E07000223\" \"E07000223\" ...\n $ authority  : chr [1:2376] \"Adur\" \"Adur\" \"Adur\" \"Adur\" ...\n $ region     : chr [1:2376] \"SE\" \"SE\" \"SE\" \"SE\" ...\n $ year       : chr [1:2376] \"2015\" \"2016\" \"2017\" \"2018\" ...\n $ sfa        : num [1:2376] 3.02 2.39 1.92 1.7 1.74 ...\n $ under_index: num [1:2376] 0.0234 0.0234 0.0248 0.039 0.0567 ...\n $ ct_total   : num [1:2376] 5.47 5.68 5.85 6.08 6.35 ...\n $ nhb        : num [1:2376] 0.652 0.767 0.553 0.202 0.126 ...\n $ nhb_return : num [1:2376] 0.00523 0.00374 0.00397 0 0 ...\n $ rsdg       : num [1:2376] 0 0 0 0 0 ...\n\n\nNotice that the new year variable is recognised as a character, not a numeric variable as we would like. This is because these values were taken from variable names, which R treats as characters. To fix this, we can use the mutate function to convert the new variable into a numeric variable.\nWe may also wish to calculate the total core spending power for each local authority per year to compare this over time:\n\n# Create a new object based on the long data\ncsp_long2 &lt;- mutate(csp_long, \n                    # Convert year to a numeric variable\n                    year = as.numeric(year),\n                    # Create a new total spend variable\n                    total_spend = sfa + under_index + ct_total + nhb + \n                      nhb_return + rsdg)\n\nAfter manipulating and transforming the data into the format we need for analysis and visualisation, we can save this object to reload later. Tibbles and data frame objects can be saved as CSV files using the write_csv function. Remember to save the data with a different name than the raw data to avoid overwriting these files.\n\nwrite_csv(csp_long2, file = \"data/CSP_long_201520.csv\")\n\n\n\n4.1.4 Summary tables\nSummary tables can be created using the summarise function. This returns tables in a tibble format, meaning they can easily be customised and exported as CSV files (using the write_csv function).\nThe summarise function is set up similarly to the mutate function: summaries are listed and given variable names, separated by a comma. The difference between these functions is that summarise collapses the tibble into a single summary row, and the new variables must be created using a summary function.\nCommon examples of summary functions include:\n\nmean\nmedian\nrange (gives the minimum and maximum values)\nmin\nmax\nIQR (interquartile range, gives the range of the middle 50% of the sample)\nsd (standard deviation, a measure of the spread when data are normally distributed)\nsum\nn (counts the number of rows the summary is calculated from)\n\nFor a full list of compatible summary functions, view the helpfile ?summarise.\nIf we wanted to summarise the total core spending power between 2015 and 2020 across all local authorities, we can apply summarise to the long format data from the previous section:\n\nsummarise(csp_long2, \n          # Return sum of the total_spend variable\n          total_spend_all = sum(total_spend),\n          # Return the mean total spend\n          mean_total_spend = mean(total_spend),\n          # Return the median total spend\n          median_total_spend = median(total_spend),\n          # Return the 10th percentile (the value that 10% of the sample lies below)\n          quantile10_total_spend = quantile(total_spend, 0.1),\n          # Count the number of rows that have been summarised\n          total_obs = n())\n\n# A tibble: 1 × 5\n  total_spend_all mean_total_spend median_total_spend quantile10_total_spend\n            &lt;dbl&gt;            &lt;dbl&gt;              &lt;dbl&gt;                  &lt;dbl&gt;\n1         263484.             111.               17.6                   8.34\n# ℹ 1 more variable: total_obs &lt;int&gt;\n\n\nThe summarise function can be used to produce grouped summaries. This is done by first grouping the data with the group_by function. For example, if we wished to produce a summary table with a row per local authority, summarising the total spending between 2015 and 2020, we would use the following:\n\ncsp_long2 %&gt;% \n  # Group by the local authority's unique identifiers\n  group_by(ons_code, authority) %&gt;% \n  # Total spend 2015 - 2020\n  summarise(total_spend_all = sum(total_spend),\n            # Mean spend 2015 - 2020  \n            mean_total_spend = mean(total_spend),\n            # Median spend 2015 - 2020\n            median_total_spend = median(total_spend),\n            # 10th percentile of total spend\n            quantile10_total_spend = quantile(total_spend, 0.1),\n            # Number of rows summarised over\n            total_obs = n()) %&gt;%\n  # Remove grouping structure\n  ungroup()\n\n# A tibble: 396 × 7\n   ons_code  authority       total_spend_all mean_total_spend median_total_spend\n   &lt;chr&gt;     &lt;chr&gt;                     &lt;dbl&gt;            &lt;dbl&gt;              &lt;dbl&gt;\n 1 -         Greater London…          12416.           2069.              2022. \n 2 E06000001 Hartlepool                 485.             80.8               80.3\n 3 E06000002 Middlesbrough              711.            119.               118. \n 4 E06000003 Redcar And Cle…            660.            110.               109. \n 5 E06000004 Stockton-on-Te…            832.            139.               138. \n 6 E06000005 Darlington                 474.             79.0               78.5\n 7 E06000006 Halton                     598.             99.7               99.0\n 8 E06000007 Warrington                 806.            134.               133. \n 9 E06000008 Blackburn with…            692.            115.               115. \n10 E06000009 Blackpool                  750.            125.               124. \n# ℹ 386 more rows\n# ℹ 2 more variables: quantile10_total_spend &lt;dbl&gt;, total_obs &lt;int&gt;\n\n\n\n\n\n\n\n\nWarning\n\n\n\nWhenever using group_by, make sure to ungroup the data before proceeding. The grouping structure can be large and slow analysis down, or may interact with other functions to produce unexpected analyses.\n\n\n\n\nExercise 4\n\nCreate a data frame with the minimum, maximum and median total spend per year for each region.\nProduce a frequency table containing the number and percentage of local authorities in each region.\nConvert the data object csp_long2 back into wide format, with one row per local authority and one variable per total spend per year (HINT: start by selecting only the variables you need from the long data frame). Use the help file ?pivot_wider and vignette(\"pivot\") for more hints.\nUsing your new wide data frame, calculate the difference in total spending for each local authority between 2015 and 2020. How many local authorities have had an overall reduction in spending since 2015?",
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+    "text": "5.1 Data visualisation with ggplot2\nData visualisation is a powerful tool with multiple important uses. First, visualisations allow us to explore the data, identify potential outliers and errors, or check that the variables behave in the way we would expect them to if they had been recorded correctly. Visualisations can also be used as an analysis tool, allowing us to identify trends in the data or differences between groups. Finally, visualisations can help to convey messages to an audience in a clear, concise way that is often more powerful than presenting them using numbers or text. In some cases, data visualisations can show results so clearly that further analysis is arguably unnecessary.",
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+    "text": "5.1.1 Choosing the most appropriate visualisation\nThe most appropriate choice of visualisation will depend on the type of variable(s) we wish to display, the number of variables and the message we are trying to disseminate. Common plots used to display combinations of different types of data are given in following table:\n\n\n\nTable 6.1: Common visualisations by number and type of variables, with ggplot2 geom\n\n\nR is very flexible when it comes to visualising data and contains a wide variety of options to customise graphs. This section will focus on the Tidyverse package ggplot2 and introduce some of the more commonly used graphical functions and parameters but is by no means comprehensive.\n\n\n5.1.2 The ggplot2 package\nThe ggplot2 package implements the ‘grammar of graphics’, a system that aims to describe all statistical graphics in terms of their components or layers. All graphics can be broken down into the same components: the data, a coordinate system (or plot area) and some visual markings of the data. More complex plots may have additional layers but all must contain these three.\nFor example, in the csp_2020 dataset, we may wish to explore the relationship between the settlement funding assessment (sfa_2020) and council tax total (ct_total_2020) spending for each local authority. To visualise the relationship between two continuous numeric variables, a scatterplot would be most appropriate.\nWithin the ggplot2 package, we first use the ggplot function to create a coordinate system (a blank plot space) that we can add layers and objects to. Within this function, we specify the data that we wish to display on the coordinate system:\n\nggplot(data = csp_2020)\n\nTo add information to this graph, we add a geom layer: a visual representation of the data. There are many different geom objects built into the ggplot2 package (begin typing ?geom into the console to see a list). The geom_point function is used to create scatterplots.\nEach geom object must contain a mapping argument, coupled with the aes function which defines how the variables in the dataset are visualised. In this case, we use the aes function to specify the variables on the x and y axes but it can also be used to set the colour, size or symbol based on variable values.\n\n\n\n\n\n\nWarning\n\n\n\nAlthough ggplot2 is a tidyverse package, it uses a different method of piping to the other packages. Use the + symbol to add an extra layer when working in ggplot.\n\n\n\n# Generate the chart area and specify the data\nggplot(data = csp_2020) + \n  # Add points, defined by sfa_2020 and ct_total_2020 \n  geom_point(mapping = aes(x = sfa_2020, y = ct_total_2020))\n\n\n\n\n\n\n\n\nThe resulting scatterplot shows a positive association between the SFA and council tax spending in English local authorities during 2020. We can identify an outlier in the top right corner of the graph. Before proceding, we want to ensure that this observation is an outlier and not an error to be removed from the data. We can use the filter function to return the name of the local authority that matches these values:\n\n# Using the data csp_2020\ncsp_2020 %&gt;% \n  # Return just rows where sfa_2020 is over 1000, and then\n  filter(sfa_2020 &gt; 1000) %&gt;% \n  # Return the authority names\n  select(authority)\n## # A tibble: 1 × 1\n##   authority               \n##   &lt;chr&gt;                   \n## 1 Greater London Authority\n\nThis outlier is the Greater London Authority which is a combination of local authorities that are already included in the dataset. Including this observation would introduce duplicates into the analysis, and so this observation should be removed to avoid invalid results. To remove the Greater London Authority observation, we can combine the filter and ggplot functions using pipes:\n\n# Take the csp_2020 data, and then\ncsp_2020 %&gt;% \n  # Return all rows where authority is not equal to Greater London Authority,\n  # and then\n  filter(authority != \"Greater London Authority\") %&gt;% \n  # Generate a plot\n  ggplot( ) + \n  # Add visual markings based on the data\n  geom_point(aes(x = sfa_2020, y = ct_total_2020))\n\n\n\n\n\n\n\n\nGraphs appear in the plot window in RStudio and can be opened in a new window using the  icon. Graphs in this window can also be copied and pasted into other documents using the  icon and selecting Copy to clipboard.\nNew graphs will replace existing ones in this window but all graphs created in the current session of R can be explored using the  icons.\nGraphs can be stored as objects using the &lt;- symbol. These objects can then be saved as picture or PDF files using the ggsave function:\n\n# Create a new object, beginning from csp_2020, and then\nsfa_ct_plot &lt;- csp_2020 %&gt;% \n  # Return all rows where authority name is not GLA, and then\n  filter(authority != \"Greater London Authority\") %&gt;%\n  # Create a ggplot area\n  ggplot( ) + \n  # Add visual markings from the data\n  geom_point(aes(x = sfa_2020, y = ct_total_2020))\n\n# Save the graph object as a png file\nggsave(sfa_ct_plot, filename = \"sfa_ct_plot.png\")\n\n\n\nExercise 5\n\nCreate a new data object containing the 2020 CSP data without the Greater London Authority observation. Name this data frame csp_nolon_2020.\nUsing the csp_nolon_2020 data, create a data visualisation to check the distribution (or shape) of the SFA variable.\nBased on the visualisation above, create a summary table for the SFA variable containing the minimum and maximum, and appropriate measures of the centre/average and spread.\n\n\n\n5.1.3 Customising visualisations\nAdditional variables can be included into a visualisation within the mapping argument of a geom function. For example, we could explore the relationship between SFA and council tax across regions by colouring points based on the region:\n\nggplot(data = csp_nolon_2020) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region))\n\n\n\n\n\n\n\n\nBy default, R uses alphabetical ordering for character variables. To change this order, the variable must be converted into a factor. A factor is how R recognises categorical variables. For example, to order the region legend so that the London region appears first, followed by other regions from north to south, we would use the mutate function, combined with the factor function to create a new, ordered variable. The argument levels allows us to specify the order of categories in a factor:\n\ncsp_nolon_2020_new &lt;- csp_nolon_2020 %&gt;% \n  mutate(region_fct = factor(region, \n                             levels = c(\"L\", \"NW\", \"NE\", \"YH\", \"WM\", \n                                        \"EM\", \"EE\", \"SW\", \"SE\")))\n\nggplot(data = csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct))\n\n\n\n\n\n\n\n\nArguments that can be adjusted within geoms include:\n\ncolour: change the colour (if point or line) or outline (if bar or histogram) of the markings\nsize: change the size of the markings (if point used)\nshape: change the shape of markings (for points)\nfill: Change the colour of bars in bar charts or histograms\nlinewidth: Change the line width\nlinetype: Choose the type of line (e.g. dotted)\nalpha: Change the transparency of a visualisation\n\n\n\n\n\n\n\nWarning\n\n\n\nAlthough it may be tempting to add many variables to the same visualisation, be sure that you are not overcomplicating the graph and losing important messages. It is better to have multiple, clear but simpler visualisations, than fewer confusing ones.\n\n\nAesthetic properties of the geom object may also be set manually, outside of the aes function, using the same argument but with a shared value rather than a variable. For example:\n\nggplot(csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020), \n             # Adding the colour outside of the aes wrapper as it is not \n             # from the data\n             colour = \"blue\")\n\n\n\n\n\n\n\n\n\n\nExercise 6\n\nWhat is the problem with the following code? Fix the code to change the shape of all the points.\n\n\nggplot(csp_nolon_2020) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, shape = \"*\"))\n\n\nAdd a line of best fit to the scatterplot showing the relationship between SFA and council tax total (hint: use ?geom_smooth).\nAdd a line of best fit for each region (hint: make each line a different colour).\n\n\n\n5.1.4 Scale functions\n\n5.1.4.1 Customising axes\nScale functions allow us to customise aesthetics defined in geom objects such as colours and axes labels. They take the form scale_'aesthetic to customise'_'scale of variable’. For example, scale_x_continuous customises the x axis when the variable is continuous, and scale_x_discrete can be used where the variable is discrete or categorical. Arguments to customise the x or y axes include:\n\nname = to change the axis title\nlimits = c(...) sets the axis limits\nbreaks = c(...) defines tick marks\nlabels = c(...) attaches labels to break values\ntrans = transforms the scale that the axis is shown on.\n\n\nggplot(csp_nolon_2020_new) + \n  # Scatterplot with SFA on x, CT on y, and colour by region\n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct)) +\n  # Add title to x axis\n  scale_x_continuous(name = \"Settlement funding assessment (£ millions)\", \n                     # Set x axis limits from 0 to 600\n                     limits = c(0, 600), \n                     # Set tick marks ever 200\n                     breaks = c(0, 200, 400, 600)) +\n  # Add title to y axis\n  scale_y_continuous(name = \"Council tax (£ millions)\", \n                     # Show the y axis on a square root scale\n                     trans = \"sqrt\")\n\n\n\n\n\n\n\n\nA common transformation that can be useful to explore the relationship between variables which have clusters of smaller values is the logarithm (or log) function. Applying a log function to a scale increases the difference between smaller values (stretching out these clusters), while reducing the difference between the smaller values and largest ones. Log functions can only be applied to positive, non-zero numbers. Where a sample may contain zeroes, the transformation log1p can be applied instead which adds 1 to each value before applying the log transformation (\\(log(n + 1)\\)):\n\nggplot(csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct)) +\n  scale_x_continuous(name = \"SFA\", limits = c(0, 600), \n                     breaks = c(0, 200, 400, 600),\n                     trans = \"log1p\") +\n  scale_y_continuous(name = \"Council tax\", \n                     trans = \"log1p\") \n\n\n\n\n\n\n\n\nWe can now clearly see the strong positive association between SFA and council tax spending in local authorities with lower values of this without losing any information.\n\n\n5.1.4.2 6.3.2 Customising colour scales\nThere are a wide range of options for customising the colour aesthetics of geoms. These include pre-defined colour palettes, such as scale_colour_viridis_c for continuous variables, or scale_colour_viridis_d for discrete or categorical variables. Viridis colour palettes are designed to be colourblind friendly and print well in grey scale. There are also many R packages containing colour palettes for different scenarios.\nColour palettes can be created manually for categorical variables using the scale_colour_manual function. Here, the argument values allows us to specify a colour per category.\n\n\n\n\n\n\nStyle tip\n\n\n\nR contains a list of 657 pre-programmed colours that can be used to create palettes (run colours() in the console for a full list).\nHexadecimal codes can also be included instead in the form #rrggbb (where rr (red), gg (green), and bb (blue) are numbers between 00 and 99 giving the level of intensity of each colour).\n\n\nWhere a colour palette will be used across multiple plots, defining this list of colours as a vector and then entering this into scale_colour_manual will reduce repetition:\n\nregion_palette &lt;- c(\"aquamarine2\", \"blue\", \"chartreuse2\", \"coral\", \"orchid\",\n                    \"firebrick\", \"gold3\", \"violetred\", \"grey50\")\n\nggplot(csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct)) +\n  scale_x_continuous(name = \"SFA\",  trans = \"log1p\") +\n  scale_y_continuous(name = \"Council tax\", trans = \"log1p\") +\n  scale_colour_manual(name = \"Region\", values = region_palette)\n\n\n\n\n\n\n\n\nPalettes can also be created using gradients with the scale_colour_gradient function, that specifies a two colour gradient from low to high, scale_colour_gradient2 that creates a diverging gradient using low, medium, and high colours, and scale_colour_gradientn that creates an n-colour gradient.\n\n\n\n5.1.5 Other labelling functions\nAlthough axis and legend labels can be updated within scale functions, the labs function exist as an alternative. This function also allows us to add titles and subtitles to visualisations:\n\nlabs(x = “x-axis name”, y = “y-axis name”,\n    colour = “Grouping variable name”, title = “Main title”,\n    subtitle = “Subtitle”, caption = “Footnote”)\n\nThe annotate function allows us to add text and other objects to a ggplot object. For example:\n\nannotate(“text”, x = 50, y = 200, label = “Text label here”)\n\nAdds “Text label here” to a plot at the coordinates (50, 200) on a graph, and\n\nannotate(“rect”, xmin = 0, xmax = 10, ymin = 20, ymax = 50, alpha = 0.2)\n\nadds a rectangle to the graph.\n\n\n5.1.6 Theme functions\nThe theme function modifies non-data components of the visualisation. For example, the legend position, label fonts, the graph background, and gridlines. There are many options that exist within the theme function (use ?theme to list them all).\n\n\n\n\n\n\nNote\n\n\n\nMany of the elements that can be customised within the theme function require an element wrapper. This wrapper is determined by the type of object we are customising (e.g. element_text when customising text, element_rect when customising a background, element_blank to remove something). Check ?theme for more information.\n\n\nOne of the most common theme options is legend.position which can be used to move the legend to the top or bottom of the graph space (legend.position = “top” or legend.position = “bottom”) or remove the legend completely (legend.position = “none”).\nggplot also contains a number of pre-defined ‘complete themes’ which change all non-data elements of the plot to a programmed default. For example theme_void removes all gridlines and axes, theme_light changes the graph background white and the gridlines and axes light grey:\n\nggplot(csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct)) +\n  scale_x_continuous(name = \"SFA\",  trans = \"log1p\") +\n  scale_y_continuous(name = \"Council tax\", trans = \"log1p\") +\n  scale_colour_manual(name = \"Region\", values = region_palette) + \n  theme_void( )\n\n\n\n\n\n\n\n\nOne benefit of using themes is that all visualisations will be consistent in terms of colour scheme, font size and gridlines. Although there are pre-built themes, we are able to create our own and save them as functions. These can then be used in place of R’s themes. For example:\n\n# Create a theme function\ntheme_intro_course &lt;- function( ) {\n  # Move the legend to the bottom \n  theme(legend.position =  \"bottom\",\n        # Make the axis labels font size 10\n        axis.text = element_text(size = 10),\n        # Make the axis titles font size 15\n        axis.title = element_text(size = 15),\n        # Make the graph title font size 20\n        title = element_text(size = 20),\n        # Make the plot area white with a grey outline\n        panel.background = element_rect(fill = \"white\", colour = \"grey50\"))\n}\n\nThe function theme_intro_course can be added to the end of any visualisation and will move the legend to the bottom of the graph, change the axis text to size 10, the axis titles to size 15, the plot title to size 20, and the graph background to white with a grey outline:\n\nggplot(csp_nolon_2020_new) + \n  geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct)) +\n  scale_x_continuous(name = \"SFA\",  trans = \"log1p\") +\n  scale_y_continuous(name = \"Council tax\", trans = \"log1p\") +\n  scale_colour_manual(name = \"Region\", values = region_palette) + \n  theme_intro_course( )\n\n\n\n\n\n\n\n\nCreating a custom theme is useful to ensure all visualisations are formatted consistently.\n\n\n5.1.7 Facet functions\nFaceting allows us to divide a plot into subplots based on some grouping variable within the data. This allows us to show multiple variables in the same visualisation without risking overloading the plot and losing the intended message.\nFor example, if we wish to show the relationship between SFA, council tax total and regions over the entire time period, we may wish to create a scatterplot per year. Faceting allows us to do this in one piece of code rather than repeating it per year. Faceting will also ensure that plots are on the same scale and therefore easier to compare. The function facet_wrap creates these facetted plots:\n\n# Take the long formatted dataset\ncsp_long2 %&gt;% \n  # Remove the Greater London Authority row\n  filter(authority != \"Greater London Authority\") %&gt;% \n  ggplot( ) +\n  # Plot the SFA against CT total and colour by region\n  geom_point(aes(x = sfa, y = ct_total, colour = region)) +\n  # Use the region colour palette\n  scale_colour_manual(name = \"Region\", values = region_palette) + \n  # Change the axis titles\n  labs(x = \"Settlement funding assessment (£ millions)\", \n       y = \"Council tax total (£ millions)\", colour = \"Region\") +\n  # Separate data into a plot per region\n  facet_wrap(~ year) +\n  # Use the intro course theme\n  theme_intro_course()\n\n\n\n\n\n\n\n\n\n\nExercise 7\nUse an appropriate data visualisation to show how the total spend in each local authority has changed over the years between 2015 and 2020. Choose a visualisation that shows these trends over time and allows us to compare them between regions.",
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+    "text": "6.1 Introduction to RMarkdown\nRMarkdown is a tool that is used to author high-quality documents, making it easy to communicate results efficiently. One of the main appeals of RMarkdown is that it is easy to integrate R code and output seamlessly into a document, encouraging openness and reproducibility in research.\nThere are a number of ways we can use RMarkdown to enhance the research process, such as:\nBefore we begin working with RMarkdown in RStudio, we must first download and install the rmarkdown package as we would any other package:\ninstall.packages(\"rmarkdown\")\n\nlibrary(rmarkdown)",
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+    "text": "Generating reports to show the latest findings in a project, combining research output with interpretations. Reports can be automated within RMarkdown, to ensure outputs show the latest data.\nKeeping track of projects as an alternative to a notebook. Documents can include R code and visualisations alongside thoughts and comments on findings so far.\nCreating a collaborative document that can be shared with colleagues. The inclusion of R code in documents provides an audit trail, making it easy to carry out quality assurance and resolve discrepancies in results.\n\n\n\n\n6.1.1 Creating an RMarkdown files\nRMarkdown files (.Rmd) are created and saved separately to the script files we have been using up to now on the course. To create a new RMarkdown file, either use the drop-down menu, following the File -&gt; New File -&gt; R Markdown… options, or using the  icon and selecting R Markdown….\n\n\n\nRmarkdown new file\n\n\nWhen creating a new RMarkdown file, we are given the option to set the title, author and date of the new document. We are also given options to select the type of document, presentation, or Shiny app we would like to create. This does not give a comprehensive list of documents available within RMarkdown and can be changed later. We will discuss output document types in more detail later in the session.\nClicking ‘OK’ on this window will produce an RMarkdown file (.Rmd) with some example code. If we do not want this, there is an option to ‘Create Empty Document’ on the bottom left of the window.\n\n\n6.1.2 Rmarkdown content\nRMarkdown files contain three main types of content:\n\nA YAML header (this sets the global options for the document)\nText, or syntax (this includes headings and comments)\nCode chunks containing R code\n\n\n6.1.2.1 The YAML header\nThe first part of an RMarkdown script, surrounded by ‘---’ is known as the YAML header. This sets global options for the document that will be produced by the script. YAML headers can include the title, author and date of a document, the output document type, table of contents options, and can include code to edit the appearance of text and figures.\nFor this course, we will just use the YAML to define the title, author, date, and output of our document:\n---\ntitle: \"Introduction to R with Tidyverse\"\nauthor: My name\ndate: 2024-07-15\noutput: html_document\n---\nThere are many output document types that can be produced using RMarkdown. Some of the most common include:\n\nhtml_document:HTML document,.html\npdf_document: PDF document,.pdf, created using a LaTeX template\nword_document: Microsoft word document (.docx)\nodt_document: OpenDocument text document (.odt), similar to Microsoft Word/Google Docs but compatible with free word processors)\ngithub_document: Github document (.md, markdown files that are compatible with Github and are converted to HTML when viewed there)\npowerpoint_presentation: Powerpoint presentation (.pptx)\n\nRMarkdown can also be combined with other R packages to create books (via bookdown), websites (via blogdown) and interactive dashboards (via flexdashboard).\n\n\n6.1.2.2 RMarkdown syntax\nRMarkdown text, or syntax, will generally make up the majority of a RMarkdown file. This can include headers and subheadings, equations, and any other text or comments in the document. Text is formatted using markdown syntax. A detailed list of syntax commands are given in the RMarkdown cheatsheet. Common syntax commands that may be used in an RMarkdown document include:\n\n*italic*\n**bold**\nAdd `code` into text\n# Header 1\n## Header 2\n…\n###### Header 6\n[This is a link](link url)\n![caption](image.png)\n\n- Unordered list\n  - List with indent\n1. Ordered list\n  - With indent\n2. Second item\nEquation: $r^2 = (x - a)^2 + (y - b)^2$\nRMarkdown equations are built using the same language as LaTeX. See here for a list of mathematical symbols that can be used in these equations.\n\n\n6.1.2.3 Code chunks\nCode chunks allow us to embed R code and outputs into our documents. This is one of the main draw of RMarkdown as it removes the need to copy and paste or import results from R into another document.\nCode chunks are pieces of code that begin ```{r} and end ```. For example,\n```{r}\n 1 + 1\n``` \nCode chunks can be created by manually typing these wrappers, by clicking the  icon and selecting ‘R’, or using the keyboard shortcut ctrl + alt + i on Windows, and Command + Option + i on Mac.\nCode chunks can be given titles to make an RMarkdown script easier to navigate (these will appear under the script window where lists of subheadings appear in script files). These are added inside the opening of the code chunk: ```{r chunk title}.\nThere are a number of chunk options to customise which code/output to display in the document. These are included in the opening of a chunk, after the title, separated by commas ,. Some of the most common, include:\n\necho = TRUE/FALSE: whether to display code in the output document\neval = TRUE/FALSE: whether to run the code in the chunk or not\ninclude = TRUE/FALSE: whether to include anything from the chunk (code or output) in the document\nerror/warning/message = TRUE/FALSE: whether to display error/warning/other messages in the document\n\nTop tip: It may be useful to add a setup code chunk at the beginning of an RMarkdown file that loads any packages and datasets that are required for the rest of the document. These can also include universal options for future code chunks to avoid repeating the code, using the knitr::opts_chunk$set function.\nFor example:\n```{r setup, include = FALSE} \n# Set global options for code chunks \n\n# Do not show any R code or messages unless specified \nknitr::opts_chunk$set(echo = FALSE, message = FALSE) \n\n# Load in the tidyverse package\nlibrary(tidyverse)\n```\n\n\n\n6.1.3 Compiling RMarkdown documents\nCompiling RMarkdown actually requires multiple steps and programmes. Luckily for us, this process takes place in the background so we don’t need to be aware of these steps happening!\nGenerating an output file from RMarkdown is know knitting a document. This process sends the .Rmd file to another R package knitr (which is installed alongside rmarkdown), which executes all the code chunks in the document and creates a markdown .md file including the code and output. This markdown file is then processed by another programme pandoc which converts markdown code into the finished document.\n\n\n\nRMarkdown to document process\n\n\nTo knit an RMarkdown file in RStudio is very simple. Either click the  icon above the RMarkdown script, or use the keyboard shortcut ctrl + shift + k on Windows or Command + shift + k on Mac. This initiates the process above and will return an output document (if there are no errors!) in the requested format to the working directory.\n\n\n6.1.4 Data visualisation in RMarkdown\nOutput such as graphs and tables can be embedded in code chunks, the code used to create them will be the same as it would be in any other R script.\n\n\n\n\n\n\nNote\n\n\n\nOften, when providing output in RMarkdown, we often do not want to show the code that was used to create this. Make sure to add echo = FALSE to the opening of the code chunk.\n\n\n\n6.1.4.1 Graphs in RMarkdown\nggplot can be used to create graphs that are embedded within code chunks and included in an output document. For example, we could use the data from previous sections to show the relationship between Settlement Funding Assessment (SFA) and council tax total in English local authorities in 2020, colour code by regions in a scatterplot:\n```{r scatterplot sfa_2020 and ct_total_2020 by region, message = FALSE}\n# Load and tidy the 2020 data\nread_csv(\"data/CSP_2020.csv\") %&gt;% \n  # Remove the Greater London Authority row\n  filter(authority != \"Greater London Authority\") %&gt;% \n  # Convert region variable to factor\n  mutate(region_fct = factor(region, \n                             levels = c(\"L\", \"NW\", \"NE\", \"YH\", \"WM\",\n                                        \"EM\", \"EE\", \"SW\", \"SE\"))) %&gt;% \n  # Create a ggplot \n  ggplot() +\n  # Scatterplot definition\n  geom_point(aes(x = ct_total_2020, y = sfa_2020, colour = region_fct)) +\n  # Add colour palette for region\n  scale_colour_manual(values = c(\"aquamarine2\", \"blue\", \"chartreuse2\", \n                                 \"coral\", \"orchid\", \"firebrick\", \n                                 \"gold3\", \"violetred\", \"grey50\")) +\n  # Change axis/label titles\n  labs(x = \"Council tax total (£millions)\", \n       y = \"Settlement funding assessment (£milliongs)\",\n       colour = \"Region\") +\n  theme_light()\n```\n\n\n\n\n\n\n\n\n\n\n\n6.1.4.2 Tables in RMarkdown\nThere are a number of ways to include tables within RMarkdown which can either be entered manually, or generated using an R package. The choice of approach to creating tables depends on the format and size of the data, the amount of flexibility you would like to customise the output, the type of output document you are creating, and personal preference of how it should look.\nIn this course, we will look at how tables can be created using RMarkdown syntax (without the need for additional packages), and using the kable function within the knitr package.\nManually creating tables\nTables can be created in RMarkdown syntax, using the | symbol to separate columns, and dashes - to separate column headings from the body of the table. These are created outside of code chunks within the text. For example,\n Header 1 | Header 2 | Header 3 |\n|----------|----------|----------|\n| This     | Is       | A        |\n| Very     | Simple   | Table    |\nproduces the following output:\n\n\n\nHeader 1\nHeader 2\nHeader 3\n\n\n\n\nThis\nIs\nA\n\n\nVery\nSimple\nTable\n\n\n\nColons can be added to the header/body separator row of the table to control the justification of the text in each column. For example,\n| Left | Right | Center  | Default   |\n|:-----|------:|:-------:|-----------|\n| This | Is    | Another | Simple    |\n| Table | But   | It is  | Justified |\nproduces the following output:\n\n\n\nLeft\nRight\nCenter\nDefault\n\n\n\n\nThis\nIs\nAnother\nSimple\n\n\nTable\nBut\nIt is\nJustified\n\n\n\nCreating tables from data frames\nThe knitr package that compiles RMarkdown files contains the kable function that can be used to create simple data tables. The kable function requires data to be stored as a matrix, data frame, or tibble object (although these can be easily created using the matrix, data.frame or tibble functions). Accessing the help file ?knitr::kable gives a list of arguments that can be used to customise these tables.\n\n\n\n\n\n\nNote\n\n\n\nAs these tables are created using R functions, they must be generated within a code chunk.\n\n\nFor example, we can create a simple data table using kable showing the first 6 rows of the mtcars dataset (a dataset pre-loaded into base R):\n```{r mtcars table, echo = FALSE} \nknitr::kable(head(mtcars))\n``` \nwhich produces the following output:\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmpg\ncyl\ndisp\nhp\ndrat\nwt\nqsec\nvs\nam\ngear\ncarb\n\n\n\n\nMazda RX4\n21.0\n6\n160\n110\n3.90\n2.620\n16.46\n0\n1\n4\n4\n\n\nMazda RX4 Wag\n21.0\n6\n160\n110\n3.90\n2.875\n17.02\n0\n1\n4\n4\n\n\nDatsun 710\n22.8\n4\n108\n93\n3.85\n2.320\n18.61\n1\n1\n4\n1\n\n\nHornet 4 Drive\n21.4\n6\n258\n110\n3.08\n3.215\n19.44\n1\n0\n3\n1\n\n\nHornet Sportabout\n18.7\n8\n360\n175\n3.15\n3.440\n17.02\n0\n0\n3\n2\n\n\nValiant\n18.1\n6\n225\n105\n2.76\n3.460\n20.22\n1\n0\n3\n1\n\n\n\n\n\nWhere data are not already saved as an object, we need to create them first before generating a table. For example, the table we created manually earlier can be recreated using the kable function, by first creating a data frame with the information, and then piping it through to the function:\n```{r kable table}\n# Create a data frame with the table information\ndata.frame(col1 = c(\"This\", \"Very\"),\n           col2 = c(\"Is\", \"Simple\"),\n           col3 = c(\"A\", \"Table\")) %&gt;% \n  knitr::kable(., col.names = c(\"Header 1\", \"Header 2\", \"Header 3\"))\n``` \n\n\n\n\n\nHeader 1\nHeader 2\nHeader 3\n\n\n\n\nThis\nIs\nA\n\n\nVery\nSimple\nTable\n\n\n\n\n\nOther ways to create tables\nAlthough the kable function and RMarkdown syntax tables do not require additional R packages to be installed, they are fairly simple and do not give many options to customise the tables. For a more flexible alternative, I would recommend looking at the flextable package, which gives a much wider range of customisible features. The flextable user manual can be accessed for free from this website.\n\n\n\nExercise 8\nCreate an RMarkdown file that creates a html report describing the trends in core spending power in English local authorities between 2015 and 2020. Your report should include:\n\nA summary table of the total spending per year per region\nA suitable visualisation showing how the total annual spending has changed over this period, compared between regions\nA short interpretation of the table and visualisation\n\n\n\n\n\n\n\nNote\n\n\n\nYou are not expected to be an expert in this data! Interpret these outputs as you would any other numeric variable measured over time.",
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+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./session5_notes.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text"><span class="chapter-number">6</span>&nbsp; <span class="chapter-title">Reproducible research with RMarkdown</span></span></a>
+  </div>
+</li>
+    </ul>
+    </div>
+</nav>
+<div id="quarto-sidebar-glass" class="quarto-sidebar-collapse-item" data-bs-toggle="collapse" data-bs-target=".quarto-sidebar-collapse-item"></div>
+<!-- margin-sidebar -->
+    <div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
+        <nav id="TOC" role="doc-toc" class="toc-active">
+    <h2 id="toc-title">Table of contents</h2>
+   
+  <ul>
+  <li><a href="#the-rstudio-interface" id="toc-the-rstudio-interface" class="nav-link active" data-scroll-target="#the-rstudio-interface"><span class="header-section-number">2.1</span> The RStudio interface</a>
+  <ul class="collapse">
+  <li><a href="#exercise-1" id="toc-exercise-1" class="nav-link" data-scroll-target="#exercise-1">Exercise 1</a></li>
+  </ul></li>
+  <li><a href="#r-syntax" id="toc-r-syntax" class="nav-link" data-scroll-target="#r-syntax"><span class="header-section-number">2.2</span> R syntax</a>
+  <ul class="collapse">
+  <li><a href="#exercise-2" id="toc-exercise-2" class="nav-link" data-scroll-target="#exercise-2">Exercise 2</a></li>
+  </ul></li>
+  <li><a href="#r-objects-and-functions" id="toc-r-objects-and-functions" class="nav-link" data-scroll-target="#r-objects-and-functions"><span class="header-section-number">2.3</span> R objects and functions</a>
+  <ul class="collapse">
+  <li><a href="#objects" id="toc-objects" class="nav-link" data-scroll-target="#objects"><span class="header-section-number">2.3.1</span> Objects</a></li>
+  <li><a href="#functions" id="toc-functions" class="nav-link" data-scroll-target="#functions"><span class="header-section-number">2.3.2</span> Functions</a></li>
+  <li><a href="#help-files" id="toc-help-files" class="nav-link" data-scroll-target="#help-files"><span class="header-section-number">2.3.3</span> Help files</a></li>
+  <li><a href="#error-and-warning-messages" id="toc-error-and-warning-messages" class="nav-link" data-scroll-target="#error-and-warning-messages"><span class="header-section-number">2.3.4</span> Error and warning messages</a></li>
+  <li><a href="#cleaning-the-environment" id="toc-cleaning-the-environment" class="nav-link" data-scroll-target="#cleaning-the-environment"><span class="header-section-number">2.3.5</span> Cleaning the environment</a></li>
+  <li><a href="#r-packages" id="toc-r-packages" class="nav-link" data-scroll-target="#r-packages"><span class="header-section-number">2.3.6</span> R packages</a></li>
+  </ul></li>
+  </ul>
+</nav>
+    </div>
+<!-- main -->
+<main class="content" id="quarto-document-content">
+
+<header id="title-block-header" class="quarto-title-block default">
+<div class="quarto-title">
+<h1 class="title"><span class="chapter-number">2</span>&nbsp; <span class="chapter-title">Session 1: Introduction to R and RStudio</span></h1>
+</div>
+
+
+
+<div class="quarto-title-meta">
+
+    
+  
+    
+  </div>
+  
+
+
+</header>
+
+
+<section id="the-rstudio-interface" class="level2" data-number="2.1">
+<h2 data-number="2.1" class="anchored" data-anchor-id="the-rstudio-interface"><span class="header-section-number">2.1</span> The RStudio interface</h2>
+<p>There are a number of software packages based on the R programming language aimed at making writing and running analyses easier for users. They all run R in the background but look different and contain different features.</p>
+<p><strong>RStudio</strong> has been chosen for this course as it allows users to create script files, allowing code to be re-run, edited, and shared easily. RStudio also provides tools to help easily identify errors in R code, integrates help documentation into the main console and uses colour-coding to help read code at a glance.</p>
+<p>Before installing RStudio, we must ensure that R is downloaded onto the machine. R is available to download for free for Windows, Mac, or Linux via the <a href="https://cran.r-project.org/"><strong>CRAN</strong></a> website.</p>
+<p>Rstudio is also free to download from the <a href="https://posit.co/"><strong>Posit</strong></a> website.</p>
+<section id="the-rstudio-console-window" class="level4" data-number="2.1.0.1">
+<h4 data-number="2.1.0.1" class="anchored" data-anchor-id="the-rstudio-console-window"><span class="header-section-number">2.1.0.1</span> The RStudio console window</h4>
+<p>The screenshot below shows the RStudio interface which comprises of four windows:</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="images/rstudio_ide.png" class="img-fluid figure-img"></p>
+<figcaption>RStudio interface</figcaption>
+</figure>
+</div>
+<p><strong>Window A: R script files</strong></p>
+<p>All analysis and actions in R are carried out using the R syntax language. R script files allow you to write and edit code before running it in the console window.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Limit script files to 80 characters per line to ensure it is readable.</p>
+<p>RStudio has an option to add a margin that makes this easier to adhere to. Under the <em>Tools</em> drop-down menu, select <em>Global options</em>. Select <em>Code</em> from the list on the right, then under the <em>Display</em> tab, tick the <em>Show margin</em> box.</p>
+</div>
+</div>
+<p>If this window is not visible, create a new script file using <em>File -&gt; New File -&gt; R Script</em> from the drop-down menus or clicking the <img src="images/new_file_shortcut.png" class="img-fluid" alt="New file icon"> icon above the console and selecting <em>R Script</em>. This will open a new, blank script file. More than one script file can be open at the same time.</p>
+<p>Code entered into the script file does not run automatically. To run commands from the script, highlight the code and click the <img src="images/run_shortcut.png" class="img-fluid" alt="Run icon"> icon above the top right corner of the script window (this can be carried out by pressing <code>Ctrl + Enter</code> in Windows or <code>Command + Enter</code> on a Mac computer). More than one command can be run at the same time by highlighting all of them.</p>
+<p>The main advantage of using the script file rather than entering the code directly into the console is that it can be saved, edited and shared. To save a script file, use <em>File -&gt; Save As…</em> from the drop down menu, or click the <img src="images/save_shortcut.png" class="img-fluid" alt="save icon"> icon at the top of the window. It is important to save the script files at regular intervals to avoid losing work. Once the script file has been saved, we can also use the keyboard shortcuts <code>Ctrl + s</code> on Windows and <code>Command + s</code> on Mac to save the latest script file.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Script file names should be meaningful, lower case, and end in <code>.R</code>. Avoid using special characters in file names, including spaces. Use <code>_</code> instead of spaces.</p>
+<p>Where files should be run in a specific order, prefix the file name with numbers.</p>
+</div>
+</div>
+<p>Past script files can be opened using <em>File -&gt; Open File…</em> from the drop-down menu or by clicking the <img src="images/open_shortcut.png" class="img-fluid" alt="open icon"> icon and selecting a <code>.R</code> file. The keyboard shortcut to open an existing script file is <code>Ctrl + o</code> on Windows, and <code>Command + o</code> on Macs.</p>
+<p><strong>Window B: The R console</strong></p>
+<p>The R console window is where all commands run from the script file, results (other than plots), and messages, such as errors, are displayed. Commands can be written directly into the R console after the <code>&gt;</code> symbol and executed using <code>Enter</code> on the keyboard. It is not recommended to write code directly into the console as it is cannot be saved or replicated.</p>
+<p>Every time a new R session is opened, details about version and citations of R will be given by default. To clear text from the console window, use the keyboard shortcut <code>control + l</code> (this is the same for both Windows and Mac users). Be aware that this clears all text from the console, including any results. Before running this command, check that any results can be replicated within the script file.</p>
+<p><strong>Window C: Environment and history</strong></p>
+<p>This window lists all data and objects currently loaded into R. More details on the types of objects and how to use the Environment window are given in later sections.</p>
+<p><strong>Window D: Files, plots, packages and help</strong></p>
+<p>This window has many potential uses: graphics are displayed and can be saved from here, and R help files will appear here. This window is only available in the RStudio interface and not in the basic R package.</p>
+</section>
+<section id="exercise-1" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-1">Exercise 1</h3>
+<ol type="1">
+<li>Open a new script file if you have not already done so.</li>
+<li>Save this script file into an appropriate location.</li>
+</ol>
+</section>
+</section>
+<section id="r-syntax" class="level2" data-number="2.2">
+<h2 data-number="2.2" class="anchored" data-anchor-id="r-syntax"><span class="header-section-number">2.2</span> R syntax</h2>
+<p>All analyses within R are carried out using <strong>syntax</strong>, the R programming language. It is important to note that R is case-sensitive, so always ensure that you use the correct combination of upper and lower case letters when running functions or calling objects.</p>
+<p>Any text written in the R console or script file can be treated the same as text from other documents or programmes: text can be highlighted, copied and pasted to make coding more efficient.</p>
+<p>When creating script files, it is important to ensure they are clear and easy to read. Comments can be added to script files using the <code>#</code> symbol. R will ignore any text following the <code>#</code> on the same line.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Combining <code>#</code> and <code>-</code> creates sections within a script file, making them easier to navigate and organise.</p>
+<p>For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Load data ----------</span></span>
+<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Tidy data ----------</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</div>
+</div>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Helpful hint
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>To comment out chunks of code, highlight the rows and use the keyboard shortcut <em>ctrl + shift + c</em> on Windows, and <em>Command + shift + c</em> on Mac</p>
+</div>
+</div>
+<p>The choice of brackets in R coding is particularly important as they all have different functions:</p>
+<ul>
+<li>Round brackets <code>( )</code> are the most commonly used as they define arguments of functions. Any text followed by round brackets is assumed to be a function and R will attempt to run it. If the name of a function is not followed by round brackets, R will return the algorithm used to create the function within the console.</li>
+<li>Square brackets <code>[ ]</code> are used to set criteria or conditions within a function or object.</li>
+<li>Curly brackets <code>{ }</code> are used within loops, when creating a new function, and within <code>for</code> and <code>if</code> functions.</li>
+</ul>
+<p>All standard notation for mathematical calculations (<code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>^</code>, etc.) are compatible with R. At its simplest level, R is just a very powerful calculator!</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Although R will work whether a space is added before/after a mathematical operator, the <a href="https://style.tidyverse.org/syntax.html">style guide</a> recommends to add them surrounding most mathematical operations (<code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>), but not around <code>^</code>.</p>
+<p>For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Stylish code</span></span>
+<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="dv">1959</span> <span class="sc">-</span> <span class="dv">683</span></span>
+<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>(<span class="dv">351</span> <span class="sc">+</span> <span class="dv">457</span>)<span class="sc">^</span><span class="dv">2</span> <span class="sc">-</span> (<span class="dv">213</span> <span class="sc">+</span> <span class="dv">169</span>)<span class="sc">^</span><span class="dv">2</span></span>
+<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="co"># Un-stylish code</span></span>
+<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="dv">1959-683</span></span>
+<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>(<span class="dv">351</span><span class="sc">+</span><span class="dv">457</span>)<span class="sc">^</span><span class="dv">2</span> <span class="sc">-</span> (<span class="dv">213</span> <span class="sc">+</span> <span class="dv">169</span>) <span class="sc">^</span> <span class="dv">2</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</div>
+</div>
+<section id="exercise-2" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-2">Exercise 2</h3>
+<ol type="1">
+<li>Add your name and the date to the top of your script file (hint: comment this out so R does not try to run it)</li>
+<li>Use R to calculate the following calculations. Add the result to the same line of the script file in a way that ensures there are no errors in the code.</li>
+</ol>
+<ol type="a">
+<li><span class="math inline">\(64^2\)</span></li>
+<li><span class="math inline">\(3432 \div 8\)</span></li>
+<li><span class="math inline">\(96 \times 72\)</span></li>
+</ol>
+<p>When you have finished this exercise, select the entire script file (using <code>ctrl + a</code> on windows or <code>Command + a</code> on Mac) and run it to ensure there are no errors in the code.</p>
+</section>
+</section>
+<section id="r-objects-and-functions" class="level2" data-number="2.3">
+<h2 data-number="2.3" class="anchored" data-anchor-id="r-objects-and-functions"><span class="header-section-number">2.3</span> R objects and functions</h2>
+<section id="objects" class="level3" data-number="2.3.1">
+<h3 data-number="2.3.1" class="anchored" data-anchor-id="objects"><span class="header-section-number">2.3.1</span> Objects</h3>
+<p>One of the main advantages to using R over other software packages such as SPSS is that more than one dataset can be accessed at the same time. A collection of data stored in any format within the R session is known as an <strong>object</strong>. Objects can include single numbers, single variables, entire datasets, lists of datasets, or even tables and graphs.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Object names should only contain lower case letters, numbers and <code>_</code> (instead of a space to separate words). The should be meaningful and concise.</p>
+</div>
+</div>
+<p>Objects are defined in R using the <code>&lt;-</code> or <code>=</code> symbols. For example,</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>object_1 <span class="ot">&lt;-</span> <span class="dv">81</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Creates an object in the environment named <code>object_1</code>, which takes the value <code>81</code>. This will appear in the environment window of the console (window C from the interface shown earlier).</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Although both work, use <code>&lt;-</code> for assignment, not <code>=</code>.</p>
+</div>
+</div>
+<p>To retrieve an object, type its name into the script or console and run it. This object can then be included in functions or operations in place of the value assigned to it:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>object_1</span>
+<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="do">## [1] 81</span></span>
+<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>object_1 <span class="sc">*</span> <span class="dv">2</span></span>
+<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="do">## [1] 162</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>R has some mathematical objects stored by default such as pi that can be used in calculations.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>pi</span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="do">## [1] 3.141593</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>The <code>[1]</code> that appears at the beginning of each output line indicates that this is the first element in the object. If there were two lines then the second line would start with the number of that element in square brackets.</p>
+<p>For example, if we had an object with 6 elements and when called the first line contained the first 5 elements, each line would begin with <code>[1]</code> and <code>[6]</code> respectively.</p>
+</section>
+<section id="functions" class="level3" data-number="2.3.2">
+<h3 data-number="2.3.2" class="anchored" data-anchor-id="functions"><span class="header-section-number">2.3.2</span> Functions</h3>
+<p><strong>Functions</strong> are built-in commands that allow R users to run analyses. All functions require the definition of arguments within round brackets <code>()</code>. Each function requires different information and has different arguments that can be used to customise the analysis. A detailed list of these arguments and a description of the function can be found in the function’s associated <strong>help file</strong>.</p>
+</section>
+<section id="help-files" class="level3" data-number="2.3.3">
+<h3 data-number="2.3.3" class="anchored" data-anchor-id="help-files"><span class="header-section-number">2.3.3</span> Help files</h3>
+<p>Each function that exists within R has an associated help file. RStudio does not require an internet connection to access these help files if the function is available in the current session of R.</p>
+<p>To retrieve help files, enter <code>?</code> followed by the function name into the console window, e.g <code>?mean</code>. The help file will appear in window D of the interface shown in the introduction.</p>
+<p>Help files contain the following information:</p>
+<ul>
+<li>Description: what the function is used for</li>
+<li>Usage: how the function is used</li>
+<li>Arguments: required and optional arguments entered into round brackets necessary for the function to work</li>
+<li>Details: relevant details about the function in question</li>
+<li>References</li>
+<li>See also: links to other relevant functions</li>
+<li>Examples: example code with applications of the function</li>
+</ul>
+</section>
+<section id="error-and-warning-messages" class="level3" data-number="2.3.4">
+<h3 data-number="2.3.4" class="anchored" data-anchor-id="error-and-warning-messages"><span class="header-section-number">2.3.4</span> Error and warning messages</h3>
+<p>Where a function or object has not been correctly specified, or their is some mistake in the syntax that has been sent to the console, R will return an error message. These messages are generally informative and include the location of the error.</p>
+<p>The most common errors include misspelling functions or objects:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sqrt</span>(ojbect_1)</span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="do">## Error in eval(expr, envir, enclos): object 'ojbect_1' not found</span></span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="fu">Sqrt</span>(object_1)</span>
+<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="do">## Error in Sqrt(object_1): could not find function "Sqrt"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Or where an object has not yet been specified:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(x, y)</span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="do">## Error in eval(expr, envir, enclos): object 'x' not found</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>When R returns an error message, this means that the operation has been completely halted. R may also return warning messages which look similar to errors but does not necessarily mean the operation has been stopped.</p>
+<p>Warnings are included to indicate that R suspects something in the operation may be wrong and should be checked. There are occasions where warnings can be ignored but this is only after the operation has been checked.</p>
+<p>When working within the R console, if an incomplete command is run, a <code>+</code> symbol will appear in the console, rather than the usual <code>&gt;</code>. This indicates that R expects you to keep writing the previous code. To overcome this issue, either finish the command on the next line of the console, or press the <code>esc</code> button on your keyboard to start from scratch.</p>
+<p>One of the benefits of using RStudio rather than the basic R package is that it will suggest object or function names after typing the first few letters. This avoids spelling mistakes and accidental errors when running code. To accept the suggestion, either click the correct choice with your mouse or use the <code>tab</code> button on your keyboard.</p>
+</section>
+<section id="cleaning-the-environment" class="level3" data-number="2.3.5">
+<h3 data-number="2.3.5" class="anchored" data-anchor-id="cleaning-the-environment"><span class="header-section-number">2.3.5</span> Cleaning the environment</h3>
+<p>To remove objects from the RStudio environment, we can use the <code>rm</code> function. This can be combined with the <code>ls()</code> function, which lists all objects in the environment, to remove all objects currently loaded:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rm</span>(<span class="at">list =</span> <span class="fu">ls</span>())</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>There are no undo and redo buttons for R syntax. The <code>rm</code> function will permanently delete objects from the environment. The only way to reverse this is to re-run the code that created the objects originally from the script file.</p>
+</div>
+</div>
+</section>
+<section id="r-packages" class="level3" data-number="2.3.6">
+<h3 data-number="2.3.6" class="anchored" data-anchor-id="r-packages"><span class="header-section-number">2.3.6</span> R packages</h3>
+<p>R packages are a collection of functions and datasets developed by R users that expand existing R capabilities or add completely new ones. Packages allow users to apply the most up-to-date methods shortly after they are developed, unlike other statistical software packages that require an entirely new version.</p>
+<section id="installing-packages-from-cran" class="level4" data-number="2.3.6.1">
+<h4 data-number="2.3.6.1" class="anchored" data-anchor-id="installing-packages-from-cran"><span class="header-section-number">2.3.6.1</span> Installing packages from CRAN</h4>
+<p>The quickest way to install a package in R is by using the <code>install.packages</code> function. This sends RStudio to the online repository of tested and verified R packages (known as <a href="https://cran.r-project.org/">CRAN</a>) and downloads the package files onto the machine you are currently working from in temporary files. Ensure that the package you wish to install is spelled correctly and surrounded by <code>''</code>.</p>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>The <code>install.packages</code> function requires an internet connection, and can take a long time if the package has a lot of dependent packages that also need downloading.</p>
+<p>This process should only be carried out the first time a package is used on a machine, or when a substantial update has taken place, to download the latest version of the package.</p>
+</div>
+</div>
+</section>
+<section id="loading-packages-to-an-r-session" class="level4" data-number="2.3.6.2">
+<h4 data-number="2.3.6.2" class="anchored" data-anchor-id="loading-packages-to-an-r-session"><span class="header-section-number">2.3.6.2</span> Loading packages to an R session</h4>
+<p>Every time a new session of RStudio is opened, packages must be reloaded. To load a package into R (and gain access to the associated functions and data), use the <code>library</code> function.</p>
+<p>Loading a package does not require an internet connection, but will only work if the package has already been installed and saved onto the computer you are working from. If you are unsure, use the function <code>installed.packages</code> to return a list of all packages that are loaded onto the machine you are working from.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Add your <code>library</code> function at the beginning of your script file. This reminds you to re-load packages when opening a new R session, and reduces the chance of error messages from functions requiring these packages.</p>
+</div>
+</div>
+
+
+</section>
+</section>
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+      <a href="./index.html" class="pagination-link" aria-label="Welcome!">
+        <i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">1</span>&nbsp; <span class="chapter-title">Welcome!</span></span>
+      </a>          
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+  <div class="nav-page nav-page-next">
+      <a href="./session2_notes.html" class="pagination-link" aria-label="Session 2: Introduction to tidyverse and data wrangling">
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+  <li><a href="#opening-and-exploring-data" id="toc-opening-and-exploring-data" class="nav-link active" data-scroll-target="#opening-and-exploring-data"><span class="header-section-number">3.1</span> Opening and exploring data</a>
+  <ul class="collapse">
+  <li><a href="#styles-of-r-coding" id="toc-styles-of-r-coding" class="nav-link" data-scroll-target="#styles-of-r-coding"><span class="header-section-number">3.1.1</span> Styles of R coding</a></li>
+  <li><a href="#the-working-directory" id="toc-the-working-directory" class="nav-link" data-scroll-target="#the-working-directory"><span class="header-section-number">3.1.2</span> The working directory</a></li>
+  </ul></li>
+  <li><a href="#data-input" id="toc-data-input" class="nav-link" data-scroll-target="#data-input"><span class="header-section-number">3.2</span> 4.3 Data input</a>
+  <ul class="collapse">
+  <li><a href="#selecting-variables" id="toc-selecting-variables" class="nav-link" data-scroll-target="#selecting-variables"><span class="header-section-number">3.2.1</span> Selecting variables</a></li>
+  <li><a href="#filtering-data" id="toc-filtering-data" class="nav-link" data-scroll-target="#filtering-data"><span class="header-section-number">3.2.2</span> Filtering data</a></li>
+  <li><a href="#pipes" id="toc-pipes" class="nav-link" data-scroll-target="#pipes"><span class="header-section-number">3.2.3</span> Pipes</a></li>
+  <li><a href="#creating-new-variables" id="toc-creating-new-variables" class="nav-link" data-scroll-target="#creating-new-variables"><span class="header-section-number">3.2.4</span> Creating new variables</a></li>
+  <li><a href="#exercise-3" id="toc-exercise-3" class="nav-link" data-scroll-target="#exercise-3">Exercise 3</a></li>
+  </ul></li>
+  </ul>
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+<main class="content" id="quarto-document-content">
+
+<header id="title-block-header" class="quarto-title-block default">
+<div class="quarto-title">
+<h1 class="title"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Session 2: Introduction to tidyverse and data wrangling</span></h1>
+</div>
+
+
+
+<div class="quarto-title-meta">
+
+    
+  
+    
+  </div>
+  
+
+
+</header>
+
+
+<section id="opening-and-exploring-data" class="level2" data-number="3.1">
+<h2 data-number="3.1" class="anchored" data-anchor-id="opening-and-exploring-data"><span class="header-section-number">3.1</span> Opening and exploring data</h2>
+<section id="styles-of-r-coding" class="level3" data-number="3.1.1">
+<h3 data-number="3.1.1" class="anchored" data-anchor-id="styles-of-r-coding"><span class="header-section-number">3.1.1</span> Styles of R coding</h3>
+<p>Up to this point, we have not thought about the style of R coding we will be using. There are different approaches to R coding that we can use, they can be thought of as different dialects of the R programming language.</p>
+<p>The choice of R ‘dialect’ depends on personal preference. Some prefer to use the ‘base R’ approach that does not rely on any packages that may need updating, making it a more stable approach. However, base R can be difficult to read for those not comfortable with coding.</p>
+<div class="cell">
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="images/r_meme.png" class="img-fluid figure-img" style="width:75.0%"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>The alternative approach that we will be adopting in this course is the ‘tidyverse’ approach. Tidyverse is a set of packages that have been designed to make R coding more readable and efficient. They have been designed with reproducibility in mind, which means there is a wealth of online (mostly free), well-written resources available to help use these packages.</p>
+<p>If you have not done so already, install the tidyverse packages to your machine using the following code:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">'tidyverse'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>This can take a long time if you have never downloaded the tidyverse packages before as there are many dependencies that are required. Do not stress if you get a lot of text in the console! This is normal, but watch out for any error messages.</p>
+</div>
+</div>
+<p>Once the tidyverse package is installed, we must load it into the current working session. At the beginning of your script file add the following syntax:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Begin every script file with the <code>library</code> command, loading packages in before any data. This avoids any potential errors arising where functions are called before the necessary package has been loaded into the current session.</p>
+</div>
+</div>
+</section>
+<section id="the-working-directory" class="level3" data-number="3.1.2">
+<h3 data-number="3.1.2" class="anchored" data-anchor-id="the-working-directory"><span class="header-section-number">3.1.2</span> The working directory</h3>
+<p>The working directory is a file path on your computer that R sets as the default location when opening, saving, or exporting documents, files, and graphics. This file path can be specified manually but setting the working directory saves time and makes code more efficient.</p>
+<p>The working directory can be set manually by using the <em>Session -&gt; Set Working Directory -&gt; Change Directory…</em> option from the drop-down menu, or the <code>setwd</code> function. Both options require the directory to be specified each time R is restarted, are sensitive to changes in folders within the file path, and cannot be used when script files are shared between colleagues.</p>
+<p>An alternative approach that overcomes these issues is to create an R project.</p>
+<section id="r-projects" class="level4" data-number="3.1.2.1">
+<h4 data-number="3.1.2.1" class="anchored" data-anchor-id="r-projects"><span class="header-section-number">3.1.2.1</span> R projects</h4>
+<p>R projects are files (saved with the <code>.Rproj</code> extension) that keep associated files (including scripts, data, and outputs) grouped together. An R project automatically sets the working directory relative to its current location, which makes collaborative work easier, and avoids issues when a file path is changed.</p>
+<p>Projects are created by using the <em>File -&gt; New project</em> option from the drop-down menu, or using the <img src="images/project_icon.png" class="img-fluid" alt="R project icon"> icon from the top-right corner of the RStudio interface. Existing projects can be opened under the <em>File -&gt; Open project…</em> drop-down menu or using the project icon.</p>
+<p>When creating a new project, we must choose whether we want to create a new directory or use an existing one. Usually, we will have already set up a folder containing data or other documents related to the analysis we plan to carry out. If this is the case, we are using an existing directory and selecting the analysis folder as the project directory.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Have a clear order to your analysis folder. Consider creating separate folders within a project for input and output data, documentation, and outputs such as graphs or tables.</p>
+</div>
+</div>
+</section>
+</section>
+</section>
+<section id="data-input" class="level2" data-number="3.2">
+<h2 data-number="3.2" class="anchored" data-anchor-id="data-input"><span class="header-section-number">3.2</span> 4.3 Data input</h2>
+<p>To ensure our code is collaborative and reproducible, we should strive to store data in formats that can be used across multiple platforms. One of the best ways to do this is to store data as a comma-delimited file (.csv). CSV files can be opened by a range of different softwares (including R, SPSS, STATA and excel), and base R can be used to open these files without requiring additional packages.</p>
+<p>Before loading files in R, it is essential to check that they are correctly formatted. Data files should only contain one sheet with no pictures or graphics, each row should correspond to a case or observation and each column should correspond to a variable.</p>
+<p>To avoid any errors arising from spelling mistakes, we can use the <code>list.files</code> function to return a list of files and folders from the current working directory. The file names can be copied from the console and pasted into the script file. As the data are saved in a folder within the working directory, we must add the argument <code>path =</code> to specify the folder we want to list files from.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">list.files</span>(<span class="at">path =</span> <span class="st">"data"</span>)</span>
+<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="do">## [1] "CSP_2015.csv"         "CSP_2016.csv"         "CSP_2017.csv"        </span></span>
+<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="do">## [4] "CSP_2018.csv"         "CSP_2019.csv"         "CSP_2020.csv"        </span></span>
+<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="do">## [7] "CSP_long_201520.csv"  "data_description.pdf"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>This list should contain 6 CSV files with the core spending power in local authorities in England between 2015 and 2020. We will first load and explore the 2020 data using the <code>read_csv</code> function and attaching the data to an object. Remember to add the <code>data</code> folder to the file name.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>csp_2020 <span class="ot">&lt;-</span> <span class="fu">read_csv</span>(<span class="st">"data/CSP_2020.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Imported datasets will appear in the Environment window of the console once they are saved as objects. This Environment also displays the number of variables and observations in each object. To preview the contents of an object, click on its name in the Environment window or use the function <code>View(data)</code>.</p>
+<p>Other useful functions that help explore a dataset include:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return variable names from a dataset object</span></span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="fu">names</span>(csp_2020)</span>
+<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="do">## [1] "ons_code"         "authority"        "region"           "sfa_2020"        </span></span>
+<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="do">## [5] "under_index_2020" "ct_total_2020"    "nhb_2020"         "nhb_return_2020" </span></span>
+<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="do">## [9] "rsdg_2020"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Variable names should follow the same style rules as object names: only contain lower case letters, numbers, and use <code>_</code> to separate words. They should be meaningful and concise.</p>
+</div>
+</div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Display information about the structure of an object</span></span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(csp_2020)</span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="do">## spc_tbl_ [396 × 9] (S3: spec_tbl_df/tbl_df/tbl/data.frame)</span></span>
+<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ ons_code        : chr [1:396] "E07000223" "E07000026" "E07000032" "E07000224" ...</span></span>
+<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ authority       : chr [1:396] "Adur" "Allerdale" "Amber Valley" "Arun" ...</span></span>
+<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ region          : chr [1:396] "SE" "NW" "EM" "SE" ...</span></span>
+<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ sfa_2020        : num [1:396] 1.77 3.85 3.23 3.67 4.08 ...</span></span>
+<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ under_index_2020: num [1:396] 0.0708 0.1465 0.1292 0.147 0.1557 ...</span></span>
+<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ ct_total_2020   : num [1:396] 6.53 5.4 6.85 11.61 6.42 ...</span></span>
+<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ nhb_2020        : num [1:396] 0.0881 0.6061 1.5786 2.2949 1.1547 ...</span></span>
+<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ nhb_return_2020 : num [1:396] 0 0 0 0 0 0 0 0 0 0 ...</span></span>
+<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ rsdg_2020       : num [1:396] 0 0.326 0 0 0 ...</span></span>
+<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  - attr(*, "spec")=</span></span>
+<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a><span class="do">##   .. cols(</span></span>
+<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   ons_code = col_character(),</span></span>
+<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   authority = col_character(),</span></span>
+<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   region = col_character(),</span></span>
+<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   sfa_2020 = col_double(),</span></span>
+<span id="cb6-19"><a href="#cb6-19" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   under_index_2020 = col_double(),</span></span>
+<span id="cb6-20"><a href="#cb6-20" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   ct_total_2020 = col_double(),</span></span>
+<span id="cb6-21"><a href="#cb6-21" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   nhb_2020 = col_double(),</span></span>
+<span id="cb6-22"><a href="#cb6-22" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   nhb_return_2020 = col_double(),</span></span>
+<span id="cb6-23"><a href="#cb6-23" aria-hidden="true" tabindex="-1"></a><span class="do">##   ..   rsdg_2020 = col_double()</span></span>
+<span id="cb6-24"><a href="#cb6-24" aria-hidden="true" tabindex="-1"></a><span class="do">##   .. )</span></span>
+<span id="cb6-25"><a href="#cb6-25" aria-hidden="true" tabindex="-1"></a><span class="do">##  - attr(*, "problems")=&lt;externalptr&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Output from the <code>str</code> function differs depending on the type of object it is applied to. For example, this object is a <code>tibble</code> (<code>tbl</code>, Tidyverse’s name for a dataset). The information given about tibbles includes the object dimensions (<code>396 x 9</code>, or 396 rows and 9 columns), variable names, and variable types.</p>
+<p>It is important to check that R has correctly recognised variable type when data are loaded, before generating any visualisations or analysis. If variables are incorrectly specified, this could either lead to errors or invalid analyses. We will see how to change variables types later in this session.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return the first 6 rows of the tibble</span></span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(csp_2020)</span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 6 × 9</span></span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="do">##   ons_code  authority    region sfa_2020 under_index_2020 ct_total_2020 nhb_2020</span></span>
+<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a><span class="do">##   &lt;chr&gt;     &lt;chr&gt;        &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;</span></span>
+<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a><span class="do">## 1 E07000223 Adur         SE         1.77           0.0708          6.53   0.0881</span></span>
+<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="do">## 2 E07000026 Allerdale    NW         3.85           0.147           5.40   0.606 </span></span>
+<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a><span class="do">## 3 E07000032 Amber Valley EM         3.23           0.129           6.85   1.58  </span></span>
+<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a><span class="do">## 4 E07000224 Arun         SE         3.67           0.147          11.6    2.29  </span></span>
+<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a><span class="do">## 5 E07000170 Ashfield     EM         4.08           0.156           6.42   1.15  </span></span>
+<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a><span class="do">## 6 E07000105 Ashford      SE         2.88           0.115           7.92   3.05  </span></span>
+<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return the final 6 rows of the tibble.</span></span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="fu">tail</span>(csp_2020)</span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 6 × 9</span></span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="do">##   ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020</span></span>
+<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="do">##   &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;</span></span>
+<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a><span class="do">## 1 E07000229 Worthing    SE         2.69            0.108          9.52    0.961</span></span>
+<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="do">## 2 E07000238 Wychavon    WM         2.65            0.106          6.29    4.73 </span></span>
+<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a><span class="do">## 3 E07000007 Wycombe     SE         0               0              0       0    </span></span>
+<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a><span class="do">## 4 E07000128 Wyre        NW         3.41            0.137          7.64    1.28 </span></span>
+<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a><span class="do">## 5 E07000239 Wyre Forest WM         2.84            0.114          7.45    0.262</span></span>
+<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a><span class="do">## 6 E06000014 York        YH        27.1             1.06          93.8     2.68 </span></span>
+<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<section id="selecting-variables" class="level3" data-number="3.2.1">
+<h3 data-number="3.2.1" class="anchored" data-anchor-id="selecting-variables"><span class="header-section-number">3.2.1</span> Selecting variables</h3>
+<p>Often, our analysis will not require every variable in a downloaded dataset, and we may wish to create a smaller analysis tibble. We may also wish to select individual variables from the tibble to apply functions to them without including the entire dataset.</p>
+<p>To select one or more variable and return them as a new tibble, we can use the <code>select</code> function from tidyverse’s <code>dplyr</code> package.</p>
+<p>For example, if we wanted to return the new homes bonus (<code>nhb</code>) for each local authority (the seventh column of the dataset), we can either <code>select</code> this based on the variable name or its location in the object:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return the nhb_2020 variable from the csp_2020 object</span></span>
+<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="fu">select</span>(csp_2020, nhb_2020)</span>
+<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 396 × 1</span></span>
+<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    nhb_2020</span></span>
+<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a><span class="do">##       &lt;dbl&gt;</span></span>
+<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  1   0.0881</span></span>
+<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  2   0.606 </span></span>
+<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  3   1.58  </span></span>
+<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  4   2.29  </span></span>
+<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  5   1.15  </span></span>
+<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  6   3.05  </span></span>
+<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  7   0     </span></span>
+<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  8   0     </span></span>
+<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  9   1.05  </span></span>
+<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 10   1.85  </span></span>
+<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 386 more rows</span></span>
+<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a><span class="co"># Return the 7th variable of the csp_2020 object</span></span>
+<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a><span class="fu">select</span>(csp_2020, <span class="dv">7</span>)</span>
+<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 396 × 1</span></span>
+<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a><span class="do">##    nhb_2020</span></span>
+<span id="cb9-22"><a href="#cb9-22" aria-hidden="true" tabindex="-1"></a><span class="do">##       &lt;dbl&gt;</span></span>
+<span id="cb9-23"><a href="#cb9-23" aria-hidden="true" tabindex="-1"></a><span class="do">##  1   0.0881</span></span>
+<span id="cb9-24"><a href="#cb9-24" aria-hidden="true" tabindex="-1"></a><span class="do">##  2   0.606 </span></span>
+<span id="cb9-25"><a href="#cb9-25" aria-hidden="true" tabindex="-1"></a><span class="do">##  3   1.58  </span></span>
+<span id="cb9-26"><a href="#cb9-26" aria-hidden="true" tabindex="-1"></a><span class="do">##  4   2.29  </span></span>
+<span id="cb9-27"><a href="#cb9-27" aria-hidden="true" tabindex="-1"></a><span class="do">##  5   1.15  </span></span>
+<span id="cb9-28"><a href="#cb9-28" aria-hidden="true" tabindex="-1"></a><span class="do">##  6   3.05  </span></span>
+<span id="cb9-29"><a href="#cb9-29" aria-hidden="true" tabindex="-1"></a><span class="do">##  7   0     </span></span>
+<span id="cb9-30"><a href="#cb9-30" aria-hidden="true" tabindex="-1"></a><span class="do">##  8   0     </span></span>
+<span id="cb9-31"><a href="#cb9-31" aria-hidden="true" tabindex="-1"></a><span class="do">##  9   1.05  </span></span>
+<span id="cb9-32"><a href="#cb9-32" aria-hidden="true" tabindex="-1"></a><span class="do">## 10   1.85  </span></span>
+<span id="cb9-33"><a href="#cb9-33" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 386 more rows</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>We can select multiple variables and return them as a tibble by separating the variable names or numbers with commas:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return three variables from the csp_2020 object</span></span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="fu">select</span>(csp_2020, ons_code, authority, region)</span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 396 × 3</span></span>
+<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    ons_code  authority            region</span></span>
+<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;     &lt;chr&gt;                &lt;chr&gt; </span></span>
+<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 E07000223 Adur                 SE    </span></span>
+<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 E07000026 Allerdale            NW    </span></span>
+<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 E07000032 Amber Valley         EM    </span></span>
+<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 E07000224 Arun                 SE    </span></span>
+<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 E07000170 Ashfield             EM    </span></span>
+<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 E07000105 Ashford              SE    </span></span>
+<span id="cb10-12"><a href="#cb10-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 E31000001 Avon Fire            SW    </span></span>
+<span id="cb10-13"><a href="#cb10-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 E07000004 Aylesbury Vale       SE    </span></span>
+<span id="cb10-14"><a href="#cb10-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 E07000200 Babergh              EE    </span></span>
+<span id="cb10-15"><a href="#cb10-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 E09000002 Barking And Dagenham L     </span></span>
+<span id="cb10-16"><a href="#cb10-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 386 more rows</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>When selecting consecutive variables, a shortcut can be used that gives the first and last variable in the list, separated by a colon, <code>:</code>. The previous example can be carried out using the following code:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return variables from ons_code upt to and including region</span></span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a><span class="fu">select</span>(csp_2020, ons_code<span class="sc">:</span>region)</span>
+<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 396 × 3</span></span>
+<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    ons_code  authority            region</span></span>
+<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;     &lt;chr&gt;                &lt;chr&gt; </span></span>
+<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 E07000223 Adur                 SE    </span></span>
+<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 E07000026 Allerdale            NW    </span></span>
+<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 E07000032 Amber Valley         EM    </span></span>
+<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 E07000224 Arun                 SE    </span></span>
+<span id="cb11-10"><a href="#cb11-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 E07000170 Ashfield             EM    </span></span>
+<span id="cb11-11"><a href="#cb11-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 E07000105 Ashford              SE    </span></span>
+<span id="cb11-12"><a href="#cb11-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 E31000001 Avon Fire            SW    </span></span>
+<span id="cb11-13"><a href="#cb11-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 E07000004 Aylesbury Vale       SE    </span></span>
+<span id="cb11-14"><a href="#cb11-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 E07000200 Babergh              EE    </span></span>
+<span id="cb11-15"><a href="#cb11-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 E09000002 Barking And Dagenham L     </span></span>
+<span id="cb11-16"><a href="#cb11-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 386 more rows</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>The <code>select</code> function can also be combined with a number of ‘selection helper’ functions that help us select variables based on naming conventions:</p>
+<ul>
+<li><code>starts_with("xyz")</code> returns all variables with names beginning <code>xyz</code></li>
+<li><code>ends_with("xyz")</code> returns all variables with names ending <code>xyz</code></li>
+<li><code>contains("xyz")</code> returns all variables that have <code>xyz</code> within their name</li>
+</ul>
+<p>Or based on whether they match a condition:</p>
+<ul>
+<li><code>where(is.numeric)</code> returns all variables that are classed as numeric</li>
+</ul>
+<p>For a full list of these selection helpers, access the helpfile using <code>?tidyr_tidy_select</code>.</p>
+<p>The <code>select</code> function can also be used to remove variables from a tibble by adding a <code>-</code> before the variable name or number. For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Remove the ons_code variable </span></span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="fu">select</span>(csp_2020, <span class="sc">-</span>ons_code)</span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 396 × 8</span></span>
+<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    authority            region sfa_2020 under_index_2020 ct_total_2020 nhb_2020</span></span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;                &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;</span></span>
+<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 Adur                 SE         1.77           0.0708          6.53   0.0881</span></span>
+<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 Allerdale            NW         3.85           0.147           5.40   0.606 </span></span>
+<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 Amber Valley         EM         3.23           0.129           6.85   1.58  </span></span>
+<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 Arun                 SE         3.67           0.147          11.6    2.29  </span></span>
+<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 Ashfield             EM         4.08           0.156           6.42   1.15  </span></span>
+<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 Ashford              SE         2.88           0.115           7.92   3.05  </span></span>
+<span id="cb12-12"><a href="#cb12-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 Avon Fire            SW        16.0            0.437          27.8    0     </span></span>
+<span id="cb12-13"><a href="#cb12-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 Aylesbury Vale       SE         0              0               0      0     </span></span>
+<span id="cb12-14"><a href="#cb12-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 Babergh              EE         2.14           0.0857          5.77   1.05  </span></span>
+<span id="cb12-15"><a href="#cb12-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 Barking And Dagenham L         75.7            2.31           65.8    1.85  </span></span>
+<span id="cb12-16"><a href="#cb12-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 386 more rows</span></span>
+<span id="cb12-17"><a href="#cb12-17" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>The <code>select</code> function returns the variable(s) in the form of a tibble (or dataset). However, some functions, such as basic summary functions, require data to be entered as a <code>vector</code> (a list of values). Tibbles with a single variable can be converted into a vector using the <code>as.vector</code> function, or we can use the base R approach to selecting a single variable. To return a single variable as a vector in base R, we can use the <code>$</code> symbol between the data name and the variable to return:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>csp_2020<span class="sc">$</span>nhb_2020</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>It is important to save any changes made to the existing dataset. This can be done using the <code>write_csv</code> function:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">write_csv</span>(csp_2020, <span class="at">file =</span> <span class="st">"data/csp_2020_new.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>When saving updated tibbles as files, use a different file name to the original raw data. Using the same name will overwrite the original file. We always want a copy of the raw data in case of any errors or issues.</p>
+</div>
+</div>
+</section>
+<section id="filtering-data" class="level3" data-number="3.2.2">
+<h3 data-number="3.2.2" class="anchored" data-anchor-id="filtering-data"><span class="header-section-number">3.2.2</span> Filtering data</h3>
+<p>The <code>filter</code> function, from tidyverse’s <code>dplyr</code> package allows us to return subgroups of the data based on conditional statements. These conditional statements can include mathematical operators, e.g.&nbsp;<code>&lt;=</code> (less than or equal to), <code>==</code> (is equal to), and <code>!=</code> (is not equal to), or can be based on conditional functions, e.g.&nbsp;<code>is.na(variable)</code> (is missing), <code>between(a, b)</code> (number lies between a and b).</p>
+<p>A more comprehensive list of conditional statements can be found in the help file using <code>?filter</code>.</p>
+<p>For example, to return the core spending power for local authorities in the North West region of England, we use the following:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return rows where region is equal to NW from the csp_2020 object</span></span>
+<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="fu">filter</span>(csp_2020, region <span class="sc">==</span> <span class="st">"NW"</span>)</span>
+<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 46 × 9</span></span>
+<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020</span></span>
+<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;</span></span>
+<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 E07000026 Allerdale   NW         3.85            0.147          5.40   0.606 </span></span>
+<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 E07000027 Barrow-in-… NW         4.40            0.125          4.74   0.0111</span></span>
+<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 E06000008 Blackburn … NW        58.1             1.79          55.9    0.999 </span></span>
+<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 E06000009 Blackpool   NW        63.3             1.94          60.1    0.266 </span></span>
+<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 E08000001 Bolton      NW        84.2             2.73         115.     0.506 </span></span>
+<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 E07000117 Burnley     NW         5.90            0.171          7.16   0.694 </span></span>
+<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 E08000002 Bury        NW        42.3             1.44          89.0    0.458 </span></span>
+<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 E07000028 Carlisle    NW         3.34            0.134          7.49   1.49  </span></span>
+<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 E06000049 Cheshire E… NW        42.5             1.70         230.    11.2   </span></span>
+<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 E31000006 Cheshire F… NW        13.5             0.380         30.1    0     </span></span>
+<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 36 more rows</span></span>
+<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Multiple conditional statements can be added to the same function by separating them with a comma <code>,</code>. For example, to return a subgroup of local authorities in the North West region that had a settlement funding assessment (SFA) of over £40 million, we use the following:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">filter</span>(csp_2020, region <span class="sc">==</span> <span class="st">"NW"</span>, sfa_2020 <span class="sc">&gt;</span> <span class="dv">40</span>)</span>
+<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 23 × 9</span></span>
+<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="do">##    ons_code  authority   region sfa_2020 under_index_2020 ct_total_2020 nhb_2020</span></span>
+<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;     &lt;chr&gt;       &lt;chr&gt;     &lt;dbl&gt;            &lt;dbl&gt;         &lt;dbl&gt;    &lt;dbl&gt;</span></span>
+<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 E06000008 Blackburn … NW         58.1             1.79          55.9    0.999</span></span>
+<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 E06000009 Blackpool   NW         63.3             1.94          60.1    0.266</span></span>
+<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 E08000001 Bolton      NW         84.2             2.73         115.     0.506</span></span>
+<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 E08000002 Bury        NW         42.3             1.44          89.0    0.458</span></span>
+<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 E06000049 Cheshire E… NW         42.5             1.70         230.    11.2  </span></span>
+<span id="cb16-10"><a href="#cb16-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 E06000050 Cheshire W… NW         56.3             2.12         196.    10.2  </span></span>
+<span id="cb16-11"><a href="#cb16-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 E10000006 Cumbria     NW        107.              3.56         248.     0.824</span></span>
+<span id="cb16-12"><a href="#cb16-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 E47000001 Greater Ma… NW         50.6             1.28          50.5    0    </span></span>
+<span id="cb16-13"><a href="#cb16-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 E06000006 Halton      NW         45.6             1.45          52.2    2.21 </span></span>
+<span id="cb16-14"><a href="#cb16-14" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 E08000011 Knowsley    NW         84.1             2.50          56.8    2.10 </span></span>
+<span id="cb16-15"><a href="#cb16-15" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 13 more rows</span></span>
+<span id="cb16-16"><a href="#cb16-16" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 2 more variables: nhb_return_2020 &lt;dbl&gt;, rsdg_2020 &lt;dbl&gt;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="pipes" class="level3" data-number="3.2.3">
+<h3 data-number="3.2.3" class="anchored" data-anchor-id="pipes"><span class="header-section-number">3.2.3</span> Pipes</h3>
+<p>When creating an analysis-ready dataset, we often want to combine functions such as <code>select</code> and <code>filter</code>. Previously, these would need to be carried out separately and a new object would need to be created or overwritten at each step, clogging up the environment.</p>
+<p>In tidyverse, we combine multiple functions into a single process by using the ‘pipe’ symbol <code>%&gt;%</code>, which is read as ‘and then’ within the code.</p>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Helpful hint
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>To save time when piping, use the keyboard shortcut <em>ctrl + shift + m</em> for Windows, and <em>Command + shift + m</em> for Mac to create a pipe.</p>
+</div>
+</div>
+<p>For example, we can return a list of local authority names from the North West region:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Using the csp_2020 object</span></span>
+<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return just rows where region is equal to NW, and then</span></span>
+<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(region <span class="sc">==</span> <span class="st">"NW"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Select just the authority variable</span></span>
+<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(authority)</span>
+<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 46 × 1</span></span>
+<span id="cb17-8"><a href="#cb17-8" aria-hidden="true" tabindex="-1"></a><span class="do">##    authority            </span></span>
+<span id="cb17-9"><a href="#cb17-9" aria-hidden="true" tabindex="-1"></a><span class="do">##    &lt;chr&gt;                </span></span>
+<span id="cb17-10"><a href="#cb17-10" aria-hidden="true" tabindex="-1"></a><span class="do">##  1 Allerdale            </span></span>
+<span id="cb17-11"><a href="#cb17-11" aria-hidden="true" tabindex="-1"></a><span class="do">##  2 Barrow-in-Furness    </span></span>
+<span id="cb17-12"><a href="#cb17-12" aria-hidden="true" tabindex="-1"></a><span class="do">##  3 Blackburn with Darwen</span></span>
+<span id="cb17-13"><a href="#cb17-13" aria-hidden="true" tabindex="-1"></a><span class="do">##  4 Blackpool            </span></span>
+<span id="cb17-14"><a href="#cb17-14" aria-hidden="true" tabindex="-1"></a><span class="do">##  5 Bolton               </span></span>
+<span id="cb17-15"><a href="#cb17-15" aria-hidden="true" tabindex="-1"></a><span class="do">##  6 Burnley              </span></span>
+<span id="cb17-16"><a href="#cb17-16" aria-hidden="true" tabindex="-1"></a><span class="do">##  7 Bury                 </span></span>
+<span id="cb17-17"><a href="#cb17-17" aria-hidden="true" tabindex="-1"></a><span class="do">##  8 Carlisle             </span></span>
+<span id="cb17-18"><a href="#cb17-18" aria-hidden="true" tabindex="-1"></a><span class="do">##  9 Cheshire East        </span></span>
+<span id="cb17-19"><a href="#cb17-19" aria-hidden="true" tabindex="-1"></a><span class="do">## 10 Cheshire Fire        </span></span>
+<span id="cb17-20"><a href="#cb17-20" aria-hidden="true" tabindex="-1"></a><span class="do">## # ℹ 36 more rows</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tips
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>When combining multiple functions within a process using pipes, it is good practice to start the code with the data and pipe that into the functions, rather than including it in the function itself.</p>
+</div>
+</div>
+<p>The pipe can also be combined with the <code>filter</code> function to <code>count</code> the number of observations that lie within a subgroup:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Take the csp_2020 object</span></span>
+<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return just rows where region is equal to NW, and then</span></span>
+<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(region <span class="sc">==</span> <span class="st">"NW"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Count the number of rows</span></span>
+<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">count</span>()</span>
+<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 1 × 1</span></span>
+<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a><span class="do">##       n</span></span>
+<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a><span class="do">##   &lt;int&gt;</span></span>
+<span id="cb18-10"><a href="#cb18-10" aria-hidden="true" tabindex="-1"></a><span class="do">## 1    46</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="creating-new-variables" class="level3" data-number="3.2.4">
+<h3 data-number="3.2.4" class="anchored" data-anchor-id="creating-new-variables"><span class="header-section-number">3.2.4</span> Creating new variables</h3>
+<p>The function <code>mutate</code> from tidyverse’s <code>dplyr</code> package allows us to add new variables to a dataset, either by manually specifying them or by creating them from existing variables. We can add multiple variables within the same function, separating each with a comma <code>,</code>.</p>
+<p>For example, we can create a new variables with the squared settlement funding assessment (<code>sfa_2020</code>), and another that recodes the council tax variable (<code>ct_total_2020</code>) into a categorical variable with three levels (low: below £5 million, medium: between £5 million and £15 million, and high: above £15 million):</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a new object, csp_2020_new, starting with the object csp_2020</span></span>
+<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>csp_2020_new <span class="ot">&lt;-</span> csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add a new variable, sfa_2020_sq, by squaring the current sfa_2020 variable</span></span>
+<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">sfa_2020_sq =</span> sfa_2020 <span class="sc">^</span> <span class="dv">2</span>,</span>
+<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a>         <span class="co"># Create ct_2020-cat by cutting the ct_total_2020 object</span></span>
+<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a>         <span class="at">ct_2020_cat =</span> <span class="fu">cut</span>(ct_total_2020, </span>
+<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Create categories by cutting at 0, 5 and 15</span></span>
+<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a>                           <span class="at">breaks =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">5</span>, <span class="dv">15</span>, <span class="cn">Inf</span>),</span>
+<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Add labels to these new groups</span></span>
+<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a>                           <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">"Low"</span>, <span class="st">"Medium"</span>, <span class="st">"High"</span>),</span>
+<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Include the lowest break point in each group</span></span>
+<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a>                           <span class="at">include_lowest =</span> <span class="cn">TRUE</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Helpful hint
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>The <code>c</code> function takes a list of values separated by commas and returns them as a <code>vector</code>. This is useful when a function argument requires multiple values (and we don’t want R to move onto the next argument, which is what a comma inside functions usually means).</p>
+</div>
+</div>
+<p>The <code>mutate</code> function is also useful for reclassifying variables when R did not correctly choose the variable type. In this example, the <code>region</code> variable is a grouping variable, but <code>str(csp_2020)</code> shows it is recognised by R as a <code>character</code>. Grouping variables in R are known as <code>factors</code>. To convert the <code>region</code> variable to a <code>factor</code>, we use the <code>factor</code> function inside <code>mutate</code>:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>csp_2020_new <span class="ot">&lt;-</span> csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add a new variable, sfa_2020_sq, by squaring the current sfa_2020 variable</span></span>
+<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">sfa_2020_sq =</span> sfa_2020 <span class="sc">^</span> <span class="dv">2</span>,</span>
+<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>         <span class="co"># Create ct_2020-cat by cutting the ct_total_2020 object</span></span>
+<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a>         <span class="at">ct_2020_cat =</span> <span class="fu">cut</span>(ct_total_2020, </span>
+<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Create categories by cutting at 0, 5 and 15</span></span>
+<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a>                           <span class="at">breaks =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">5</span>, <span class="dv">15</span>, <span class="cn">Inf</span>),</span>
+<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Add labels to these new groups</span></span>
+<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a>                           <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">"Low"</span>, <span class="st">"Medium"</span>, <span class="st">"High"</span>),</span>
+<span id="cb20-10"><a href="#cb20-10" aria-hidden="true" tabindex="-1"></a>                           <span class="co"># Include the lowest break point in each group</span></span>
+<span id="cb20-11"><a href="#cb20-11" aria-hidden="true" tabindex="-1"></a>                           <span class="at">include_lowest =</span> <span class="cn">TRUE</span>),</span>
+<span id="cb20-12"><a href="#cb20-12" aria-hidden="true" tabindex="-1"></a>         <span class="at">region_fct =</span> <span class="fu">factor</span>(region, </span>
+<span id="cb20-13"><a href="#cb20-13" aria-hidden="true" tabindex="-1"></a>                             <span class="co"># To order the variable, use the levels argument</span></span>
+<span id="cb20-14"><a href="#cb20-14" aria-hidden="true" tabindex="-1"></a>                             <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"L"</span>, <span class="st">"NW"</span>, <span class="st">"NE"</span>, <span class="st">"YH"</span>, <span class="st">"WM"</span>, </span>
+<span id="cb20-15"><a href="#cb20-15" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"EM"</span>, <span class="st">"EE"</span>, <span class="st">"SW"</span>, <span class="st">"SE"</span>)))</span>
+<span id="cb20-16"><a href="#cb20-16" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb20-17"><a href="#cb20-17" aria-hidden="true" tabindex="-1"></a><span class="co"># Check variables are correctly classified</span></span>
+<span id="cb20-18"><a href="#cb20-18" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(csp_2020_new)</span>
+<span id="cb20-19"><a href="#cb20-19" aria-hidden="true" tabindex="-1"></a><span class="do">## tibble [396 × 12] (S3: tbl_df/tbl/data.frame)</span></span>
+<span id="cb20-20"><a href="#cb20-20" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ ons_code        : chr [1:396] "E07000223" "E07000026" "E07000032" "E07000224" ...</span></span>
+<span id="cb20-21"><a href="#cb20-21" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ authority       : chr [1:396] "Adur" "Allerdale" "Amber Valley" "Arun" ...</span></span>
+<span id="cb20-22"><a href="#cb20-22" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ region          : chr [1:396] "SE" "NW" "EM" "SE" ...</span></span>
+<span id="cb20-23"><a href="#cb20-23" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ sfa_2020        : num [1:396] 1.77 3.85 3.23 3.67 4.08 ...</span></span>
+<span id="cb20-24"><a href="#cb20-24" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ under_index_2020: num [1:396] 0.0708 0.1465 0.1292 0.147 0.1557 ...</span></span>
+<span id="cb20-25"><a href="#cb20-25" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ ct_total_2020   : num [1:396] 6.53 5.4 6.85 11.61 6.42 ...</span></span>
+<span id="cb20-26"><a href="#cb20-26" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ nhb_2020        : num [1:396] 0.0881 0.6061 1.5786 2.2949 1.1547 ...</span></span>
+<span id="cb20-27"><a href="#cb20-27" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ nhb_return_2020 : num [1:396] 0 0 0 0 0 0 0 0 0 0 ...</span></span>
+<span id="cb20-28"><a href="#cb20-28" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ rsdg_2020       : num [1:396] 0 0.326 0 0 0 ...</span></span>
+<span id="cb20-29"><a href="#cb20-29" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ sfa_2020_sq     : num [1:396] 3.12 14.86 10.41 13.46 16.66 ...</span></span>
+<span id="cb20-30"><a href="#cb20-30" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ ct_2020_cat     : Factor w/ 3 levels "Low","Medium",..: 2 2 2 2 2 2 3 NA 2 3 ...</span></span>
+<span id="cb20-31"><a href="#cb20-31" aria-hidden="true" tabindex="-1"></a><span class="do">##  $ region_fct      : Factor w/ 9 levels "L","NW","NE",..: 9 2 6 9 6 9 8 9 7 1 ...</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Although there is no real ordering to the regions in England, attaching this order allows us to control how the are displayed in outputs. By default, character variables are displayed in alphabetical order. By adding the order to this variable, we will produce output where the reference region (London) will be displayed first, followed by regions from north to south.</p>
+</section>
+<section id="exercise-3" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-3">Exercise 3</h3>
+<ol type="1">
+<li><p>How many local authorities were included in the London region?</p></li>
+<li><p>Give three different ways that it would be possible to select all spend variables (sfa_2020, nhb_2020, etc.) from the CSP_2020 dataset.</p></li>
+<li><p>Create a new tibble, <code>em_2020</code>, that just includes local authorities from the East Midlands (EM) region.</p></li>
+</ol>
+<ul>
+<li>How many local authorities in the East Midlands had an SFA of between £5 and 10 million?</li>
+<li>Create a new variable with the total overall spend in 2020 for local authorities in the East Midlands.</li>
+</ul>
+
+
+</section>
+</section>
+
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+  <li><a href="#data-wrangling-and-summarising" id="toc-data-wrangling-and-summarising" class="nav-link active" data-scroll-target="#data-wrangling-and-summarising"><span class="header-section-number">4.1</span> Data wrangling and summarising</a>
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+  <li><a href="#combining-two-datasets" id="toc-combining-two-datasets" class="nav-link" data-scroll-target="#combining-two-datasets"><span class="header-section-number">4.1.1</span> Combining two datasets</a></li>
+  <li><a href="#joining-multiple-datasets" id="toc-joining-multiple-datasets" class="nav-link" data-scroll-target="#joining-multiple-datasets"><span class="header-section-number">4.1.2</span> Joining multiple datasets</a></li>
+  <li><a href="#transforming-data" id="toc-transforming-data" class="nav-link" data-scroll-target="#transforming-data"><span class="header-section-number">4.1.3</span> Transforming data</a></li>
+  <li><a href="#summary-tables" id="toc-summary-tables" class="nav-link" data-scroll-target="#summary-tables"><span class="header-section-number">4.1.4</span> Summary tables</a></li>
+  <li><a href="#exercise-4" id="toc-exercise-4" class="nav-link" data-scroll-target="#exercise-4">Exercise 4</a></li>
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+</div>
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+<section id="data-wrangling-and-summarising" class="level2" data-number="4.1">
+<h2 data-number="4.1" class="anchored" data-anchor-id="data-wrangling-and-summarising"><span class="header-section-number">4.1</span> Data wrangling and summarising</h2>
+<section id="combining-two-datasets" class="level3" data-number="4.1.1">
+<h3 data-number="4.1.1" class="anchored" data-anchor-id="combining-two-datasets"><span class="header-section-number">4.1.1</span> Combining two datasets</h3>
+<p>We may need to combine data from different files within R to perform an analysis. For example, in our case we have the core spending power for each year between 2015 and 2020. If our analysis required comparing this spending over the time period, we would need to combine these files together.</p>
+<p>Before the data can be combined, it must be loaded into R. We will begin combining data from 2015 and 2016, then extend this to the entire period.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return a list of files to copy from the working directory</span></span>
+<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">list.files</span>(<span class="at">path =</span> <span class="st">"data"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] "CSP_2015.csv"         "CSP_2016.csv"         "CSP_2017.csv"        
+[4] "CSP_2018.csv"         "CSP_2019.csv"         "CSP_2020.csv"        
+[7] "CSP_long_201520.csv"  "data_description.pdf"</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Load the 2015 data and attach as an object</span></span>
+<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>CSP_2015 <span class="ot">&lt;-</span> <span class="fu">read_csv</span>(<span class="st">"data/CSP_2015.csv"</span>)</span>
+<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Load the 2016 data and attach as an object</span></span>
+<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>CSP_2016 <span class="ot">&lt;-</span> <span class="fu">read_csv</span>(<span class="st">"data/CSP_2016.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Next, we will combine these datasets by joining them using key variable(s) which are shared between them. In this case, each local authority has a unique identifier code (<code>ons_code</code>) and naming variable (<code>authority</code>), they also should have the same <code>region</code> listed across both datasets.</p>
+<p>In Tidyverse, there is a family of ‘joining’ functions that combine two datasets at a time. The choice of function depends on which observations we wish to keep where the joining variables do not match between data. In this example, we expect all local authority values to be the same across years, so will use the <code>full_join</code> function.</p>
+<p>For more information about different joining options, check the helpfile via <code>?full_join</code>.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a new object by joining the two datasets</span></span>
+<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>csp_201516 <span class="ot">&lt;-</span> <span class="fu">full_join</span>(CSP_2015, CSP_2016, </span>
+<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>                        <span class="co"># List the key joining variables (in speech marks)</span></span>
+<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>                        <span class="at">by =</span> <span class="fu">c</span>(<span class="st">"ons_code"</span>, <span class="st">"authority"</span>, <span class="st">"region"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="joining-multiple-datasets" class="level3" data-number="4.1.2">
+<h3 data-number="4.1.2" class="anchored" data-anchor-id="joining-multiple-datasets"><span class="header-section-number">4.1.2</span> Joining multiple datasets</h3>
+<p>R’s joining functions can only be applied to two datasets at a time. To combine all 6 core spending power datasets from 2015 to 2020 in this way would require a lot of repetitive coding (which we want to avoid where necessary).</p>
+<p>An alternative approach would be to automate this process by using <strong>functional programming</strong>, implemented using tidyverse’s <code>purrr</code> package.</p>
+<p>The first step of this process requires loading all csv files into R by repeatedly applying <code>read_csv</code>. This requires a list of file names from the working directory. The function <code>list.files</code> introduced earlier contains an optional argument, <code>pattern</code> which can be used to return files and folders that match a naming pattern. In this case, all csv files begin “CSP_20”, so to return this list of names from the <em>data</em> folder, we use the function:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>csp_201520 <span class="ot">&lt;-</span> <span class="fu">list.files</span>(<span class="at">path =</span> <span class="st">"data"</span>, <span class="at">pattern =</span> <span class="st">"CSP_20"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Next, we apply <code>read_csv</code> to each element of the list of file names. The function <code>map</code> allows us to do this and return a list of tibbles. As the data lies in a folder in the working directory, we must add this file path to the file names:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return a list of files in the data folder containing CSP_20</span></span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>csp_201520 <span class="ot">&lt;-</span> <span class="fu">list.files</span>(<span class="at">path =</span> <span class="st">"data"</span>, <span class="at">pattern =</span> <span class="st">"CSP_20"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add "data/" to each of these file names</span></span>
+<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">paste0</span>(<span class="st">"data/"</span>, .) <span class="sc">%&gt;%</span> </span>
+<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Apply read_csv to every element of the list (of file names)</span></span>
+<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">map</span>(read_csv)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Finally, we require a function that apply <code>full_join</code> iteratively to the list of tibbles and reduce it to a single tibble containing core spending powers for all years. The function that does this is <code>reduce</code>:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Return a list of files in the data folder containing CSP_20</span></span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>csp_201520 <span class="ot">&lt;-</span> <span class="fu">list.files</span>(<span class="at">path =</span> <span class="st">"data"</span>, <span class="at">pattern =</span> <span class="st">"CSP_20"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add "data/" to each of these file names</span></span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">paste0</span>(<span class="st">"data/"</span>, .) <span class="sc">%&gt;%</span> </span>
+<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Apply read_csv to every element of the list (of file names)</span></span>
+<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">map</span>(read_csv) <span class="sc">%&gt;%</span> </span>
+<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Reduce the list of tibbles to a single object by iteratively joining</span></span>
+<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">reduce</span>(full_join, <span class="at">by =</span> <span class="fu">c</span>(<span class="st">"ons_code"</span>, <span class="st">"authority"</span>, <span class="st">"region"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="transforming-data" class="level3" data-number="4.1.3">
+<h3 data-number="4.1.3" class="anchored" data-anchor-id="transforming-data"><span class="header-section-number">4.1.3</span> Transforming data</h3>
+<p>The dataset containing core spending power in England between 2015 and 2020 is currently in what is known as <strong>wide format</strong>. This means there is a variable per measure per year, making the object very wide.</p>
+<p>Some analyses and visualisations, particularly those used for temporal data, require a time variable in the dataset (for example, year). This requires the data to be in a different format, known as <strong>long format</strong>. Long format is where each row contains an observation per year (making the data much longer and narrower).</p>
+<p>To convert data between wide and long formats, we can use the tidyverse functions <code>pivot_longer</code> and <code>pivot_wider</code>.</p>
+<p>The first argument required by <code>pivot_longer</code> is the data we wish to transform. This is followed by the columns we wish to pivot (in this case, all variable other than the local authority codes, names, and regions). The next steps will depend on the format of data we wish to transform, format of the data we would like to generate, the values we need to include in the long dataset, and where this information will be extracted from.</p>
+<p>For worked examples and a detailed explanation of different approaches that can be used to pivot data, access the vignette for these function by entering <code>vignette("pivot")</code> into the R console.</p>
+<p>In the core spending power example, the new dataset will contain a row per local authority per year. A new <code>year</code> variable will be created using the suffix of the original variable names, and the prefix of the original names (e.g.&nbsp;<code>sfa</code>) will be retained for the new variable names.</p>
+<p>Using a combination of the helpfile (<code>?pivot_longer</code>) and vignette, the arguments required to convert this data are <code>names_to</code>, to specify the old variable names will be used in the new data, and <code>names_pattern</code> to define how the old variable names will be separated.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create an object csp_long by pivotting csp_201520</span></span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>csp_long <span class="ot">&lt;-</span> <span class="fu">pivot_longer</span>(csp_201520, </span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># Pivot columns sfa_2015 up to and including rsdg_2020</span></span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>                         <span class="at">cols =</span> sfa_2015<span class="sc">:</span>rsdg_2020,</span>
+<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># Separate the old variable names in two, </span></span>
+<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># keep the prefix as it was, and put the suffix </span></span>
+<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># into a new variable, year</span></span>
+<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>                         <span class="at">names_to =</span> <span class="fu">c</span>(<span class="st">".value"</span>, <span class="st">"year"</span>),</span>
+<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># The name prefix and suffix were separated by an _,</span></span>
+<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># the prefix can take different lengths, the suffix </span></span>
+<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a>                         <span class="co"># is always the final 4 characters</span></span>
+<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a>                         <span class="at">names_pattern =</span> <span class="st">"(.*)_(....)"</span>)</span>
+<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Check the new, long dataset's structure</span></span>
+<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(csp_long)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>tibble [2,376 × 10] (S3: tbl_df/tbl/data.frame)
+ $ ons_code   : chr [1:2376] "E07000223" "E07000223" "E07000223" "E07000223" ...
+ $ authority  : chr [1:2376] "Adur" "Adur" "Adur" "Adur" ...
+ $ region     : chr [1:2376] "SE" "SE" "SE" "SE" ...
+ $ year       : chr [1:2376] "2015" "2016" "2017" "2018" ...
+ $ sfa        : num [1:2376] 3.02 2.39 1.92 1.7 1.74 ...
+ $ under_index: num [1:2376] 0.0234 0.0234 0.0248 0.039 0.0567 ...
+ $ ct_total   : num [1:2376] 5.47 5.68 5.85 6.08 6.35 ...
+ $ nhb        : num [1:2376] 0.652 0.767 0.553 0.202 0.126 ...
+ $ nhb_return : num [1:2376] 0.00523 0.00374 0.00397 0 0 ...
+ $ rsdg       : num [1:2376] 0 0 0 0 0 ...</code></pre>
+</div>
+</div>
+<p>Notice that the new <code>year</code> variable is recognised as a character, not a numeric variable as we would like. This is because these values were taken from variable names, which R treats as characters. To fix this, we can use the <code>mutate</code> function to convert the new variable into a numeric variable.</p>
+<p>We may also wish to calculate the total core spending power for each local authority per year to compare this over time:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a new object based on the long data</span></span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>csp_long2 <span class="ot">&lt;-</span> <span class="fu">mutate</span>(csp_long, </span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>                    <span class="co"># Convert year to a numeric variable</span></span>
+<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>                    <span class="at">year =</span> <span class="fu">as.numeric</span>(year),</span>
+<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a>                    <span class="co"># Create a new total spend variable</span></span>
+<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a>                    <span class="at">total_spend =</span> sfa <span class="sc">+</span> under_index <span class="sc">+</span> ct_total <span class="sc">+</span> nhb <span class="sc">+</span> </span>
+<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a>                      nhb_return <span class="sc">+</span> rsdg)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>After manipulating and transforming the data into the format we need for analysis and visualisation, we can save this object to reload later. Tibbles and data frame objects can be saved as CSV files using the <code>write_csv</code> function. Remember to save the data with a different name than the raw data to avoid overwriting these files.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">write_csv</span>(csp_long2, <span class="at">file =</span> <span class="st">"data/CSP_long_201520.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="summary-tables" class="level3" data-number="4.1.4">
+<h3 data-number="4.1.4" class="anchored" data-anchor-id="summary-tables"><span class="header-section-number">4.1.4</span> Summary tables</h3>
+<p>Summary tables can be created using the <code>summarise</code> function. This returns tables in a tibble format, meaning they can easily be customised and exported as CSV files (using the <code>write_csv</code> function).</p>
+<p>The <code>summarise</code> function is set up similarly to the <code>mutate</code> function: summaries are listed and given variable names, separated by a comma. The difference between these functions is that <code>summarise</code> collapses the tibble into a single summary row, and the new variables must be created using a summary function.</p>
+<p>Common examples of summary functions include:</p>
+<ul>
+<li><code>mean</code></li>
+<li><code>median</code></li>
+<li><code>range</code> (gives the minimum and maximum values)</li>
+<li><code>min</code></li>
+<li><code>max</code></li>
+<li><code>IQR</code> (interquartile range, gives the range of the middle 50% of the sample)</li>
+<li><code>sd</code> (standard deviation, a measure of the spread when data are normally distributed)</li>
+<li><code>sum</code></li>
+<li><code>n</code> (counts the number of rows the summary is calculated from)</li>
+</ul>
+<p>For a full list of compatible summary functions, view the helpfile <code>?summarise</code>.</p>
+<p>If we wanted to summarise the total core spending power between 2015 and 2020 across all local authorities, we can apply <code>summarise</code> to the long format data from the previous section:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summarise</span>(csp_long2, </span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>          <span class="co"># Return sum of the total_spend variable</span></span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>          <span class="at">total_spend_all =</span> <span class="fu">sum</span>(total_spend),</span>
+<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>          <span class="co"># Return the mean total spend</span></span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>          <span class="at">mean_total_spend =</span> <span class="fu">mean</span>(total_spend),</span>
+<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>          <span class="co"># Return the median total spend</span></span>
+<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>          <span class="at">median_total_spend =</span> <span class="fu">median</span>(total_spend),</span>
+<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>          <span class="co"># Return the 10th percentile (the value that 10% of the sample lies below)</span></span>
+<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a>          <span class="at">quantile10_total_spend =</span> <span class="fu">quantile</span>(total_spend, <span class="fl">0.1</span>),</span>
+<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a>          <span class="co"># Count the number of rows that have been summarised</span></span>
+<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a>          <span class="at">total_obs =</span> <span class="fu">n</span>())</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code># A tibble: 1 × 5
+  total_spend_all mean_total_spend median_total_spend quantile10_total_spend
+            &lt;dbl&gt;            &lt;dbl&gt;              &lt;dbl&gt;                  &lt;dbl&gt;
+1         263484.             111.               17.6                   8.34
+# ℹ 1 more variable: total_obs &lt;int&gt;</code></pre>
+</div>
+</div>
+<p>The <code>summarise</code> function can be used to produce grouped summaries. This is done by first grouping the data with the <code>group_by</code> function. For example, if we wished to produce a summary table with a row per local authority, summarising the total spending between 2015 and 2020, we would use the following:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>csp_long2 <span class="sc">%&gt;%</span> </span>
+<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Group by the local authority's unique identifiers</span></span>
+<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">group_by</span>(ons_code, authority) <span class="sc">%&gt;%</span> </span>
+<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Total spend 2015 - 2020</span></span>
+<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">summarise</span>(<span class="at">total_spend_all =</span> <span class="fu">sum</span>(total_spend),</span>
+<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a>            <span class="co"># Mean spend 2015 - 2020  </span></span>
+<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a>            <span class="at">mean_total_spend =</span> <span class="fu">mean</span>(total_spend),</span>
+<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a>            <span class="co"># Median spend 2015 - 2020</span></span>
+<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a>            <span class="at">median_total_spend =</span> <span class="fu">median</span>(total_spend),</span>
+<span id="cb14-10"><a href="#cb14-10" aria-hidden="true" tabindex="-1"></a>            <span class="co"># 10th percentile of total spend</span></span>
+<span id="cb14-11"><a href="#cb14-11" aria-hidden="true" tabindex="-1"></a>            <span class="at">quantile10_total_spend =</span> <span class="fu">quantile</span>(total_spend, <span class="fl">0.1</span>),</span>
+<span id="cb14-12"><a href="#cb14-12" aria-hidden="true" tabindex="-1"></a>            <span class="co"># Number of rows summarised over</span></span>
+<span id="cb14-13"><a href="#cb14-13" aria-hidden="true" tabindex="-1"></a>            <span class="at">total_obs =</span> <span class="fu">n</span>()) <span class="sc">%&gt;%</span></span>
+<span id="cb14-14"><a href="#cb14-14" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Remove grouping structure</span></span>
+<span id="cb14-15"><a href="#cb14-15" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ungroup</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code># A tibble: 396 × 7
+   ons_code  authority       total_spend_all mean_total_spend median_total_spend
+   &lt;chr&gt;     &lt;chr&gt;                     &lt;dbl&gt;            &lt;dbl&gt;              &lt;dbl&gt;
+ 1 -         Greater London…          12416.           2069.              2022. 
+ 2 E06000001 Hartlepool                 485.             80.8               80.3
+ 3 E06000002 Middlesbrough              711.            119.               118. 
+ 4 E06000003 Redcar And Cle…            660.            110.               109. 
+ 5 E06000004 Stockton-on-Te…            832.            139.               138. 
+ 6 E06000005 Darlington                 474.             79.0               78.5
+ 7 E06000006 Halton                     598.             99.7               99.0
+ 8 E06000007 Warrington                 806.            134.               133. 
+ 9 E06000008 Blackburn with…            692.            115.               115. 
+10 E06000009 Blackpool                  750.            125.               124. 
+# ℹ 386 more rows
+# ℹ 2 more variables: quantile10_total_spend &lt;dbl&gt;, total_obs &lt;int&gt;</code></pre>
+</div>
+</div>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Whenever using <code>group_by</code>, make sure to <code>ungroup</code> the data before proceeding. The grouping structure can be large and slow analysis down, or may interact with other functions to produce unexpected analyses.</p>
+</div>
+</div>
+</section>
+<section id="exercise-4" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-4">Exercise 4</h3>
+<ol type="1">
+<li>Create a data frame with the minimum, maximum and median total spend per year for each region.</li>
+<li>Produce a frequency table containing the number and percentage of local authorities in each region.</li>
+<li>Convert the data object <code>csp_long2</code> back into wide format, with one row per local authority and one variable per total spend per year (<strong>HINT:</strong> start by selecting only the variables you need from the long data frame). Use the help file <code>?pivot_wider</code> and <code>vignette("pivot")</code> for more hints.</li>
+<li>Using your new wide data frame, calculate the difference in total spending for each local authority between 2015 and 2020. How many local authorities have had an overall reduction in spending since 2015?</li>
+</ol>
+
+
+</section>
+</section>
+
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+  <li><a href="#choosing-the-most-appropriate-visualisation" id="toc-choosing-the-most-appropriate-visualisation" class="nav-link" data-scroll-target="#choosing-the-most-appropriate-visualisation"><span class="header-section-number">5.1.1</span> Choosing the most appropriate visualisation</a></li>
+  <li><a href="#the-ggplot2-package" id="toc-the-ggplot2-package" class="nav-link" data-scroll-target="#the-ggplot2-package"><span class="header-section-number">5.1.2</span> The ggplot2 package</a></li>
+  <li><a href="#exercise-5" id="toc-exercise-5" class="nav-link" data-scroll-target="#exercise-5">Exercise 5</a></li>
+  <li><a href="#customising-visualisations" id="toc-customising-visualisations" class="nav-link" data-scroll-target="#customising-visualisations"><span class="header-section-number">5.1.3</span> Customising visualisations</a></li>
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+  <li><a href="#theme-functions" id="toc-theme-functions" class="nav-link" data-scroll-target="#theme-functions"><span class="header-section-number">5.1.6</span> Theme functions</a></li>
+  <li><a href="#facet-functions" id="toc-facet-functions" class="nav-link" data-scroll-target="#facet-functions"><span class="header-section-number">5.1.7</span> Facet functions</a></li>
+  <li><a href="#exercise-7" id="toc-exercise-7" class="nav-link" data-scroll-target="#exercise-7">Exercise 7</a></li>
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+
+
+<section id="data-visualisation-with-ggplot2" class="level2" data-number="5.1">
+<h2 data-number="5.1" class="anchored" data-anchor-id="data-visualisation-with-ggplot2"><span class="header-section-number">5.1</span> Data visualisation with ggplot2</h2>
+<p>Data visualisation is a powerful tool with multiple important uses. First, visualisations allow us to explore the data, identify potential outliers and errors, or check that the variables behave in the way we would expect them to if they had been recorded correctly. Visualisations can also be used as an analysis tool, allowing us to identify trends in the data or differences between groups. Finally, visualisations can help to convey messages to an audience in a clear, concise way that is often more powerful than presenting them using numbers or text. In some cases, data visualisations can show results so clearly that further analysis is arguably unnecessary.</p>
+<section id="choosing-the-most-appropriate-visualisation" class="level3" data-number="5.1.1">
+<h3 data-number="5.1.1" class="anchored" data-anchor-id="choosing-the-most-appropriate-visualisation"><span class="header-section-number">5.1.1</span> Choosing the most appropriate visualisation</h3>
+<p>The most appropriate choice of visualisation will depend on the type of variable(s) we wish to display, the number of variables and the message we are trying to disseminate. Common plots used to display combinations of different types of data are given in following table:</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="images/visualisation_table.png" class="img-fluid figure-img"></p>
+<figcaption>Table 6.1: Common visualisations by number and type of variables, with ggplot2 geom</figcaption>
+</figure>
+</div>
+<p>R is very flexible when it comes to visualising data and contains a wide variety of options to customise graphs. This section will focus on the Tidyverse package <code>ggplot2</code> and introduce some of the more commonly used graphical functions and parameters but is by no means comprehensive.</p>
+</section>
+<section id="the-ggplot2-package" class="level3" data-number="5.1.2">
+<h3 data-number="5.1.2" class="anchored" data-anchor-id="the-ggplot2-package"><span class="header-section-number">5.1.2</span> The ggplot2 package</h3>
+<p>The <code>ggplot2</code> package implements the ‘grammar of graphics’, a system that aims to describe all statistical graphics in terms of their components or layers. All graphics can be broken down into the same components: the data, a coordinate system (or plot area) and some visual markings of the data. More complex plots may have additional layers but all must contain these three.</p>
+<p>For example, in the <code>csp_2020</code> dataset, we may wish to explore the relationship between the settlement funding assessment (<code>sfa_2020</code>) and council tax total (<code>ct_total_2020</code>) spending for each local authority. To visualise the relationship between two continuous numeric variables, a <strong>scatterplot</strong> would be most appropriate.</p>
+<p>Within the <code>ggplot2</code> package, we first use the <code>ggplot</code> function to create a coordinate system (a blank plot space) that we can add layers and objects to. Within this function, we specify the data that we wish to display on the coordinate system:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="at">data =</span> csp_2020)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>To add information to this graph, we add a <strong>geom</strong> layer: a visual representation of the data. There are many different geom objects built into the ggplot2 package (begin typing <code>?geom</code> into the console to see a list). The <code>geom_point</code> function is used to create scatterplots.</p>
+<p>Each geom object must contain a mapping argument, coupled with the <code>aes</code> function which defines how the variables in the dataset are visualised. In this case, we use the <code>aes</code> function to specify the variables on the x and y axes but it can also be used to set the colour, size or symbol based on variable values.</p>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Although <code>ggplot2</code> is a tidyverse package, it uses a different method of piping to the other packages. Use the <code>+</code> symbol to add an extra layer when working in <code>ggplot</code>.</p>
+</div>
+</div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Generate the chart area and specify the data</span></span>
+<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="at">data =</span> csp_2020) <span class="sc">+</span> </span>
+<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add points, defined by sfa_2020 and ct_total_2020 </span></span>
+<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">mapping =</span> <span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Scatterplot SFA and CT total 2020-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>The resulting scatterplot shows a positive association between the SFA and council tax spending in English local authorities during 2020. We can identify an outlier in the top right corner of the graph. Before proceding, we want to ensure that this observation is an outlier and not an error to be removed from the data. We can use the <code>filter</code> function to return the name of the local authority that matches these values:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Using the data csp_2020</span></span>
+<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return just rows where sfa_2020 is over 1000, and then</span></span>
+<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(sfa_2020 <span class="sc">&gt;</span> <span class="dv">1000</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return the authority names</span></span>
+<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(authority)</span>
+<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="do">## # A tibble: 1 × 1</span></span>
+<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a><span class="do">##   authority               </span></span>
+<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a><span class="do">##   &lt;chr&gt;                   </span></span>
+<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="do">## 1 Greater London Authority</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>This outlier is the Greater London Authority which is a combination of local authorities that are already included in the dataset. Including this observation would introduce duplicates into the analysis, and so this observation should be removed to avoid invalid results. To remove the Greater London Authority observation, we can combine the <code>filter</code> and <code>ggplot</code> functions using pipes:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Take the csp_2020 data, and then</span></span>
+<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return all rows where authority is not equal to Greater London Authority,</span></span>
+<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>  <span class="co"># and then</span></span>
+<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(authority <span class="sc">!=</span> <span class="st">"Greater London Authority"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Generate a plot</span></span>
+<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>( ) <span class="sc">+</span> </span>
+<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add visual markings based on the data</span></span>
+<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Scatter without London-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>Graphs appear in the plot window in RStudio and can be opened in a new window using the <img src="images/zoom_shortcut.png" class="img-fluid" alt="zoom icon"> icon. Graphs in this window can also be copied and pasted into other documents using the <img src="images/export_shortcut.png" class="img-fluid" alt="export icon"> icon and selecting <em>Copy to clipboard</em>.</p>
+<p>New graphs will replace existing ones in this window but all graphs created in the current session of R can be explored using the <img src="images/arrow_shortcut.png" class="img-fluid" alt="arrows icon"> icons.</p>
+<p>Graphs can be stored as objects using the <code>&lt;-</code> symbol. These objects can then be saved as picture or PDF files using the <code>ggsave</code> function:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a new object, beginning from csp_2020, and then</span></span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>sfa_ct_plot <span class="ot">&lt;-</span> csp_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Return all rows where authority name is not GLA, and then</span></span>
+<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(authority <span class="sc">!=</span> <span class="st">"Greater London Authority"</span>) <span class="sc">%&gt;%</span></span>
+<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Create a ggplot area</span></span>
+<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>( ) <span class="sc">+</span> </span>
+<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add visual markings from the data</span></span>
+<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020))</span>
+<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Save the graph object as a png file</span></span>
+<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="fu">ggsave</span>(sfa_ct_plot, <span class="at">filename =</span> <span class="st">"sfa_ct_plot.png"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="exercise-5" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-5">Exercise 5</h3>
+<ol type="1">
+<li>Create a new data object containing the 2020 CSP data without the Greater London Authority observation. Name this data frame <code>csp_nolon_2020</code>.</li>
+<li>Using the <code>csp_nolon_2020</code> data, create a data visualisation to check the distribution (or shape) of the SFA variable.</li>
+<li>Based on the visualisation above, create a summary table for the SFA variable containing the minimum and maximum, and appropriate measures of the centre/average and spread.</li>
+</ol>
+</section>
+<section id="customising-visualisations" class="level3" data-number="5.1.3">
+<h3 data-number="5.1.3" class="anchored" data-anchor-id="customising-visualisations"><span class="header-section-number">5.1.3</span> Customising visualisations</h3>
+<p>Additional variables can be included into a visualisation within the mapping argument of a <code>geom</code> function. For example, we could explore the relationship between SFA and council tax across regions by colouring points based on the region:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="at">data =</span> csp_nolon_2020) <span class="sc">+</span> </span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Scatterplot, SFA and council tax by region-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>By default, R uses alphabetical ordering for character variables. To change this order, the variable must be converted into a <strong>factor</strong>. A factor is how R recognises categorical variables. For example, to order the region legend so that the London region appears first, followed by other regions from north to south, we would use the <code>mutate</code> function, combined with the <code>factor</code> function to create a new, ordered variable. The argument <code>levels</code> allows us to specify the order of categories in a factor:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>csp_nolon_2020_new <span class="ot">&lt;-</span> csp_nolon_2020 <span class="sc">%&gt;%</span> </span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">region_fct =</span> <span class="fu">factor</span>(region, </span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>                             <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"L"</span>, <span class="st">"NW"</span>, <span class="st">"NE"</span>, <span class="st">"YH"</span>, <span class="st">"WM"</span>, </span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"EM"</span>, <span class="st">"EE"</span>, <span class="st">"SW"</span>, <span class="st">"SE"</span>)))</span>
+<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="at">data =</span> csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Factor region-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>Arguments that can be adjusted within geoms include:</p>
+<ul>
+<li><code>colour</code>: change the colour (if point or line) or outline (if bar or histogram) of the markings</li>
+<li><code>size</code>: change the size of the markings (if point used)</li>
+<li><code>shape</code>: change the shape of markings (for points)</li>
+<li><code>fill</code>: Change the colour of bars in bar charts or histograms</li>
+<li><code>linewidth</code>: Change the line width</li>
+<li><code>linetype</code>: Choose the type of line (e.g.&nbsp;<code>dotted</code>)</li>
+<li><code>alpha</code>: Change the transparency of a visualisation</li>
+</ul>
+<div class="callout callout-style-default callout-warning callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Warning
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Although it may be tempting to add many variables to the same visualisation, be sure that you are not overcomplicating the graph and losing important messages. It is better to have multiple, clear but simpler visualisations, than fewer confusing ones.</p>
+</div>
+</div>
+<p>Aesthetic properties of the geom object may also be set manually, outside of the <code>aes</code> function, using the same argument but with a shared value rather than a variable. For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020), </span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>             <span class="co"># Adding the colour outside of the aes wrapper as it is not </span></span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>             <span class="co"># from the data</span></span>
+<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>             <span class="at">colour =</span> <span class="st">"blue"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Manually setting aesthetics-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+</section>
+<section id="exercise-6" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-6">Exercise 6</h3>
+<ol type="1">
+<li>What is the problem with the following code? Fix the code to change the shape of all the points.</li>
+</ol>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020) <span class="sc">+</span> </span>
+<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">shape =</span> <span class="st">"*"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<ol start="2" type="1">
+<li><p>Add a line of best fit to the scatterplot showing the relationship between SFA and council tax total (hint: use <code>?geom_smooth</code>).</p></li>
+<li><p>Add a line of best fit for each region (hint: make each line a different colour).</p></li>
+</ol>
+</section>
+<section id="scale-functions" class="level3" data-number="5.1.4">
+<h3 data-number="5.1.4" class="anchored" data-anchor-id="scale-functions"><span class="header-section-number">5.1.4</span> Scale functions</h3>
+<section id="customising-axes" class="level4" data-number="5.1.4.1">
+<h4 data-number="5.1.4.1" class="anchored" data-anchor-id="customising-axes"><span class="header-section-number">5.1.4.1</span> Customising axes</h4>
+<p>Scale functions allow us to customise aesthetics defined in geom objects such as colours and axes labels. They take the form <code>scale_'aesthetic to customise'_'scale of variable’</code>. For example, <code>scale_x_continuous</code> customises the x axis when the variable is continuous, and <code>scale_x_discrete</code> can be used where the variable is discrete or categorical. Arguments to customise the x or y axes include:</p>
+<ul>
+<li><code>name =</code> to change the axis title</li>
+<li><code>limits = c(...)</code> sets the axis limits</li>
+<li><code>breaks = c(...)</code> defines tick marks</li>
+<li><code>labels = c(...)</code> attaches labels to break values</li>
+<li><code>trans =</code> transforms the scale that the axis is shown on.</li>
+</ul>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Scatterplot with SFA on x, CT on y, and colour by region</span></span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct)) <span class="sc">+</span></span>
+<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add title to x axis</span></span>
+<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_continuous</span>(<span class="at">name =</span> <span class="st">"Settlement funding assessment (£ millions)"</span>, </span>
+<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a>                     <span class="co"># Set x axis limits from 0 to 600</span></span>
+<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">limits =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">600</span>), </span>
+<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a>                     <span class="co"># Set tick marks ever 200</span></span>
+<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a>                     <span class="at">breaks =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">200</span>, <span class="dv">400</span>, <span class="dv">600</span>)) <span class="sc">+</span></span>
+<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Add title to y axis</span></span>
+<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_y_continuous</span>(<span class="at">name =</span> <span class="st">"Council tax (£ millions)"</span>, </span>
+<span id="cb10-12"><a href="#cb10-12" aria-hidden="true" tabindex="-1"></a>                     <span class="co"># Show the y axis on a square root scale</span></span>
+<span id="cb10-13"><a href="#cb10-13" aria-hidden="true" tabindex="-1"></a>                     <span class="at">trans =</span> <span class="st">"sqrt"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/scale_x and scale_y-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>A common transformation that can be useful to explore the relationship between variables which have clusters of smaller values is the logarithm (or <code>log</code>) function. Applying a <code>log</code> function to a scale increases the difference between smaller values (stretching out these clusters), while reducing the difference between the smaller values and largest ones. Log functions can only be applied to positive, non-zero numbers. Where a sample may contain zeroes, the transformation <code>log1p</code> can be applied instead which adds 1 to each value before applying the log transformation (<span class="math inline">\(log(n + 1)\)</span>):</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct)) <span class="sc">+</span></span>
+<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_continuous</span>(<span class="at">name =</span> <span class="st">"SFA"</span>, <span class="at">limits =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">600</span>), </span>
+<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>                     <span class="at">breaks =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">200</span>, <span class="dv">400</span>, <span class="dv">600</span>),</span>
+<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>                     <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_y_continuous</span>(<span class="at">name =</span> <span class="st">"Council tax"</span>, </span>
+<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>                     <span class="at">trans =</span> <span class="st">"log1p"</span>) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/log1p transformation-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>We can now clearly see the strong positive association between SFA and council tax spending in local authorities with lower values of this without losing any information.</p>
+</section>
+<section id="customising-colour-scales" class="level4" data-number="5.1.4.2">
+<h4 data-number="5.1.4.2" class="anchored" data-anchor-id="customising-colour-scales"><span class="header-section-number">5.1.4.2</span> 6.3.2 Customising colour scales</h4>
+<p>There are a wide range of options for customising the colour aesthetics of geoms. These include pre-defined colour palettes, such as <code>scale_colour_viridis_c</code> for continuous variables, or <code>scale_colour_viridis_d</code> for discrete or categorical variables. Viridis colour palettes are designed to be colourblind friendly and print well in grey scale. There are also many R packages containing colour palettes for different scenarios.</p>
+<p>Colour palettes can be created manually for categorical variables using the <code>scale_colour_manual</code> function. Here, the argument <code>values</code> allows us to specify a colour per category.</p>
+<div class="callout callout-style-default callout-tip callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Style tip
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>R contains a list of 657 pre-programmed colours that can be used to create palettes (run <code>colours()</code> in the console for a full list).</p>
+<p>Hexadecimal codes can also be included instead in the form <code>#rrggbb</code> (where rr (red), gg (green), and bb (blue) are numbers between 00 and 99 giving the level of intensity of each colour).</p>
+</div>
+</div>
+<p>Where a colour palette will be used across multiple plots, defining this list of colours as a vector and then entering this into <code>scale_colour_manual</code> will reduce repetition:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>region_palette <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"aquamarine2"</span>, <span class="st">"blue"</span>, <span class="st">"chartreuse2"</span>, <span class="st">"coral"</span>, <span class="st">"orchid"</span>,</span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>                    <span class="st">"firebrick"</span>, <span class="st">"gold3"</span>, <span class="st">"violetred"</span>, <span class="st">"grey50"</span>)</span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct)) <span class="sc">+</span></span>
+<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_continuous</span>(<span class="at">name =</span> <span class="st">"SFA"</span>,  <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_y_continuous</span>(<span class="at">name =</span> <span class="st">"Council tax"</span>, <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_colour_manual</span>(<span class="at">name =</span> <span class="st">"Region"</span>, <span class="at">values =</span> region_palette)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/region colour palette-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>Palettes can also be created using gradients with the <code>scale_colour_gradient</code> function, that specifies a two colour gradient from low to high, <code>scale_colour_gradient2</code> that creates a diverging gradient using low, medium, and high colours, and <code>scale_colour_gradientn</code> that creates an n-colour gradient.</p>
+</section>
+</section>
+<section id="other-labelling-functions" class="level3" data-number="5.1.5">
+<h3 data-number="5.1.5" class="anchored" data-anchor-id="other-labelling-functions"><span class="header-section-number">5.1.5</span> Other labelling functions</h3>
+<p>Although axis and legend labels can be updated within scale functions, the <code>labs</code> function exist as an alternative. This function also allows us to add titles and subtitles to visualisations:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">labs</span>(<span class="at">x =</span> “x<span class="sc">-</span>axis name”, <span class="at">y =</span> “y<span class="sc">-</span>axis name”,</span>
+<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>    <span class="at">colour =</span> “Grouping variable name”, <span class="at">title =</span> “Main title”,</span>
+<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">subtitle =</span> “Subtitle”, <span class="at">caption =</span> “Footnote”)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>The <code>annotate</code> function allows us to add text and other objects to a ggplot object. For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">annotate</span>(“text”, <span class="at">x =</span> <span class="dv">50</span>, <span class="at">y =</span> <span class="dv">200</span>, <span class="at">label =</span> “Text label here”)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>Adds “Text label here” to a plot at the coordinates (50, 200) on a graph, and</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">annotate</span>(“rect”, <span class="at">xmin =</span> <span class="dv">0</span>, <span class="at">xmax =</span> <span class="dv">10</span>, <span class="at">ymin =</span> <span class="dv">20</span>, <span class="at">ymax =</span> <span class="dv">50</span>, <span class="at">alpha =</span> <span class="fl">0.2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>adds a rectangle to the graph.</p>
+</section>
+<section id="theme-functions" class="level3" data-number="5.1.6">
+<h3 data-number="5.1.6" class="anchored" data-anchor-id="theme-functions"><span class="header-section-number">5.1.6</span> Theme functions</h3>
+<p>The <code>theme</code> function modifies non-data components of the visualisation. For example, the legend position, label fonts, the graph background, and gridlines. There are many options that exist within the <code>theme</code> function (use <code>?theme</code> to list them all).</p>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Note
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Many of the elements that can be customised within the <code>theme</code> function require an <code>element</code> wrapper. This wrapper is determined by the type of object we are customising (e.g.&nbsp;<code>element_text</code> when customising text, <code>element_rect</code> when customising a background, <code>element_blank</code> to remove something). Check <code>?theme</code> for more information.</p>
+</div>
+</div>
+<p>One of the most common theme options is <code>legend.position</code> which can be used to move the legend to the top or bottom of the graph space (<code>legend.position = “top”</code> or <code>legend.position = “bottom”</code>) or remove the legend completely (<code>legend.position = “none”</code>).</p>
+<p><code>ggplot</code> also contains a number of pre-defined ‘complete themes’ which change all non-data elements of the plot to a programmed default. For example <code>theme_void</code> removes all gridlines and axes, <code>theme_light</code> changes the graph background white and the gridlines and axes light grey:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct)) <span class="sc">+</span></span>
+<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_continuous</span>(<span class="at">name =</span> <span class="st">"SFA"</span>,  <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_y_continuous</span>(<span class="at">name =</span> <span class="st">"Council tax"</span>, <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_colour_manual</span>(<span class="at">name =</span> <span class="st">"Region"</span>, <span class="at">values =</span> region_palette) <span class="sc">+</span> </span>
+<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_void</span>( )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/theme void-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>One benefit of using themes is that all visualisations will be consistent in terms of colour scheme, font size and gridlines. Although there are pre-built themes, we are able to create our own and save them as functions. These can then be used in place of R’s themes. For example:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a theme function</span></span>
+<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>theme_intro_course <span class="ot">&lt;-</span> <span class="cf">function</span>( ) {</span>
+<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Move the legend to the bottom </span></span>
+<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme</span>(<span class="at">legend.position =</span>  <span class="st">"bottom"</span>,</span>
+<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a>        <span class="co"># Make the axis labels font size 10</span></span>
+<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a>        <span class="at">axis.text =</span> <span class="fu">element_text</span>(<span class="at">size =</span> <span class="dv">10</span>),</span>
+<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a>        <span class="co"># Make the axis titles font size 15</span></span>
+<span id="cb17-8"><a href="#cb17-8" aria-hidden="true" tabindex="-1"></a>        <span class="at">axis.title =</span> <span class="fu">element_text</span>(<span class="at">size =</span> <span class="dv">15</span>),</span>
+<span id="cb17-9"><a href="#cb17-9" aria-hidden="true" tabindex="-1"></a>        <span class="co"># Make the graph title font size 20</span></span>
+<span id="cb17-10"><a href="#cb17-10" aria-hidden="true" tabindex="-1"></a>        <span class="at">title =</span> <span class="fu">element_text</span>(<span class="at">size =</span> <span class="dv">20</span>),</span>
+<span id="cb17-11"><a href="#cb17-11" aria-hidden="true" tabindex="-1"></a>        <span class="co"># Make the plot area white with a grey outline</span></span>
+<span id="cb17-12"><a href="#cb17-12" aria-hidden="true" tabindex="-1"></a>        <span class="at">panel.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"white"</span>, <span class="at">colour =</span> <span class="st">"grey50"</span>))</span>
+<span id="cb17-13"><a href="#cb17-13" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>The function <code>theme_intro_course</code> can be added to the end of any visualisation and will move the legend to the bottom of the graph, change the axis text to size 10, the axis titles to size 15, the plot title to size 20, and the graph background to white with a grey outline:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(csp_nolon_2020_new) <span class="sc">+</span> </span>
+<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa_2020, <span class="at">y =</span> ct_total_2020, <span class="at">colour =</span> region_fct)) <span class="sc">+</span></span>
+<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_continuous</span>(<span class="at">name =</span> <span class="st">"SFA"</span>,  <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_y_continuous</span>(<span class="at">name =</span> <span class="st">"Council tax"</span>, <span class="at">trans =</span> <span class="st">"log1p"</span>) <span class="sc">+</span></span>
+<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_colour_manual</span>(<span class="at">name =</span> <span class="st">"Region"</span>, <span class="at">values =</span> region_palette) <span class="sc">+</span> </span>
+<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_intro_course</span>( )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Add custom theme-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<p>Creating a custom theme is useful to ensure all visualisations are formatted consistently.</p>
+</section>
+<section id="facet-functions" class="level3" data-number="5.1.7">
+<h3 data-number="5.1.7" class="anchored" data-anchor-id="facet-functions"><span class="header-section-number">5.1.7</span> Facet functions</h3>
+<p>Faceting allows us to divide a plot into subplots based on some grouping variable within the data. This allows us to show multiple variables in the same visualisation without risking overloading the plot and losing the intended message.</p>
+<p>For example, if we wish to show the relationship between SFA, council tax total and regions over the entire time period, we may wish to create a scatterplot per year. Faceting allows us to do this in one piece of code rather than repeating it per year. Faceting will also ensure that plots are on the same scale and therefore easier to compare. The function <code>facet_wrap</code> creates these facetted plots:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Take the long formatted dataset</span></span>
+<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>csp_long2 <span class="sc">%&gt;%</span> </span>
+<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Remove the Greater London Authority row</span></span>
+<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(authority <span class="sc">!=</span> <span class="st">"Greater London Authority"</span>) <span class="sc">%&gt;%</span> </span>
+<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>( ) <span class="sc">+</span></span>
+<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Plot the SFA against CT total and colour by region</span></span>
+<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">x =</span> sfa, <span class="at">y =</span> ct_total, <span class="at">colour =</span> region)) <span class="sc">+</span></span>
+<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Use the region colour palette</span></span>
+<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_colour_manual</span>(<span class="at">name =</span> <span class="st">"Region"</span>, <span class="at">values =</span> region_palette) <span class="sc">+</span> </span>
+<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Change the axis titles</span></span>
+<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">"Settlement funding assessment (£ millions)"</span>, </span>
+<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">"Council tax total (£ millions)"</span>, <span class="at">colour =</span> <span class="st">"Region"</span>) <span class="sc">+</span></span>
+<span id="cb19-13"><a href="#cb19-13" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Separate data into a plot per region</span></span>
+<span id="cb19-14"><a href="#cb19-14" aria-hidden="true" tabindex="-1"></a>  <span class="fu">facet_wrap</span>(<span class="sc">~</span> year) <span class="sc">+</span></span>
+<span id="cb19-15"><a href="#cb19-15" aria-hidden="true" tabindex="-1"></a>  <span class="co"># Use the intro course theme</span></span>
+<span id="cb19-16"><a href="#cb19-16" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_intro_course</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session4_notes_files/figure-html/Facet by region-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+</section>
+<section id="exercise-7" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-7">Exercise 7</h3>
+<p>Use an appropriate data visualisation to show how the total spend in each local authority has changed over the years between 2015 and 2020. Choose a visualisation that shows these trends over time and allows us to compare them between regions.</p>
+
+
+</section>
+</section>
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+  <li><a href="#introduction-to-rmarkdown" id="toc-introduction-to-rmarkdown" class="nav-link active" data-scroll-target="#introduction-to-rmarkdown"><span class="header-section-number">6.1</span> Introduction to RMarkdown</a>
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+  <li><a href="#creating-an-rmarkdown-files" id="toc-creating-an-rmarkdown-files" class="nav-link" data-scroll-target="#creating-an-rmarkdown-files"><span class="header-section-number">6.1.1</span> Creating an RMarkdown files</a></li>
+  <li><a href="#rmarkdown-content" id="toc-rmarkdown-content" class="nav-link" data-scroll-target="#rmarkdown-content"><span class="header-section-number">6.1.2</span> Rmarkdown content</a></li>
+  <li><a href="#compiling-rmarkdown-documents" id="toc-compiling-rmarkdown-documents" class="nav-link" data-scroll-target="#compiling-rmarkdown-documents"><span class="header-section-number">6.1.3</span> Compiling RMarkdown documents</a></li>
+  <li><a href="#data-visualisation-in-rmarkdown" id="toc-data-visualisation-in-rmarkdown" class="nav-link" data-scroll-target="#data-visualisation-in-rmarkdown"><span class="header-section-number">6.1.4</span> Data visualisation in RMarkdown</a></li>
+  <li><a href="#exercise-8" id="toc-exercise-8" class="nav-link" data-scroll-target="#exercise-8">Exercise 8</a></li>
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+<h1 class="title"><span class="chapter-number">6</span>&nbsp; <span class="chapter-title">Reproducible research with RMarkdown</span></h1>
+</div>
+
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+
+<div class="quarto-title-meta">
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+    
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+
+<section id="introduction-to-rmarkdown" class="level2" data-number="6.1">
+<h2 data-number="6.1" class="anchored" data-anchor-id="introduction-to-rmarkdown"><span class="header-section-number">6.1</span> Introduction to RMarkdown</h2>
+<p>RMarkdown is a tool that is used to author high-quality documents, making it easy to communicate results efficiently. One of the main appeals of RMarkdown is that it is easy to integrate R code and output seamlessly into a document, encouraging openness and reproducibility in research.</p>
+<p>There are a number of ways we can use RMarkdown to enhance the research process, such as:</p>
+<ul>
+<li>Generating reports to show the latest findings in a project, combining research output with interpretations. Reports can be automated within RMarkdown, to ensure outputs show the latest data.</li>
+<li>Keeping track of projects as an alternative to a notebook. Documents can include R code and visualisations alongside thoughts and comments on findings so far.</li>
+<li>Creating a collaborative document that can be shared with colleagues. The inclusion of R code in documents provides an audit trail, making it easy to carry out quality assurance and resolve discrepancies in results.</li>
+</ul>
+<p>Before we begin working with RMarkdown in RStudio, we must first download and install the <code>rmarkdown</code> package as we would any other package:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"rmarkdown"</span>)</span>
+<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(rmarkdown)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<section id="creating-an-rmarkdown-files" class="level3" data-number="6.1.1">
+<h3 data-number="6.1.1" class="anchored" data-anchor-id="creating-an-rmarkdown-files"><span class="header-section-number">6.1.1</span> Creating an RMarkdown files</h3>
+<p>RMarkdown files (<code>.Rmd</code>) are created and saved separately to the script files we have been using up to now on the course. To create a new RMarkdown file, either use the drop-down menu, following the <em>File -&gt; New File -&gt; R Markdown…</em> options, or using the <img src="images/new_file_shortcut.png" class="img-fluid" alt="new file icon"> icon and selecting <em>R Markdown…</em>.</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="images/rmarkdown_new.png" class="img-fluid figure-img"></p>
+<figcaption>Rmarkdown new file</figcaption>
+</figure>
+</div>
+<p>When creating a new RMarkdown file, we are given the option to set the title, author and date of the new document. We are also given options to select the type of document, presentation, or Shiny app we would like to create. This does not give a comprehensive list of documents available within RMarkdown and can be changed later. We will discuss output document types in more detail later in the session.</p>
+<p>Clicking ‘OK’ on this window will produce an RMarkdown file (<code>.Rmd</code>) with some example code. If we do not want this, there is an option to ‘Create Empty Document’ on the bottom left of the window.</p>
+</section>
+<section id="rmarkdown-content" class="level3" data-number="6.1.2">
+<h3 data-number="6.1.2" class="anchored" data-anchor-id="rmarkdown-content"><span class="header-section-number">6.1.2</span> Rmarkdown content</h3>
+<p>RMarkdown files contain three main types of content:</p>
+<ul>
+<li>A YAML header (this sets the global options for the document)</li>
+<li>Text, or syntax (this includes headings and comments)</li>
+<li>Code chunks containing R code</li>
+</ul>
+<section id="the-yaml-header" class="level4" data-number="6.1.2.1">
+<h4 data-number="6.1.2.1" class="anchored" data-anchor-id="the-yaml-header"><span class="header-section-number">6.1.2.1</span> The YAML header</h4>
+<p>The first part of an RMarkdown script, surrounded by ‘<code>---</code>’ is known as the <strong>YAML header</strong>. This sets global options for the document that will be produced by the script. YAML headers can include the title, author and date of a document, the output document type, table of contents options, and can include code to edit the appearance of text and figures.</p>
+<p>For this course, we will just use the YAML to define the <code>title</code>, <code>author</code>, <code>date</code>, and <code>output</code> of our document:</p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode markdown code-with-copy"><code class="sourceCode markdown"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co">---</span></span>
+<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="an">title:</span><span class="co"> "Introduction to R with Tidyverse"</span></span>
+<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="an">author:</span><span class="co"> My name</span></span>
+<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="an">date:</span><span class="co"> 2024-07-15</span></span>
+<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="an">output:</span><span class="co"> html_document</span></span>
+<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="co">---</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>There are many output document types that can be produced using RMarkdown. Some of the most common include:</p>
+<ul>
+<li><code>html_document</code>:HTML document,<code>.html</code></li>
+<li><code>pdf_document</code>: PDF document,<code>.pdf</code>, created using a LaTeX template</li>
+<li><code>word_document</code>: Microsoft word document (<code>.docx</code>)</li>
+<li><code>odt_document</code>: OpenDocument text document (<code>.odt</code>), similar to Microsoft Word/Google Docs but compatible with free word processors)</li>
+<li><code>github_document</code>: Github document (<code>.md</code>, markdown files that are compatible with Github and are converted to HTML when viewed there)</li>
+<li><code>powerpoint_presentation</code>: Powerpoint presentation (<code>.pptx</code>)</li>
+</ul>
+<p>RMarkdown can also be combined with other R packages to create books (via <code>bookdown</code>), websites (via <code>blogdown</code>) and interactive dashboards (via <code>flexdashboard</code>).</p>
+</section>
+<section id="rmarkdown-syntax" class="level4" data-number="6.1.2.2">
+<h4 data-number="6.1.2.2" class="anchored" data-anchor-id="rmarkdown-syntax"><span class="header-section-number">6.1.2.2</span> RMarkdown syntax</h4>
+<p>RMarkdown text, or syntax, will generally make up the majority of a RMarkdown file. This can include headers and subheadings, equations, and any other text or comments in the document. Text is formatted using <strong>markdown syntax</strong>. A detailed list of syntax commands are given in the RMarkdown <a href="https://rstudio.github.io/cheatsheets/html/rmarkdown.html#write-with-markdown">cheatsheet</a>. Common syntax commands that may be used in an RMarkdown document include:</p>
+<ul>
+<li><code>*italic*</code></li>
+<li><code>**bold**</code></li>
+<li>Add <code>`code`</code> into text</li>
+<li><code># Header 1</code></li>
+<li><code>## Header 2</code></li>
+<li>…</li>
+<li><code>###### Header 6</code></li>
+<li><code>[This is a link](link url)</code></li>
+<li><code>![caption](image.png)</code></li>
+</ul>
+<pre><code>- Unordered list
+  - List with indent</code></pre>
+<pre><code>1. Ordered list
+  - With indent
+2. Second item</code></pre>
+<p><code>Equation: $r^2 = (x - a)^2 + (y - b)^2$</code></p>
+<p><em>RMarkdown equations are built using the same language as LaTeX. <a href="https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols">See here</a> for a list of mathematical symbols that can be used in these equations.</em></p>
+</section>
+<section id="code-chunks" class="level4" data-number="6.1.2.3">
+<h4 data-number="6.1.2.3" class="anchored" data-anchor-id="code-chunks"><span class="header-section-number">6.1.2.3</span> Code chunks</h4>
+<p>Code chunks allow us to embed R code and outputs into our documents. This is one of the main draw of RMarkdown as it removes the need to copy and paste or import results from R into another document.</p>
+<p>Code chunks are pieces of code that begin <code>```{r}</code> and end <code>```</code>. For example,</p>
+<div class="sourceCode" id="cb5"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>```{r}</span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a> 1 + 1</span>
+<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>``` </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>Code chunks can be created by manually typing these wrappers, by clicking the <img src="images/code_chunk_icon.png" class="img-fluid" alt="code chunk icon"> icon and selecting ‘R’, or using the keyboard shortcut <code>ctrl + alt + i</code> on Windows, and <code>Command + Option + i</code> on Mac.</p>
+<p>Code chunks can be given titles to make an RMarkdown script easier to navigate (these will appear under the script window where lists of subheadings appear in script files). These are added inside the opening of the code chunk: <code>```{r chunk title}</code>.</p>
+<p>There are a number of chunk options to customise which code/output to display in the document. These are included in the opening of a chunk, after the title, separated by commas <code>,</code>. Some of the most common, include:</p>
+<ul>
+<li><code>echo = TRUE/FALSE</code>: whether to display code in the output document</li>
+<li><code>eval = TRUE/FALSE</code>: whether to run the code in the chunk or not</li>
+<li><code>include = TRUE/FALSE</code>: whether to include anything from the chunk (code or output) in the document</li>
+<li><code>error/warning/message = TRUE/FALSE</code>: whether to display error/warning/other messages in the document</li>
+</ul>
+<p><strong>Top tip:</strong> It may be useful to add a setup code chunk at the beginning of an RMarkdown file that loads any packages and datasets that are required for the rest of the document. These can also include universal options for future code chunks to avoid repeating the code, using the <code>knitr::opts_chunk$set</code> function.</p>
+<p>For example:</p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>```{r setup, include = FALSE} </span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a># Set global options for code chunks </span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a># Do not show any R code or messages unless specified </span>
+<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>knitr::opts_chunk$set(echo = FALSE, message = FALSE) </span>
+<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a># Load in the tidyverse package</span>
+<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>library(tidyverse)</span>
+<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a>```</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</section>
+</section>
+<section id="compiling-rmarkdown-documents" class="level3" data-number="6.1.3">
+<h3 data-number="6.1.3" class="anchored" data-anchor-id="compiling-rmarkdown-documents"><span class="header-section-number">6.1.3</span> Compiling RMarkdown documents</h3>
+<p>Compiling RMarkdown actually requires multiple steps and programmes. Luckily for us, this process takes place in the background so we don’t need to be aware of these steps happening!</p>
+<p>Generating an output file from RMarkdown is know <strong>knitting</strong> a document. This process sends the <code>.Rmd</code> file to another R package <code>knitr</code> (which is installed alongside <code>rmarkdown</code>), which executes all the code chunks in the document and creates a markdown <code>.md</code> file including the code and output. This markdown file is then processed by another programme <strong>pandoc</strong> which converts markdown code into the finished document.</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="images/rmarkdown_pipe.png" class="img-fluid figure-img"></p>
+<figcaption>RMarkdown to document process</figcaption>
+</figure>
+</div>
+<p>To <strong>knit</strong> an RMarkdown file in RStudio is very simple. Either click the <img src="images/knit_icon.png" class="img-fluid" alt="knit icon"> icon above the RMarkdown script, or use the keyboard shortcut <code>ctrl + shift + k</code> on Windows or <code>Command + shift + k</code> on Mac. This initiates the process above and will return an output document (if there are no errors!) in the requested format to the working directory.</p>
+</section>
+<section id="data-visualisation-in-rmarkdown" class="level3" data-number="6.1.4">
+<h3 data-number="6.1.4" class="anchored" data-anchor-id="data-visualisation-in-rmarkdown"><span class="header-section-number">6.1.4</span> Data visualisation in RMarkdown</h3>
+<p>Output such as graphs and tables can be embedded in code chunks, the code used to create them will be the same as it would be in any other R script.</p>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Note
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>Often, when providing output in RMarkdown, we often do not want to show the code that was used to create this. Make sure to add <code>echo = FALSE</code> to the opening of the code chunk.</p>
+</div>
+</div>
+<section id="graphs-in-rmarkdown" class="level4" data-number="6.1.4.1">
+<h4 data-number="6.1.4.1" class="anchored" data-anchor-id="graphs-in-rmarkdown"><span class="header-section-number">6.1.4.1</span> Graphs in RMarkdown</h4>
+<p><code>ggplot</code> can be used to create graphs that are embedded within code chunks and included in an output document. For example, we could use the data from previous sections to show the relationship between Settlement Funding Assessment (SFA) and council tax total in English local authorities in 2020, colour code by regions in a scatterplot:</p>
+<div class="sourceCode" id="cb7"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>```{r scatterplot sfa_2020 and ct_total_2020 by region, message = FALSE}</span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a># Load and tidy the 2020 data</span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>read_csv("data/CSP_2020.csv") %&gt;% </span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>  # Remove the Greater London Authority row</span>
+<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>  filter(authority != "Greater London Authority") %&gt;% </span>
+<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>  # Convert region variable to factor</span>
+<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>  mutate(region_fct = factor(region, </span>
+<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>                             levels = c("L", "NW", "NE", "YH", "WM",</span>
+<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>                                        "EM", "EE", "SW", "SE"))) %&gt;% </span>
+<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>  # Create a ggplot </span>
+<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a>  ggplot() +</span>
+<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>  # Scatterplot definition</span>
+<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>  geom_point(aes(x = ct_total_2020, y = sfa_2020, colour = region_fct)) +</span>
+<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>  # Add colour palette for region</span>
+<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>  scale_colour_manual(values = c("aquamarine2", "blue", "chartreuse2", </span>
+<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a>                                 "coral", "orchid", "firebrick", </span>
+<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a>                                 "gold3", "violetred", "grey50")) +</span>
+<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a>  # Change axis/label titles</span>
+<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a>  labs(x = "Council tax total (£millions)", </span>
+<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a>       y = "Settlement funding assessment (£milliongs)",</span>
+<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a>       colour = "Region") +</span>
+<span id="cb7-22"><a href="#cb7-22" aria-hidden="true" tabindex="-1"></a>  theme_light()</span>
+<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a>```</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell">
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="session5_notes_files/figure-html/scatterplot sfa_2020 and ct_total_2020 by region-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+</section>
+<section id="tables-in-rmarkdown" class="level4" data-number="6.1.4.2">
+<h4 data-number="6.1.4.2" class="anchored" data-anchor-id="tables-in-rmarkdown"><span class="header-section-number">6.1.4.2</span> Tables in RMarkdown</h4>
+<p>There are a number of ways to include tables within RMarkdown which can either be entered manually, or generated using an R package. The choice of approach to creating tables depends on the format and size of the data, the amount of flexibility you would like to customise the output, the type of output document you are creating, and personal preference of how it should look.</p>
+<p>In this course, we will look at how tables can be created using RMarkdown syntax (without the need for additional packages), and using the <code>kable</code> function within the <code>knitr</code> package.</p>
+<p><strong>Manually creating tables</strong></p>
+<p>Tables can be created in RMarkdown syntax, using the <code>|</code> symbol to separate columns, and dashes <code>-</code> to separate column headings from the body of the table. These are created outside of code chunks within the text. For example,</p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a> Header 1 | Header 2 | Header 3 |</span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>|----------|----------|----------|</span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>| This     | Is       | A        |</span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>| Very     | Simple   | Table    |</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>produces the following output:</p>
+<table class="table">
+<thead>
+<tr class="header">
+<th>Header 1</th>
+<th>Header 2</th>
+<th>Header 3</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td>This</td>
+<td>Is</td>
+<td>A</td>
+</tr>
+<tr class="even">
+<td>Very</td>
+<td>Simple</td>
+<td>Table</td>
+</tr>
+</tbody>
+</table>
+<p>Colons can be added to the header/body separator row of the table to control the justification of the text in each column. For example,</p>
+<div class="sourceCode" id="cb9"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>| Left | Right | Center  | Default   |</span>
+<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>|:-----|------:|:-------:|-----------|</span>
+<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>| This | Is    | Another | Simple    |</span>
+<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>| Table | But   | It is  | Justified |</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>produces the following output:</p>
+<table class="table">
+<thead>
+<tr class="header">
+<th style="text-align: left;">Left</th>
+<th style="text-align: right;">Right</th>
+<th style="text-align: center;">Center</th>
+<th>Default</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td style="text-align: left;">This</td>
+<td style="text-align: right;">Is</td>
+<td style="text-align: center;">Another</td>
+<td>Simple</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">Table</td>
+<td style="text-align: right;">But</td>
+<td style="text-align: center;">It is</td>
+<td>Justified</td>
+</tr>
+</tbody>
+</table>
+<p><strong>Creating tables from data frames</strong></p>
+<p>The <code>knitr</code> package that compiles RMarkdown files contains the <code>kable</code> function that can be used to create simple data tables. The <code>kable</code> function requires data to be stored as a matrix, data frame, or tibble object (although these can be easily created using the <code>matrix</code>, <code>data.frame</code> or <code>tibble</code> functions). Accessing the help file <code>?knitr::kable</code> gives a list of arguments that can be used to customise these tables.</p>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Note
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>As these tables are created using R functions, they must be generated within a code chunk.</p>
+</div>
+</div>
+<p>For example, we can create a simple data table using <code>kable</code> showing the first 6 rows of the <code>mtcars</code> dataset (a dataset pre-loaded into base R):</p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>```{r mtcars table, echo = FALSE} </span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>knitr::kable(head(mtcars))</span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>``` </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>which produces the following output:</p>
+<div class="cell">
+<div class="cell-output-display">
+<table class="table table-sm table-striped small">
+<colgroup>
+<col style="width: 26%">
+<col style="width: 7%">
+<col style="width: 5%">
+<col style="width: 7%">
+<col style="width: 5%">
+<col style="width: 7%">
+<col style="width: 8%">
+<col style="width: 8%">
+<col style="width: 4%">
+<col style="width: 4%">
+<col style="width: 7%">
+<col style="width: 7%">
+</colgroup>
+<thead>
+<tr class="header">
+<th style="text-align: left;"></th>
+<th style="text-align: right;">mpg</th>
+<th style="text-align: right;">cyl</th>
+<th style="text-align: right;">disp</th>
+<th style="text-align: right;">hp</th>
+<th style="text-align: right;">drat</th>
+<th style="text-align: right;">wt</th>
+<th style="text-align: right;">qsec</th>
+<th style="text-align: right;">vs</th>
+<th style="text-align: right;">am</th>
+<th style="text-align: right;">gear</th>
+<th style="text-align: right;">carb</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td style="text-align: left;">Mazda RX4</td>
+<td style="text-align: right;">21.0</td>
+<td style="text-align: right;">6</td>
+<td style="text-align: right;">160</td>
+<td style="text-align: right;">110</td>
+<td style="text-align: right;">3.90</td>
+<td style="text-align: right;">2.620</td>
+<td style="text-align: right;">16.46</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">4</td>
+<td style="text-align: right;">4</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">Mazda RX4 Wag</td>
+<td style="text-align: right;">21.0</td>
+<td style="text-align: right;">6</td>
+<td style="text-align: right;">160</td>
+<td style="text-align: right;">110</td>
+<td style="text-align: right;">3.90</td>
+<td style="text-align: right;">2.875</td>
+<td style="text-align: right;">17.02</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">4</td>
+<td style="text-align: right;">4</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">Datsun 710</td>
+<td style="text-align: right;">22.8</td>
+<td style="text-align: right;">4</td>
+<td style="text-align: right;">108</td>
+<td style="text-align: right;">93</td>
+<td style="text-align: right;">3.85</td>
+<td style="text-align: right;">2.320</td>
+<td style="text-align: right;">18.61</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">4</td>
+<td style="text-align: right;">1</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">Hornet 4 Drive</td>
+<td style="text-align: right;">21.4</td>
+<td style="text-align: right;">6</td>
+<td style="text-align: right;">258</td>
+<td style="text-align: right;">110</td>
+<td style="text-align: right;">3.08</td>
+<td style="text-align: right;">3.215</td>
+<td style="text-align: right;">19.44</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">3</td>
+<td style="text-align: right;">1</td>
+</tr>
+<tr class="odd">
+<td style="text-align: left;">Hornet Sportabout</td>
+<td style="text-align: right;">18.7</td>
+<td style="text-align: right;">8</td>
+<td style="text-align: right;">360</td>
+<td style="text-align: right;">175</td>
+<td style="text-align: right;">3.15</td>
+<td style="text-align: right;">3.440</td>
+<td style="text-align: right;">17.02</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">3</td>
+<td style="text-align: right;">2</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">Valiant</td>
+<td style="text-align: right;">18.1</td>
+<td style="text-align: right;">6</td>
+<td style="text-align: right;">225</td>
+<td style="text-align: right;">105</td>
+<td style="text-align: right;">2.76</td>
+<td style="text-align: right;">3.460</td>
+<td style="text-align: right;">20.22</td>
+<td style="text-align: right;">1</td>
+<td style="text-align: right;">0</td>
+<td style="text-align: right;">3</td>
+<td style="text-align: right;">1</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<p>Where data are not already saved as an object, we need to create them first before generating a table. For example, the table we created manually earlier can be recreated using the <code>kable</code> function, by first creating a data frame with the information, and then piping it through to the function:</p>
+<div class="sourceCode" id="cb11"><pre class="sourceCode default code-with-copy"><code class="sourceCode default"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>```{r kable table}</span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a># Create a data frame with the table information</span>
+<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a>data.frame(col1 = c("This", "Very"),</span>
+<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>           col2 = c("Is", "Simple"),</span>
+<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>           col3 = c("A", "Table")) %&gt;% </span>
+<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>  knitr::kable(., col.names = c("Header 1", "Header 2", "Header 3"))</span>
+<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>``` </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell">
+<div class="cell-output-display">
+<table class="table table-sm table-striped small">
+<thead>
+<tr class="header">
+<th style="text-align: left;">Header 1</th>
+<th style="text-align: left;">Header 2</th>
+<th style="text-align: left;">Header 3</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td style="text-align: left;">This</td>
+<td style="text-align: left;">Is</td>
+<td style="text-align: left;">A</td>
+</tr>
+<tr class="even">
+<td style="text-align: left;">Very</td>
+<td style="text-align: left;">Simple</td>
+<td style="text-align: left;">Table</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<p><strong>Other ways to create tables</strong></p>
+<p>Although the <code>kable</code> function and RMarkdown syntax tables do not require additional R packages to be installed, they are fairly simple and do not give many options to customise the tables. For a more flexible alternative, I would recommend looking at the <code>flextable</code> package, which gives a much wider range of customisible features. The <code>flextable</code> user manual can be accessed for free from <a href="https://ardata-fr.github.io/flextable-book/">this website</a>.</p>
+</section>
+</section>
+<section id="exercise-8" class="level3 unnumbered">
+<h3 class="unnumbered anchored" data-anchor-id="exercise-8">Exercise 8</h3>
+<p>Create an RMarkdown file that creates a html report describing the trends in core spending power in English local authorities between 2015 and 2020. Your report should include:</p>
+<ul>
+<li>A summary table of the total spending per year per region</li>
+<li>A suitable visualisation showing how the total annual spending has changed over this period, compared between regions</li>
+<li>A short interpretation of the table and visualisation</li>
+</ul>
+<div class="callout callout-style-default callout-note callout-titled">
+<div class="callout-header d-flex align-content-center">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<div class="callout-title-container flex-fill">
+Note
+</div>
+</div>
+<div class="callout-body-container callout-body">
+<p>You are not expected to be an expert in this data! Interpret these outputs as you would any other numeric variable measured over time.</p>
+</div>
+</div>
+
+
+</section>
+</section>
+
+</main> <!-- /main -->
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+      try { href = new URL(href).hash; } catch {}
+      const id = href.replace(/^#\/?/, "");
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+    // Strip column container classes
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+      el.classList.remove("page-full", "page-columns");
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+          stripColumnClz(child);
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+    stripColumnClz(note)
+    if (id === null || id.startsWith('sec-')) {
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+      } else {
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+      }
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+      if (url.startsWith('#')) {
+        hash = url;
+      } else {
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+      if (hash) {
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+        const note = window.document.getElementById(id);
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+            instance.setContent(html);
+          } finally {
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+            instance.show();
+          }
+        } else {
+          // See if we can fetch this
+          fetch(url.split('#')[0])
+          .then(res => res.text())
+          .then(html => {
+            const parser = new DOMParser();
+            const htmlDoc = parser.parseFromString(html, "text/html");
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+              instance.setContent(html);
+            } 
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+            instance.show();
+          });
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+        // See if we can fetch a full url (with no hash to target)
+        // This is a special case and we should probably do some content thinning / targeting
+        fetch(url)
+        .then(res => res.text())
+        .then(html => {
+          const parser = new DOMParser();
+          const htmlDoc = parser.parseFromString(html, "text/html");
+          const note = htmlDoc.querySelector('main.content');
+          if (note !== null) {
+            // This should only happen for chapter cross references
+            // (since there is no id in the URL)
+            // remove the first header
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+              note.children[0].remove();
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+            const html = processXRef(null, note);
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+        const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
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+        let height = null;
+        let parent = null;
+        if (lineIds.length > 0) {
+            //compute the position of the single el (top and bottom and make a div)
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+            top = el.offsetTop;
+            height = el.offsetHeight;
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+          }
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+            // cook up a div (if necessary) and position it 
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+            if (div === null) {
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+              div.setAttribute("id", "code-annotation-line-highlight");
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+      throttle(() => {
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+    function throttle(fn, ms) {
+    let throttle = false;
+    let timer;
+      return (...args) => {
+        if(!throttle) { // first call gets through
+            fn.apply(this, args);
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+            if(timer) clearTimeout(timer); // cancel #2
+            timer = setTimeout(() => {
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+              timer = throttle = false;
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+        }
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+    }
+      // Attach click handler to the DT
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+      for (const annoteDlNode of annoteDls) {
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+            selectCodeLines(clickedEl);
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+            clickedEl.classList.remove('code-annotation-active');
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+  const findCites = (el) => {
+    const parentEl = el.parentElement;
+    if (parentEl) {
+      const cites = parentEl.dataset.cites;
+      if (cites) {
+        return {
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+      }
+    } else {
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+  var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
+  for (var i=0; i<bibliorefs.length; i++) {
+    const ref = bibliorefs[i];
+    const citeInfo = findCites(ref);
+    if (citeInfo) {
+      tippyHover(citeInfo.el, function() {
+        var popup = window.document.createElement('div');
+        citeInfo.cites.forEach(function(cite) {
+          var citeDiv = window.document.createElement('div');
+          citeDiv.classList.add('hanging-indent');
+          citeDiv.classList.add('csl-entry');
+          var biblioDiv = window.document.getElementById('ref-' + cite);
+          if (biblioDiv) {
+            citeDiv.innerHTML = biblioDiv.innerHTML;
+          }
+          popup.appendChild(citeDiv);
+        });
+        return popup.innerHTML;
+      });
+    }
+  }
+});
+</script>
+<nav class="page-navigation">
+  <div class="nav-page nav-page-previous">
+      <a href="./session4_notes.html" class="pagination-link" aria-label="Session 4: Data visualisation with ggplot2">
+        <i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">5</span>&nbsp; <span class="chapter-title">Session 4: Data visualisation with ggplot2</span></span>
+      </a>          
+  </div>
+  <div class="nav-page nav-page-next">
+  </div>
+</nav>
+</div> <!-- /content -->
+
+
+
+
+</body></html>
\ No newline at end of file
diff --git a/_book/session5_notes_files/figure-html/scatterplot sfa_2020 and ct_total_2020 by region-1.png b/_book/session5_notes_files/figure-html/scatterplot sfa_2020 and ct_total_2020 by region-1.png
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diff --git a/_book/site_libs/bootstrap/bootstrap-icons.css b/_book/site_libs/bootstrap/bootstrap-icons.css
new file mode 100644
index 0000000..285e444
--- /dev/null
+++ b/_book/site_libs/bootstrap/bootstrap-icons.css
@@ -0,0 +1,2078 @@
+/*!
+ * Bootstrap Icons v1.11.1 (https://icons.getbootstrap.com/)
+ * Copyright 2019-2023 The Bootstrap Authors
+ * Licensed under MIT (https://github.com/twbs/icons/blob/main/LICENSE)
+ */
+
+@font-face {
+  font-display: block;
+  font-family: "bootstrap-icons";
+  src: 
+url("./bootstrap-icons.woff?2820a3852bdb9a5832199cc61cec4e65") format("woff");
+}
+
+.bi::before,
+[class^="bi-"]::before,
+[class*=" bi-"]::before {
+  display: inline-block;
+  font-family: bootstrap-icons !important;
+  font-style: normal;
+  font-weight: normal !important;
+  font-variant: normal;
+  text-transform: none;
+  line-height: 1;
+  vertical-align: -.125em;
+  -webkit-font-smoothing: antialiased;
+  -moz-osx-font-smoothing: grayscale;
+}
+
+.bi-123::before { content: "\f67f"; }
+.bi-alarm-fill::before { content: "\f101"; }
+.bi-alarm::before { content: "\f102"; }
+.bi-align-bottom::before { content: "\f103"; }
+.bi-align-center::before { content: "\f104"; }
+.bi-align-end::before { content: "\f105"; }
+.bi-align-middle::before { content: "\f106"; }
+.bi-align-start::before { content: "\f107"; }
+.bi-align-top::before { content: "\f108"; }
+.bi-alt::before { content: "\f109"; }
+.bi-app-indicator::before { content: "\f10a"; }
+.bi-app::before { content: "\f10b"; }
+.bi-archive-fill::before { content: "\f10c"; }
+.bi-archive::before { content: "\f10d"; }
+.bi-arrow-90deg-down::before { content: "\f10e"; }
+.bi-arrow-90deg-left::before { content: "\f10f"; }
+.bi-arrow-90deg-right::before { content: "\f110"; }
+.bi-arrow-90deg-up::before { content: "\f111"; }
+.bi-arrow-bar-down::before { content: "\f112"; }
+.bi-arrow-bar-left::before { content: "\f113"; }
+.bi-arrow-bar-right::before { content: "\f114"; }
+.bi-arrow-bar-up::before { content: "\f115"; }
+.bi-arrow-clockwise::before { content: "\f116"; }
+.bi-arrow-counterclockwise::before { content: "\f117"; }
+.bi-arrow-down-circle-fill::before { content: "\f118"; }
+.bi-arrow-down-circle::before { content: "\f119"; }
+.bi-arrow-down-left-circle-fill::before { content: "\f11a"; }
+.bi-arrow-down-left-circle::before { content: "\f11b"; }
+.bi-arrow-down-left-square-fill::before { content: "\f11c"; }
+.bi-arrow-down-left-square::before { content: "\f11d"; }
+.bi-arrow-down-left::before { content: "\f11e"; }
+.bi-arrow-down-right-circle-fill::before { content: "\f11f"; }
+.bi-arrow-down-right-circle::before { content: "\f120"; }
+.bi-arrow-down-right-square-fill::before { content: "\f121"; }
+.bi-arrow-down-right-square::before { content: "\f122"; }
+.bi-arrow-down-right::before { content: "\f123"; }
+.bi-arrow-down-short::before { content: "\f124"; }
+.bi-arrow-down-square-fill::before { content: "\f125"; }
+.bi-arrow-down-square::before { content: "\f126"; }
+.bi-arrow-down-up::before { content: "\f127"; }
+.bi-arrow-down::before { content: "\f128"; }
+.bi-arrow-left-circle-fill::before { content: "\f129"; }
+.bi-arrow-left-circle::before { content: "\f12a"; }
+.bi-arrow-left-right::before { content: "\f12b"; }
+.bi-arrow-left-short::before { content: "\f12c"; }
+.bi-arrow-left-square-fill::before { content: "\f12d"; }
+.bi-arrow-left-square::before { content: "\f12e"; }
+.bi-arrow-left::before { content: "\f12f"; }
+.bi-arrow-repeat::before { content: "\f130"; }
+.bi-arrow-return-left::before { content: "\f131"; }
+.bi-arrow-return-right::before { content: "\f132"; }
+.bi-arrow-right-circle-fill::before { content: "\f133"; }
+.bi-arrow-right-circle::before { content: "\f134"; }
+.bi-arrow-right-short::before { content: "\f135"; }
+.bi-arrow-right-square-fill::before { content: "\f136"; }
+.bi-arrow-right-square::before { content: "\f137"; }
+.bi-arrow-right::before { content: "\f138"; }
+.bi-arrow-up-circle-fill::before { content: "\f139"; }
+.bi-arrow-up-circle::before { content: "\f13a"; }
+.bi-arrow-up-left-circle-fill::before { content: "\f13b"; }
+.bi-arrow-up-left-circle::before { content: "\f13c"; }
+.bi-arrow-up-left-square-fill::before { content: "\f13d"; }
+.bi-arrow-up-left-square::before { content: "\f13e"; }
+.bi-arrow-up-left::before { content: "\f13f"; }
+.bi-arrow-up-right-circle-fill::before { content: "\f140"; }
+.bi-arrow-up-right-circle::before { content: "\f141"; }
+.bi-arrow-up-right-square-fill::before { content: "\f142"; }
+.bi-arrow-up-right-square::before { content: "\f143"; }
+.bi-arrow-up-right::before { content: "\f144"; }
+.bi-arrow-up-short::before { content: "\f145"; }
+.bi-arrow-up-square-fill::before { content: "\f146"; }
+.bi-arrow-up-square::before { content: "\f147"; }
+.bi-arrow-up::before { content: "\f148"; }
+.bi-arrows-angle-contract::before { content: "\f149"; }
+.bi-arrows-angle-expand::before { content: "\f14a"; }
+.bi-arrows-collapse::before { content: "\f14b"; }
+.bi-arrows-expand::before { content: "\f14c"; }
+.bi-arrows-fullscreen::before { content: "\f14d"; }
+.bi-arrows-move::before { content: "\f14e"; }
+.bi-aspect-ratio-fill::before { content: "\f14f"; }
+.bi-aspect-ratio::before { content: "\f150"; }
+.bi-asterisk::before { content: "\f151"; }
+.bi-at::before { content: "\f152"; }
+.bi-award-fill::before { content: "\f153"; }
+.bi-award::before { content: "\f154"; }
+.bi-back::before { content: "\f155"; }
+.bi-backspace-fill::before { content: "\f156"; }
+.bi-backspace-reverse-fill::before { content: "\f157"; }
+.bi-backspace-reverse::before { content: "\f158"; }
+.bi-backspace::before { content: "\f159"; }
+.bi-badge-3d-fill::before { content: "\f15a"; }
+.bi-badge-3d::before { content: "\f15b"; }
+.bi-badge-4k-fill::before { content: "\f15c"; }
+.bi-badge-4k::before { content: "\f15d"; }
+.bi-badge-8k-fill::before { content: "\f15e"; }
+.bi-badge-8k::before { content: "\f15f"; }
+.bi-badge-ad-fill::before { content: "\f160"; }
+.bi-badge-ad::before { content: "\f161"; }
+.bi-badge-ar-fill::before { content: "\f162"; }
+.bi-badge-ar::before { content: "\f163"; }
+.bi-badge-cc-fill::before { content: "\f164"; }
+.bi-badge-cc::before { content: "\f165"; }
+.bi-badge-hd-fill::before { content: "\f166"; }
+.bi-badge-hd::before { content: "\f167"; }
+.bi-badge-tm-fill::before { content: "\f168"; }
+.bi-badge-tm::before { content: "\f169"; }
+.bi-badge-vo-fill::before { content: "\f16a"; }
+.bi-badge-vo::before { content: "\f16b"; }
+.bi-badge-vr-fill::before { content: "\f16c"; }
+.bi-badge-vr::before { content: "\f16d"; }
+.bi-badge-wc-fill::before { content: "\f16e"; }
+.bi-badge-wc::before { content: "\f16f"; }
+.bi-bag-check-fill::before { content: "\f170"; }
+.bi-bag-check::before { content: "\f171"; }
+.bi-bag-dash-fill::before { content: "\f172"; }
+.bi-bag-dash::before { content: "\f173"; }
+.bi-bag-fill::before { content: "\f174"; }
+.bi-bag-plus-fill::before { content: "\f175"; }
+.bi-bag-plus::before { content: "\f176"; }
+.bi-bag-x-fill::before { content: "\f177"; }
+.bi-bag-x::before { content: "\f178"; }
+.bi-bag::before { content: "\f179"; }
+.bi-bar-chart-fill::before { content: "\f17a"; }
+.bi-bar-chart-line-fill::before { content: "\f17b"; }
+.bi-bar-chart-line::before { content: "\f17c"; }
+.bi-bar-chart-steps::before { content: "\f17d"; }
+.bi-bar-chart::before { content: "\f17e"; }
+.bi-basket-fill::before { content: "\f17f"; }
+.bi-basket::before { content: "\f180"; }
+.bi-basket2-fill::before { content: "\f181"; }
+.bi-basket2::before { content: "\f182"; }
+.bi-basket3-fill::before { content: "\f183"; }
+.bi-basket3::before { content: "\f184"; }
+.bi-battery-charging::before { content: "\f185"; }
+.bi-battery-full::before { content: "\f186"; }
+.bi-battery-half::before { content: "\f187"; }
+.bi-battery::before { content: "\f188"; }
+.bi-bell-fill::before { content: "\f189"; }
+.bi-bell::before { content: "\f18a"; }
+.bi-bezier::before { content: "\f18b"; }
+.bi-bezier2::before { content: "\f18c"; }
+.bi-bicycle::before { content: "\f18d"; }
+.bi-binoculars-fill::before { content: "\f18e"; }
+.bi-binoculars::before { content: "\f18f"; }
+.bi-blockquote-left::before { content: "\f190"; }
+.bi-blockquote-right::before { content: "\f191"; }
+.bi-book-fill::before { content: "\f192"; }
+.bi-book-half::before { content: "\f193"; }
+.bi-book::before { content: "\f194"; }
+.bi-bookmark-check-fill::before { content: "\f195"; }
+.bi-bookmark-check::before { content: "\f196"; }
+.bi-bookmark-dash-fill::before { content: "\f197"; }
+.bi-bookmark-dash::before { content: "\f198"; }
+.bi-bookmark-fill::before { content: "\f199"; }
+.bi-bookmark-heart-fill::before { content: "\f19a"; }
+.bi-bookmark-heart::before { content: "\f19b"; }
+.bi-bookmark-plus-fill::before { content: "\f19c"; }
+.bi-bookmark-plus::before { content: "\f19d"; }
+.bi-bookmark-star-fill::before { content: "\f19e"; }
+.bi-bookmark-star::before { content: "\f19f"; }
+.bi-bookmark-x-fill::before { content: "\f1a0"; }
+.bi-bookmark-x::before { content: "\f1a1"; }
+.bi-bookmark::before { content: "\f1a2"; }
+.bi-bookmarks-fill::before { content: "\f1a3"; }
+.bi-bookmarks::before { content: "\f1a4"; }
+.bi-bookshelf::before { content: "\f1a5"; }
+.bi-bootstrap-fill::before { content: "\f1a6"; }
+.bi-bootstrap-reboot::before { content: "\f1a7"; }
+.bi-bootstrap::before { content: "\f1a8"; }
+.bi-border-all::before { content: "\f1a9"; }
+.bi-border-bottom::before { content: "\f1aa"; }
+.bi-border-center::before { content: "\f1ab"; }
+.bi-border-inner::before { content: "\f1ac"; }
+.bi-border-left::before { content: "\f1ad"; }
+.bi-border-middle::before { content: "\f1ae"; }
+.bi-border-outer::before { content: "\f1af"; }
+.bi-border-right::before { content: "\f1b0"; }
+.bi-border-style::before { content: "\f1b1"; }
+.bi-border-top::before { content: "\f1b2"; }
+.bi-border-width::before { content: "\f1b3"; }
+.bi-border::before { content: "\f1b4"; }
+.bi-bounding-box-circles::before { content: "\f1b5"; }
+.bi-bounding-box::before { content: "\f1b6"; }
+.bi-box-arrow-down-left::before { content: "\f1b7"; }
+.bi-box-arrow-down-right::before { content: "\f1b8"; }
+.bi-box-arrow-down::before { content: "\f1b9"; }
+.bi-box-arrow-in-down-left::before { content: "\f1ba"; }
+.bi-box-arrow-in-down-right::before { content: "\f1bb"; }
+.bi-box-arrow-in-down::before { content: "\f1bc"; }
+.bi-box-arrow-in-left::before { content: "\f1bd"; }
+.bi-box-arrow-in-right::before { content: "\f1be"; }
+.bi-box-arrow-in-up-left::before { content: "\f1bf"; }
+.bi-box-arrow-in-up-right::before { content: "\f1c0"; }
+.bi-box-arrow-in-up::before { content: "\f1c1"; }
+.bi-box-arrow-left::before { content: "\f1c2"; }
+.bi-box-arrow-right::before { content: "\f1c3"; }
+.bi-box-arrow-up-left::before { content: "\f1c4"; }
+.bi-box-arrow-up-right::before { content: "\f1c5"; }
+.bi-box-arrow-up::before { content: "\f1c6"; }
+.bi-box-seam::before { content: "\f1c7"; }
+.bi-box::before { content: "\f1c8"; }
+.bi-braces::before { content: "\f1c9"; }
+.bi-bricks::before { content: "\f1ca"; }
+.bi-briefcase-fill::before { content: "\f1cb"; }
+.bi-briefcase::before { content: "\f1cc"; }
+.bi-brightness-alt-high-fill::before { content: "\f1cd"; }
+.bi-brightness-alt-high::before { content: "\f1ce"; }
+.bi-brightness-alt-low-fill::before { content: "\f1cf"; }
+.bi-brightness-alt-low::before { content: "\f1d0"; }
+.bi-brightness-high-fill::before { content: "\f1d1"; }
+.bi-brightness-high::before { content: "\f1d2"; }
+.bi-brightness-low-fill::before { content: "\f1d3"; }
+.bi-brightness-low::before { content: "\f1d4"; }
+.bi-broadcast-pin::before { content: "\f1d5"; }
+.bi-broadcast::before { content: "\f1d6"; }
+.bi-brush-fill::before { content: "\f1d7"; }
+.bi-brush::before { content: "\f1d8"; }
+.bi-bucket-fill::before { content: "\f1d9"; }
+.bi-bucket::before { content: "\f1da"; }
+.bi-bug-fill::before { content: "\f1db"; }
+.bi-bug::before { content: "\f1dc"; }
+.bi-building::before { content: "\f1dd"; }
+.bi-bullseye::before { content: "\f1de"; }
+.bi-calculator-fill::before { content: "\f1df"; }
+.bi-calculator::before { content: "\f1e0"; }
+.bi-calendar-check-fill::before { content: "\f1e1"; }
+.bi-calendar-check::before { content: "\f1e2"; }
+.bi-calendar-date-fill::before { content: "\f1e3"; }
+.bi-calendar-date::before { content: "\f1e4"; }
+.bi-calendar-day-fill::before { content: "\f1e5"; }
+.bi-calendar-day::before { content: "\f1e6"; }
+.bi-calendar-event-fill::before { content: "\f1e7"; }
+.bi-calendar-event::before { content: "\f1e8"; }
+.bi-calendar-fill::before { content: "\f1e9"; }
+.bi-calendar-minus-fill::before { content: "\f1ea"; }
+.bi-calendar-minus::before { content: "\f1eb"; }
+.bi-calendar-month-fill::before { content: "\f1ec"; }
+.bi-calendar-month::before { content: "\f1ed"; }
+.bi-calendar-plus-fill::before { content: "\f1ee"; }
+.bi-calendar-plus::before { content: "\f1ef"; }
+.bi-calendar-range-fill::before { content: "\f1f0"; }
+.bi-calendar-range::before { content: "\f1f1"; }
+.bi-calendar-week-fill::before { content: "\f1f2"; }
+.bi-calendar-week::before { content: "\f1f3"; }
+.bi-calendar-x-fill::before { content: "\f1f4"; }
+.bi-calendar-x::before { content: "\f1f5"; }
+.bi-calendar::before { content: "\f1f6"; }
+.bi-calendar2-check-fill::before { content: "\f1f7"; }
+.bi-calendar2-check::before { content: "\f1f8"; }
+.bi-calendar2-date-fill::before { content: "\f1f9"; }
+.bi-calendar2-date::before { content: "\f1fa"; }
+.bi-calendar2-day-fill::before { content: "\f1fb"; }
+.bi-calendar2-day::before { content: "\f1fc"; }
+.bi-calendar2-event-fill::before { content: "\f1fd"; }
+.bi-calendar2-event::before { content: "\f1fe"; }
+.bi-calendar2-fill::before { content: "\f1ff"; }
+.bi-calendar2-minus-fill::before { content: "\f200"; }
+.bi-calendar2-minus::before { content: "\f201"; }
+.bi-calendar2-month-fill::before { content: "\f202"; }
+.bi-calendar2-month::before { content: "\f203"; }
+.bi-calendar2-plus-fill::before { content: "\f204"; }
+.bi-calendar2-plus::before { content: "\f205"; }
+.bi-calendar2-range-fill::before { content: "\f206"; }
+.bi-calendar2-range::before { content: "\f207"; }
+.bi-calendar2-week-fill::before { content: "\f208"; }
+.bi-calendar2-week::before { content: "\f209"; }
+.bi-calendar2-x-fill::before { content: "\f20a"; }
+.bi-calendar2-x::before { content: "\f20b"; }
+.bi-calendar2::before { content: "\f20c"; }
+.bi-calendar3-event-fill::before { content: "\f20d"; }
+.bi-calendar3-event::before { content: "\f20e"; }
+.bi-calendar3-fill::before { content: "\f20f"; }
+.bi-calendar3-range-fill::before { content: "\f210"; }
+.bi-calendar3-range::before { content: "\f211"; }
+.bi-calendar3-week-fill::before { content: "\f212"; }
+.bi-calendar3-week::before { content: "\f213"; }
+.bi-calendar3::before { content: "\f214"; }
+.bi-calendar4-event::before { content: "\f215"; }
+.bi-calendar4-range::before { content: "\f216"; }
+.bi-calendar4-week::before { content: "\f217"; }
+.bi-calendar4::before { content: "\f218"; }
+.bi-camera-fill::before { content: "\f219"; }
+.bi-camera-reels-fill::before { content: "\f21a"; }
+.bi-camera-reels::before { content: "\f21b"; }
+.bi-camera-video-fill::before { content: "\f21c"; }
+.bi-camera-video-off-fill::before { content: "\f21d"; }
+.bi-camera-video-off::before { content: "\f21e"; }
+.bi-camera-video::before { content: "\f21f"; }
+.bi-camera::before { content: "\f220"; }
+.bi-camera2::before { content: "\f221"; }
+.bi-capslock-fill::before { content: "\f222"; }
+.bi-capslock::before { content: "\f223"; }
+.bi-card-checklist::before { content: "\f224"; }
+.bi-card-heading::before { content: "\f225"; }
+.bi-card-image::before { content: "\f226"; }
+.bi-card-list::before { content: "\f227"; }
+.bi-card-text::before { content: "\f228"; }
+.bi-caret-down-fill::before { content: "\f229"; }
+.bi-caret-down-square-fill::before { content: "\f22a"; }
+.bi-caret-down-square::before { content: "\f22b"; }
+.bi-caret-down::before { content: "\f22c"; }
+.bi-caret-left-fill::before { content: "\f22d"; }
+.bi-caret-left-square-fill::before { content: "\f22e"; }
+.bi-caret-left-square::before { content: "\f22f"; }
+.bi-caret-left::before { content: "\f230"; }
+.bi-caret-right-fill::before { content: "\f231"; }
+.bi-caret-right-square-fill::before { content: "\f232"; }
+.bi-caret-right-square::before { content: "\f233"; }
+.bi-caret-right::before { content: "\f234"; }
+.bi-caret-up-fill::before { content: "\f235"; }
+.bi-caret-up-square-fill::before { content: "\f236"; }
+.bi-caret-up-square::before { content: "\f237"; }
+.bi-caret-up::before { content: "\f238"; }
+.bi-cart-check-fill::before { content: "\f239"; }
+.bi-cart-check::before { content: "\f23a"; }
+.bi-cart-dash-fill::before { content: "\f23b"; }
+.bi-cart-dash::before { content: "\f23c"; }
+.bi-cart-fill::before { content: "\f23d"; }
+.bi-cart-plus-fill::before { content: "\f23e"; }
+.bi-cart-plus::before { content: "\f23f"; }
+.bi-cart-x-fill::before { content: "\f240"; }
+.bi-cart-x::before { content: "\f241"; }
+.bi-cart::before { content: "\f242"; }
+.bi-cart2::before { content: "\f243"; }
+.bi-cart3::before { content: "\f244"; }
+.bi-cart4::before { content: "\f245"; }
+.bi-cash-stack::before { content: "\f246"; }
+.bi-cash::before { content: "\f247"; }
+.bi-cast::before { content: "\f248"; }
+.bi-chat-dots-fill::before { content: "\f249"; }
+.bi-chat-dots::before { content: "\f24a"; }
+.bi-chat-fill::before { content: "\f24b"; }
+.bi-chat-left-dots-fill::before { content: "\f24c"; }
+.bi-chat-left-dots::before { content: "\f24d"; }
+.bi-chat-left-fill::before { content: "\f24e"; }
+.bi-chat-left-quote-fill::before { content: "\f24f"; }
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diff --git a/_book/site_libs/bootstrap/bootstrap.min.css b/_book/site_libs/bootstrap/bootstrap.min.css
new file mode 100644
index 0000000..08c2f54
--- /dev/null
+++ b/_book/site_libs/bootstrap/bootstrap.min.css
@@ -0,0 +1,12 @@
+/*!
+ * Bootstrap  v5.3.1 (https://getbootstrap.com/)
+ * Copyright 2011-2023 The Bootstrap Authors
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+ */@import"https://fonts.googleapis.com/css2?family=Source+Sans+Pro:wght@300;400;700&display=swap";:root,[data-bs-theme=light]{--bs-blue: #2780e3;--bs-indigo: #6610f2;--bs-purple: #613d7c;--bs-pink: #e83e8c;--bs-red: #ff0039;--bs-orange: #f0ad4e;--bs-yellow: #ff7518;--bs-green: #3fb618;--bs-teal: #20c997;--bs-cyan: #9954bb;--bs-black: #000;--bs-white: #fff;--bs-gray: #6c757d;--bs-gray-dark: #343a40;--bs-gray-100: #f8f9fa;--bs-gray-200: #e9ecef;--bs-gray-300: #dee2e6;--bs-gray-400: #ced4da;--bs-gray-500: #adb5bd;--bs-gray-600: #6c757d;--bs-gray-700: #495057;--bs-gray-800: #343a40;--bs-gray-900: #212529;--bs-default: #343a40;--bs-primary: #2780e3;--bs-secondary: #343a40;--bs-success: #3fb618;--bs-info: #9954bb;--bs-warning: #ff7518;--bs-danger: #ff0039;--bs-light: #f8f9fa;--bs-dark: #343a40;--bs-default-rgb: 52, 58, 64;--bs-primary-rgb: 39, 128, 227;--bs-secondary-rgb: 52, 58, 64;--bs-success-rgb: 63, 182, 24;--bs-info-rgb: 153, 84, 187;--bs-warning-rgb: 255, 117, 24;--bs-danger-rgb: 255, 0, 57;--bs-light-rgb: 248, 249, 250;--bs-dark-rgb: 52, 58, 64;--bs-primary-text-emphasis: #10335b;--bs-secondary-text-emphasis: #15171a;--bs-success-text-emphasis: #19490a;--bs-info-text-emphasis: #3d224b;--bs-warning-text-emphasis: #662f0a;--bs-danger-text-emphasis: #660017;--bs-light-text-emphasis: #495057;--bs-dark-text-emphasis: #495057;--bs-primary-bg-subtle: #d4e6f9;--bs-secondary-bg-subtle: #d6d8d9;--bs-success-bg-subtle: #d9f0d1;--bs-info-bg-subtle: #ebddf1;--bs-warning-bg-subtle: #ffe3d1;--bs-danger-bg-subtle: #ffccd7;--bs-light-bg-subtle: #fcfcfd;--bs-dark-bg-subtle: #ced4da;--bs-primary-border-subtle: #a9ccf4;--bs-secondary-border-subtle: #aeb0b3;--bs-success-border-subtle: #b2e2a3;--bs-info-border-subtle: #d6bbe4;--bs-warning-border-subtle: #ffc8a3;--bs-danger-border-subtle: #ff99b0;--bs-light-border-subtle: #e9ecef;--bs-dark-border-subtle: #adb5bd;--bs-white-rgb: 255, 255, 255;--bs-black-rgb: 0, 0, 0;--bs-font-sans-serif: "Source Sans Pro", -apple-system, 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.navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-md .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-md .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-md .navbar-nav-scroll{overflow:visible}.navbar-expand-md .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-md .navbar-toggler{display:none}.navbar-expand-md .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-md .offcanvas .offcanvas-header{display:none}.navbar-expand-md .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}@media(min-width: 992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}@media(min-width: 1200px){.navbar-expand-xl{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-xl .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-xl .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-xl .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-xl .navbar-nav-scroll{overflow:visible}.navbar-expand-xl .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-xl .navbar-toggler{display:none}.navbar-expand-xl .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xl .offcanvas .offcanvas-header{display:none}.navbar-expand-xl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}@media(min-width: 1400px){.navbar-expand-xxl{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-xxl .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-xxl .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-xxl .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-xxl .navbar-nav-scroll{overflow:visible}.navbar-expand-xxl .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-xxl .navbar-toggler{display:none}.navbar-expand-xxl .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-expand .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand .offcanvas .offcanvas-header{display:none}.navbar-expand .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}.navbar-dark,.navbar[data-bs-theme=dark]{--bs-navbar-color: #545555;--bs-navbar-hover-color: rgba(31, 78, 182, 0.8);--bs-navbar-disabled-color: rgba(84, 85, 85, 0.75);--bs-navbar-active-color: #1f4eb6;--bs-navbar-brand-color: #545555;--bs-navbar-brand-hover-color: #1f4eb6;--bs-navbar-toggler-border-color: rgba(84, 85, 85, 0);--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23545555' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}[data-bs-theme=dark] .navbar-toggler-icon{--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23545555' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}.card{--bs-card-spacer-y: 1rem;--bs-card-spacer-x: 1rem;--bs-card-title-spacer-y: 0.5rem;--bs-card-title-color: ;--bs-card-subtitle-color: ;--bs-card-border-width: 1px;--bs-card-border-color: rgba(0, 0, 0, 0.175);--bs-card-border-radius: 0.25rem;--bs-card-box-shadow: ;--bs-card-inner-border-radius: calc(0.25rem - 1px);--bs-card-cap-padding-y: 0.5rem;--bs-card-cap-padding-x: 1rem;--bs-card-cap-bg: rgba(52, 58, 64, 0.25);--bs-card-cap-color: ;--bs-card-height: ;--bs-card-color: ;--bs-card-bg: #fff;--bs-card-img-overlay-padding: 1rem;--bs-card-group-margin: 0.75rem;position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;min-width:0;height:var(--bs-card-height);color:var(--bs-body-color);word-wrap:break-word;background-color:var(--bs-card-bg);background-clip:border-box;border:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card>hr{margin-right:0;margin-left:0}.card>.list-group{border-top:inherit;border-bottom:inherit}.card>.list-group:first-child{border-top-width:0}.card>.list-group:last-child{border-bottom-width:0}.card>.card-header+.list-group,.card>.list-group+.card-footer{border-top:0}.card-body{flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-card-spacer-y) var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-0.5*var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header-tabs{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-bottom:calc(-1*var(--bs-card-cap-padding-y));margin-left:calc(-0.5*var(--bs-card-cap-padding-x));border-bottom:0}.card-header-tabs .nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-0.5*var(--bs-card-cap-padding-x));margin-left:calc(-0.5*var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media(min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}}.accordion{--bs-accordion-color: #343a40;--bs-accordion-bg: #fff;--bs-accordion-transition: color 0.15s ease-in-out, background-color 0.15s ease-in-out, border-color 0.15s ease-in-out, box-shadow 0.15s ease-in-out, border-radius 0.15s ease;--bs-accordion-border-color: #dee2e6;--bs-accordion-border-width: 1px;--bs-accordion-border-radius: 0.25rem;--bs-accordion-inner-border-radius: calc(0.25rem - 1px);--bs-accordion-btn-padding-x: 1.25rem;--bs-accordion-btn-padding-y: 1rem;--bs-accordion-btn-color: #343a40;--bs-accordion-btn-bg: #fff;--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23343a40'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-icon-width: 1.25rem;--bs-accordion-btn-icon-transform: rotate(-180deg);--bs-accordion-btn-icon-transition: transform 0.2s ease-in-out;--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%2310335b'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #93c0f1;--bs-accordion-btn-focus-box-shadow: 0 0 0 0.25rem rgba(39, 128, 227, 0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: #10335b;--bs-accordion-active-bg: #d4e6f9}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media(prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1*var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:not(:first-of-type){border-top:0}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%237db3ee'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%237db3ee'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(52, 58, 64, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(52, 58, 64, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #2761e3;--bs-pagination-bg: #fff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.25rem;--bs-pagination-hover-color: #1f4eb6;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #1f4eb6;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(39, 128, 227, 0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #2780e3;--bs-pagination-active-border-color: #2780e3;--bs-pagination-disabled-color: rgba(52, 58, 64, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.2em}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: 0.25rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 0 solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.25rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:.5rem}}.progress,.progress-stacked{--bs-progress-height: 0.5rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.25rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #2780e3;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #343a40;--bs-list-group-bg: #fff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.25rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(52, 58, 64, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #343a40;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(52, 58, 64, 0.75);--bs-list-group-disabled-bg: #fff;--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #2780e3;--bs-list-group-active-border-color: #2780e3;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(39, 128, 227, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(255, 255, 255, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.25rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(52, 58, 64, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color)}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #fff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 1px;position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform .3s ease-out;transform:translate(0, -50px)}@media(prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static 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0.5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid var(--bs-modal-header-border-color)}.modal-header .btn-close{padding:calc(var(--bs-modal-header-padding-y)*.5) calc(var(--bs-modal-header-padding-x)*.5);margin:calc(-0.5*var(--bs-modal-header-padding-y)) calc(-0.5*var(--bs-modal-header-padding-x)) calc(-0.5*var(--bs-modal-header-padding-y)) auto}.modal-title{margin-bottom:0;line-height:var(--bs-modal-title-line-height)}.modal-body{position:relative;flex:1 1 auto;-webkit-flex:1 1 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1rem)}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container:has(>.bslib-sidebar-layout:only-child){padding:0}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border=true]){border-left:none;border-right:none;border-bottom:none}.navbar+.container-fluid>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-sm>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-md>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-lg>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-xl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]),.navbar+.container-xxl>.tab-content>.tab-pane.active.html-fill-container>.bslib-sidebar-layout:only-child:not([data-bslib-sidebar-border-radius=true]){border-radius:0}.navbar+div>.bslib-sidebar-layout{border-top:var(--bslib-sidebar-border)}:root{--bslib-page-sidebar-title-bg: 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i=`scroll${e[0].toUpperCase()+e.slice(1)}`;this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(Mt),this._element.classList.add(Pt,Nt),this._element.style[e]="",N.trigger(this._element,St)}),this._element,!0),this._element.style[e]=`${this._element[i]}px`}hide(){if(this._isTransitioning||!this._isShown())return;if(N.trigger(this._element,Dt).defaultPrevented)return;const t=this._getDimension();this._element.style[t]=`${this._element.getBoundingClientRect()[t]}px`,d(this._element),this._element.classList.add(Mt),this._element.classList.remove(Pt,Nt);for(const t of this._triggerArray){const e=z.getElementFromSelector(t);e&&!this._isShown(e)&&this._addAriaAndCollapsedClass([t],!1)}this._isTransitioning=!0,this._element.style[t]="",this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(Mt),this._element.classList.add(Pt),N.trigger(this._element,$t)}),this._element,!0)}_isShown(t=this._element){return 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s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;i<t;i++)e[i]=arguments[i];return!e.some((function(t){return!(t&&"function"==typeof t.getBoundingClientRect)}))}function mi(t){void 0===t&&(t={});var e=t,i=e.defaultModifiers,n=void 0===i?[]:i,s=e.defaultOptions,o=void 0===s?fi:s;return function(t,e,i){void 0===i&&(i=o);var s,r,a={placement:"bottom",orderedModifiers:[],options:Object.assign({},fi,o),modifiersData:{},elements:{reference:t,popper:e},attributes:{},styles:{}},l=[],c=!1,h={state:a,setOptions:function(i){var s="function"==typeof 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vi=Object.freeze(Object.defineProperty({__proto__:null,afterMain:ae,afterRead:se,afterWrite:he,applyStyles:_e,arrow:je,auto:Kt,basePlacements:Qt,beforeMain:oe,beforeRead:ie,beforeWrite:le,bottom:Rt,clippingParents:Ut,computeStyles:Be,createPopper:bi,createPopperBase:gi,createPopperLite:_i,detectOverflow:ii,end:Yt,eventListeners:Re,flip:si,hide:ai,left:Vt,main:re,modifierPhases:de,offset:li,placements:ee,popper:Jt,popperGenerator:mi,popperOffsets:ci,preventOverflow:hi,read:ne,reference:Zt,right:qt,start:Xt,top:zt,variationPlacements:te,viewport:Gt,write:ce},Symbol.toStringTag,{value:"Module"})),yi="dropdown",wi=".bs.dropdown",Ai=".data-api",Ei="ArrowUp",Ti="ArrowDown",Ci=`hide${wi}`,Oi=`hidden${wi}`,xi=`show${wi}`,ki=`shown${wi}`,Li=`click${wi}${Ai}`,Si=`keydown${wi}${Ai}`,Di=`keyup${wi}${Ai}`,$i="show",Ii='[data-bs-toggle="dropdown"]:not(.disabled):not(:disabled)',Ni=`${Ii}.${$i}`,Pi=".dropdown-menu",Mi=p()?"top-end":"top-start",ji=p()?"top-start":"top-end",Fi=p()?"bottom-end":"bottom-start",Hi=p()?"bottom-start":"bottom-end",Wi=p()?"left-start":"right-start",Bi=p()?"right-start":"left-start",zi={autoClose:!0,boundary:"clippingParents",display:"dynamic",offset:[0,2],popperConfig:null,reference:"toggle"},Ri={autoClose:"(boolean|string)",boundary:"(string|element)",display:"string",offset:"(array|string|function)",popperConfig:"(null|object|function)",reference:"(string|element|object)"};class qi extends W{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=z.next(this._element,Pi)[0]||z.prev(this._element,Pi)[0]||z.findOne(Pi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return zi}static get DefaultType(){return Ri}static get NAME(){return yi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(l(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!N.trigger(this._element,xi,t).defaultPrevented){if(this._createPopper(),"ontouchstart"in document.documentElement&&!this._parent.closest(".navbar-nav"))for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._element.focus(),this._element.setAttribute("aria-expanded",!0),this._menu.classList.add($i),this._element.classList.add($i),N.trigger(this._element,ki,t)}}hide(){if(l(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!N.trigger(this._element,Ci,t).defaultPrevented){if("ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._popper&&this._popper.destroy(),this._menu.classList.remove($i),this._element.classList.remove($i),this._element.setAttribute("aria-expanded","false"),F.removeDataAttribute(this._menu,"popper"),N.trigger(this._element,Oi,t)}}_getConfig(t){if("object"==typeof(t=super._getConfig(t)).reference&&!o(t.reference)&&"function"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${yi.toUpperCase()}: Option "reference" provided type "object" without a required "getBoundingClientRect" method.`);return t}_createPopper(){if(void 0===vi)throw new TypeError("Bootstrap's dropdowns require Popper (https://popper.js.org)");let t=this._element;"parent"===this._config.reference?t=this._parent:o(this._config.reference)?t=r(this._config.reference):"object"==typeof this._config.reference&&(t=this._config.reference);const e=this._getPopperConfig();this._popper=bi(t,this._menu,e)}_isShown(){return this._menu.classList.contains($i)}_getPlacement(){const t=this._parent;if(t.classList.contains("dropend"))return Wi;if(t.classList.contains("dropstart"))return Bi;if(t.classList.contains("dropup-center"))return"top";if(t.classList.contains("dropdown-center"))return"bottom";const e="end"===getComputedStyle(this._menu).getPropertyValue("--bs-position").trim();return t.classList.contains("dropup")?e?ji:Mi:e?Hi:Fi}_detectNavbar(){return null!==this._element.closest(".navbar")}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)",this._menu).filter((t=>a(t)));i.length&&b(i,e,t===Ti,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=qi.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}static clearMenus(t){if(2===t.button||"keyup"===t.type&&"Tab"!==t.key)return;const e=z.find(Ni);for(const i of e){const e=qi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||"inside"===e._config.autoClose&&!s||"outside"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&("keyup"===t.type&&"Tab"===t.key||/input|select|option|textarea|form/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};"click"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"<div></div>"},Un={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Gn={entry:"(string|element|function|null)",selector:"(string|element)"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'<div class="tooltip" role="tooltip"><div class="tooltip-arrow"></div><div class="tooltip-inner"></div></div>',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return 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this._element.classList.contains(io)}_maybeScheduleHide(){this._config.autohide&&(this._hasMouseInteraction||this._hasKeyboardInteraction||(this._timeout=setTimeout((()=>{this.hide()}),this._config.delay)))}_onInteraction(t,e){switch(t.type){case"mouseover":case"mouseout":this._hasMouseInteraction=e;break;case"focusin":case"focusout":this._hasKeyboardInteraction=e}if(e)return void this._clearTimeout();const i=t.relatedTarget;this._element===i||this._element.contains(i)||this._maybeScheduleHide()}_setListeners(){N.on(this._element,Qs,(t=>this._onInteraction(t,!0))),N.on(this._element,Xs,(t=>this._onInteraction(t,!1))),N.on(this._element,Ys,(t=>this._onInteraction(t,!0))),N.on(this._element,Us,(t=>this._onInteraction(t,!1)))}_clearTimeout(){clearTimeout(this._timeout),this._timeout=null}static jQueryInterface(t){return this.each((function(){const e=ro.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}return 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+//# sourceMappingURL=bootstrap.bundle.min.js.map
\ No newline at end of file
diff --git a/_book/site_libs/clipboard/clipboard.min.js b/_book/site_libs/clipboard/clipboard.min.js
new file mode 100644
index 0000000..1103f81
--- /dev/null
+++ b/_book/site_libs/clipboard/clipboard.min.js
@@ -0,0 +1,7 @@
+/*!
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+ * https://clipboardjs.com/
+ *
+ * Licensed MIT © Zeno Rocha
+ */
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diff --git a/_book/site_libs/quarto-html/anchor.min.js b/_book/site_libs/quarto-html/anchor.min.js
new file mode 100644
index 0000000..5ac814d
--- /dev/null
+++ b/_book/site_libs/quarto-html/anchor.min.js
@@ -0,0 +1,9 @@
+// @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt Expat
+//
+// AnchorJS - v5.0.0 - 2023-01-18
+// https://www.bryanbraun.com/anchorjs/
+// Copyright (c) 2023 Bryan Braun; Licensed MIT
+//
+// @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt Expat
+!function(A,e){"use strict";"function"==typeof define&&define.amd?define([],e):"object"==typeof module&&module.exports?module.exports=e():(A.AnchorJS=e(),A.anchors=new A.AnchorJS)}(globalThis,function(){"use strict";return function(A){function u(A){A.icon=Object.prototype.hasOwnProperty.call(A,"icon")?A.icon:"",A.visible=Object.prototype.hasOwnProperty.call(A,"visible")?A.visible:"hover",A.placement=Object.prototype.hasOwnProperty.call(A,"placement")?A.placement:"right",A.ariaLabel=Object.prototype.hasOwnProperty.call(A,"ariaLabel")?A.ariaLabel:"Anchor",A.class=Object.prototype.hasOwnProperty.call(A,"class")?A.class:"",A.base=Object.prototype.hasOwnProperty.call(A,"base")?A.base:"",A.truncate=Object.prototype.hasOwnProperty.call(A,"truncate")?Math.floor(A.truncate):64,A.titleText=Object.prototype.hasOwnProperty.call(A,"titleText")?A.titleText:""}function d(A){var e;if("string"==typeof A||A instanceof String)e=[].slice.call(document.querySelectorAll(A));else{if(!(Array.isArray(A)||A instanceof NodeList))throw new TypeError("The selector provided to AnchorJS was invalid.");e=[].slice.call(A)}return e}this.options=A||{},this.elements=[],u(this.options),this.add=function(A){var e,t,o,i,n,s,a,r,l,c,h,p=[];if(u(this.options),0!==(e=d(A=A||"h2, h3, h4, h5, h6")).length){for(null===document.head.querySelector("style.anchorjs")&&((A=document.createElement("style")).className="anchorjs",A.appendChild(document.createTextNode("")),void 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+// @license-end
\ No newline at end of file
diff --git a/_book/site_libs/quarto-html/popper.min.js b/_book/site_libs/quarto-html/popper.min.js
new file mode 100644
index 0000000..e3726d7
--- /dev/null
+++ b/_book/site_libs/quarto-html/popper.min.js
@@ -0,0 +1,6 @@
+/**
+ * @popperjs/core v2.11.7 - MIT License
+ */
+
+!function(e,t){"object"==typeof exports&&"undefined"!=typeof module?t(exports):"function"==typeof define&&define.amd?define(["exports"],t):t((e="undefined"!=typeof globalThis?globalThis:e||self).Popper={})}(this,(function(e){"use strict";function t(e){if(null==e)return window;if("[object Window]"!==e.toString()){var t=e.ownerDocument;return t&&t.defaultView||window}return e}function n(e){return e instanceof t(e).Element||e instanceof Element}function r(e){return e instanceof t(e).HTMLElement||e instanceof HTMLElement}function o(e){return"undefined"!=typeof ShadowRoot&&(e instanceof t(e).ShadowRoot||e instanceof ShadowRoot)}var i=Math.max,a=Math.min,s=Math.round;function f(){var e=navigator.userAgentData;return null!=e&&e.brands&&Array.isArray(e.brands)?e.brands.map((function(e){return e.brand+"/"+e.version})).join(" "):navigator.userAgent}function c(){return!/^((?!chrome|android).)*safari/i.test(f())}function p(e,o,i){void 0===o&&(o=!1),void 0===i&&(i=!1);var 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t=e.state,n=e.name,r=t.rects.reference,o=t.rects.popper,i=t.modifiersData.preventOverflow,a=J(t,{elementContext:"reference"}),s=J(t,{altBoundary:!0}),f=ve(a,r),c=ve(s,o,i),p=ye(f),u=ye(c);t.modifiersData[n]={referenceClippingOffsets:f,popperEscapeOffsets:c,isReferenceHidden:p,hasPopperEscaped:u},t.attributes.popper=Object.assign({},t.attributes.popper,{"data-popper-reference-hidden":p,"data-popper-escaped":u})}},be=Z({defaultModifiers:[ee,te,oe,ie]}),xe=[ee,te,oe,ie,ae,le,he,me,ge],we=Z({defaultModifiers:xe});e.applyStyles=ie,e.arrow=me,e.computeStyles=oe,e.createPopper=we,e.createPopperLite=be,e.defaultModifiers=xe,e.detectOverflow=J,e.eventListeners=ee,e.flip=le,e.hide=ge,e.offset=ae,e.popperGenerator=Z,e.popperOffsets=te,e.preventOverflow=he,Object.defineProperty(e,"__esModule",{value:!0})}));
+
diff --git a/_book/site_libs/quarto-html/quarto-syntax-highlighting.css b/_book/site_libs/quarto-html/quarto-syntax-highlighting.css
new file mode 100644
index 0000000..d9fd98f
--- /dev/null
+++ b/_book/site_libs/quarto-html/quarto-syntax-highlighting.css
@@ -0,0 +1,203 @@
+/* quarto syntax highlight colors */
+:root {
+  --quarto-hl-ot-color: #003B4F;
+  --quarto-hl-at-color: #657422;
+  --quarto-hl-ss-color: #20794D;
+  --quarto-hl-an-color: #5E5E5E;
+  --quarto-hl-fu-color: #4758AB;
+  --quarto-hl-st-color: #20794D;
+  --quarto-hl-cf-color: #003B4F;
+  --quarto-hl-op-color: #5E5E5E;
+  --quarto-hl-er-color: #AD0000;
+  --quarto-hl-bn-color: #AD0000;
+  --quarto-hl-al-color: #AD0000;
+  --quarto-hl-va-color: #111111;
+  --quarto-hl-bu-color: inherit;
+  --quarto-hl-ex-color: inherit;
+  --quarto-hl-pp-color: #AD0000;
+  --quarto-hl-in-color: #5E5E5E;
+  --quarto-hl-vs-color: #20794D;
+  --quarto-hl-wa-color: #5E5E5E;
+  --quarto-hl-do-color: #5E5E5E;
+  --quarto-hl-im-color: #00769E;
+  --quarto-hl-ch-color: #20794D;
+  --quarto-hl-dt-color: #AD0000;
+  --quarto-hl-fl-color: #AD0000;
+  --quarto-hl-co-color: #5E5E5E;
+  --quarto-hl-cv-color: #5E5E5E;
+  --quarto-hl-cn-color: #8f5902;
+  --quarto-hl-sc-color: #5E5E5E;
+  --quarto-hl-dv-color: #AD0000;
+  --quarto-hl-kw-color: #003B4F;
+}
+
+/* other quarto variables */
+:root {
+  --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
+}
+
+pre > code.sourceCode > span {
+  color: #003B4F;
+}
+
+code span {
+  color: #003B4F;
+}
+
+code.sourceCode > span {
+  color: #003B4F;
+}
+
+div.sourceCode,
+div.sourceCode pre.sourceCode {
+  color: #003B4F;
+}
+
+code span.ot {
+  color: #003B4F;
+  font-style: inherit;
+}
+
+code span.at {
+  color: #657422;
+  font-style: inherit;
+}
+
+code span.ss {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.an {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.fu {
+  color: #4758AB;
+  font-style: inherit;
+}
+
+code span.st {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.cf {
+  color: #003B4F;
+  font-style: inherit;
+}
+
+code span.op {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.er {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.bn {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.al {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.va {
+  color: #111111;
+  font-style: inherit;
+}
+
+code span.bu {
+  font-style: inherit;
+}
+
+code span.ex {
+  font-style: inherit;
+}
+
+code span.pp {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.in {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.vs {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.wa {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.do {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.im {
+  color: #00769E;
+  font-style: inherit;
+}
+
+code span.ch {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.dt {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.fl {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.co {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.cv {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.cn {
+  color: #8f5902;
+  font-style: inherit;
+}
+
+code span.sc {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.dv {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.kw {
+  color: #003B4F;
+  font-style: inherit;
+}
+
+.prevent-inlining {
+  content: "</";
+}
+
+/*# sourceMappingURL=debc5d5d77c3f9108843748ff7464032.css.map */
diff --git a/_book/site_libs/quarto-html/quarto.js b/_book/site_libs/quarto-html/quarto.js
new file mode 100644
index 0000000..3ebd49c
--- /dev/null
+++ b/_book/site_libs/quarto-html/quarto.js
@@ -0,0 +1,899 @@
+const sectionChanged = new CustomEvent("quarto-sectionChanged", {
+  detail: {},
+  bubbles: true,
+  cancelable: false,
+  composed: false,
+});
+
+const layoutMarginEls = () => {
+  // Find any conflicting margin elements and add margins to the
+  // top to prevent overlap
+  const marginChildren = window.document.querySelectorAll(
+    ".column-margin.column-container > *, .margin-caption, .aside"
+  );
+
+  let lastBottom = 0;
+  for (const marginChild of marginChildren) {
+    if (marginChild.offsetParent !== null) {
+      // clear the top margin so we recompute it
+      marginChild.style.marginTop = null;
+      const top = marginChild.getBoundingClientRect().top + window.scrollY;
+      if (top < lastBottom) {
+        const marginChildStyle = window.getComputedStyle(marginChild);
+        const marginBottom = parseFloat(marginChildStyle["marginBottom"]);
+        const margin = lastBottom - top + marginBottom;
+        marginChild.style.marginTop = `${margin}px`;
+      }
+      const styles = window.getComputedStyle(marginChild);
+      const marginTop = parseFloat(styles["marginTop"]);
+      lastBottom = top + marginChild.getBoundingClientRect().height + marginTop;
+    }
+  }
+};
+
+window.document.addEventListener("DOMContentLoaded", function (_event) {
+  // Recompute the position of margin elements anytime the body size changes
+  if (window.ResizeObserver) {
+    const resizeObserver = new window.ResizeObserver(
+      throttle(() => {
+        layoutMarginEls();
+        if (
+          window.document.body.getBoundingClientRect().width < 990 &&
+          isReaderMode()
+        ) {
+          quartoToggleReader();
+        }
+      }, 50)
+    );
+    resizeObserver.observe(window.document.body);
+  }
+
+  const tocEl = window.document.querySelector('nav.toc-active[role="doc-toc"]');
+  const sidebarEl = window.document.getElementById("quarto-sidebar");
+  const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left");
+  const marginSidebarEl = window.document.getElementById(
+    "quarto-margin-sidebar"
+  );
+  // function to determine whether the element has a previous sibling that is active
+  const prevSiblingIsActiveLink = (el) => {
+    const sibling = el.previousElementSibling;
+    if (sibling && sibling.tagName === "A") {
+      return sibling.classList.contains("active");
+    } else {
+      return false;
+    }
+  };
+
+  // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior)
+  function fireSlideEnter(e) {
+    const event = window.document.createEvent("Event");
+    event.initEvent("slideenter", true, true);
+    window.document.dispatchEvent(event);
+  }
+  const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]');
+  tabs.forEach((tab) => {
+    tab.addEventListener("shown.bs.tab", fireSlideEnter);
+  });
+
+  // fire slideEnter for tabby tab activations (for htmlwidget resize behavior)
+  document.addEventListener("tabby", fireSlideEnter, false);
+
+  // Track scrolling and mark TOC links as active
+  // get table of contents and sidebar (bail if we don't have at least one)
+  const tocLinks = tocEl
+    ? [...tocEl.querySelectorAll("a[data-scroll-target]")]
+    : [];
+  const makeActive = (link) => tocLinks[link].classList.add("active");
+  const removeActive = (link) => tocLinks[link].classList.remove("active");
+  const removeAllActive = () =>
+    [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link));
+
+  // activate the anchor for a section associated with this TOC entry
+  tocLinks.forEach((link) => {
+    link.addEventListener("click", () => {
+      if (link.href.indexOf("#") !== -1) {
+        const anchor = link.href.split("#")[1];
+        const heading = window.document.querySelector(
+          `[data-anchor-id=${anchor}]`
+        );
+        if (heading) {
+          // Add the class
+          heading.classList.add("reveal-anchorjs-link");
+
+          // function to show the anchor
+          const handleMouseout = () => {
+            heading.classList.remove("reveal-anchorjs-link");
+            heading.removeEventListener("mouseout", handleMouseout);
+          };
+
+          // add a function to clear the anchor when the user mouses out of it
+          heading.addEventListener("mouseout", handleMouseout);
+        }
+      }
+    });
+  });
+
+  const sections = tocLinks.map((link) => {
+    const target = link.getAttribute("data-scroll-target");
+    if (target.startsWith("#")) {
+      return window.document.getElementById(decodeURI(`${target.slice(1)}`));
+    } else {
+      return window.document.querySelector(decodeURI(`${target}`));
+    }
+  });
+
+  const sectionMargin = 200;
+  let currentActive = 0;
+  // track whether we've initialized state the first time
+  let init = false;
+
+  const updateActiveLink = () => {
+    // The index from bottom to top (e.g. reversed list)
+    let sectionIndex = -1;
+    if (
+      window.innerHeight + window.pageYOffset >=
+      window.document.body.offsetHeight
+    ) {
+      sectionIndex = 0;
+    } else {
+      sectionIndex = [...sections].reverse().findIndex((section) => {
+        if (section) {
+          return window.pageYOffset >= section.offsetTop - sectionMargin;
+        } else {
+          return false;
+        }
+      });
+    }
+    if (sectionIndex > -1) {
+      const current = sections.length - sectionIndex - 1;
+      if (current !== currentActive) {
+        removeAllActive();
+        currentActive = current;
+        makeActive(current);
+        if (init) {
+          window.dispatchEvent(sectionChanged);
+        }
+        init = true;
+      }
+    }
+  };
+
+  const inHiddenRegion = (top, bottom, hiddenRegions) => {
+    for (const region of hiddenRegions) {
+      if (top <= region.bottom && bottom >= region.top) {
+        return true;
+      }
+    }
+    return false;
+  };
+
+  const categorySelector = "header.quarto-title-block .quarto-category";
+  const activateCategories = (href) => {
+    // Find any categories
+    // Surround them with a link pointing back to:
+    // #category=Authoring
+    try {
+      const categoryEls = window.document.querySelectorAll(categorySelector);
+      for (const categoryEl of categoryEls) {
+        const categoryText = categoryEl.textContent;
+        if (categoryText) {
+          const link = `${href}#category=${encodeURIComponent(categoryText)}`;
+          const linkEl = window.document.createElement("a");
+          linkEl.setAttribute("href", link);
+          for (const child of categoryEl.childNodes) {
+            linkEl.append(child);
+          }
+          categoryEl.appendChild(linkEl);
+        }
+      }
+    } catch {
+      // Ignore errors
+    }
+  };
+  function hasTitleCategories() {
+    return window.document.querySelector(categorySelector) !== null;
+  }
+
+  function offsetRelativeUrl(url) {
+    const offset = getMeta("quarto:offset");
+    return offset ? offset + url : url;
+  }
+
+  function offsetAbsoluteUrl(url) {
+    const offset = getMeta("quarto:offset");
+    const baseUrl = new URL(offset, window.location);
+
+    const projRelativeUrl = url.replace(baseUrl, "");
+    if (projRelativeUrl.startsWith("/")) {
+      return projRelativeUrl;
+    } else {
+      return "/" + projRelativeUrl;
+    }
+  }
+
+  // read a meta tag value
+  function getMeta(metaName) {
+    const metas = window.document.getElementsByTagName("meta");
+    for (let i = 0; i < metas.length; i++) {
+      if (metas[i].getAttribute("name") === metaName) {
+        return metas[i].getAttribute("content");
+      }
+    }
+    return "";
+  }
+
+  async function findAndActivateCategories() {
+    const currentPagePath = offsetAbsoluteUrl(window.location.href);
+    const response = await fetch(offsetRelativeUrl("listings.json"));
+    if (response.status == 200) {
+      return response.json().then(function (listingPaths) {
+        const listingHrefs = [];
+        for (const listingPath of listingPaths) {
+          const pathWithoutLeadingSlash = listingPath.listing.substring(1);
+          for (const item of listingPath.items) {
+            if (
+              item === currentPagePath ||
+              item === currentPagePath + "index.html"
+            ) {
+              // Resolve this path against the offset to be sure
+              // we already are using the correct path to the listing
+              // (this adjusts the listing urls to be rooted against
+              // whatever root the page is actually running against)
+              const relative = offsetRelativeUrl(pathWithoutLeadingSlash);
+              const baseUrl = window.location;
+              const resolvedPath = new URL(relative, baseUrl);
+              listingHrefs.push(resolvedPath.pathname);
+              break;
+            }
+          }
+        }
+
+        // Look up the tree for a nearby linting and use that if we find one
+        const nearestListing = findNearestParentListing(
+          offsetAbsoluteUrl(window.location.pathname),
+          listingHrefs
+        );
+        if (nearestListing) {
+          activateCategories(nearestListing);
+        } else {
+          // See if the referrer is a listing page for this item
+          const referredRelativePath = offsetAbsoluteUrl(document.referrer);
+          const referrerListing = listingHrefs.find((listingHref) => {
+            const isListingReferrer =
+              listingHref === referredRelativePath ||
+              listingHref === referredRelativePath + "index.html";
+            return isListingReferrer;
+          });
+
+          if (referrerListing) {
+            // Try to use the referrer if possible
+            activateCategories(referrerListing);
+          } else if (listingHrefs.length > 0) {
+            // Otherwise, just fall back to the first listing
+            activateCategories(listingHrefs[0]);
+          }
+        }
+      });
+    }
+  }
+  if (hasTitleCategories()) {
+    findAndActivateCategories();
+  }
+
+  const findNearestParentListing = (href, listingHrefs) => {
+    if (!href || !listingHrefs) {
+      return undefined;
+    }
+    // Look up the tree for a nearby linting and use that if we find one
+    const relativeParts = href.substring(1).split("/");
+    while (relativeParts.length > 0) {
+      const path = relativeParts.join("/");
+      for (const listingHref of listingHrefs) {
+        if (listingHref.startsWith(path)) {
+          return listingHref;
+        }
+      }
+      relativeParts.pop();
+    }
+
+    return undefined;
+  };
+
+  const manageSidebarVisiblity = (el, placeholderDescriptor) => {
+    let isVisible = true;
+    let elRect;
+
+    return (hiddenRegions) => {
+      if (el === null) {
+        return;
+      }
+
+      // Find the last element of the TOC
+      const lastChildEl = el.lastElementChild;
+
+      if (lastChildEl) {
+        // Converts the sidebar to a menu
+        const convertToMenu = () => {
+          for (const child of el.children) {
+            child.style.opacity = 0;
+            child.style.overflow = "hidden";
+          }
+
+          nexttick(() => {
+            const toggleContainer = window.document.createElement("div");
+            toggleContainer.style.width = "100%";
+            toggleContainer.classList.add("zindex-over-content");
+            toggleContainer.classList.add("quarto-sidebar-toggle");
+            toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom
+            toggleContainer.id = placeholderDescriptor.id;
+            toggleContainer.style.position = "fixed";
+
+            const toggleIcon = window.document.createElement("i");
+            toggleIcon.classList.add("quarto-sidebar-toggle-icon");
+            toggleIcon.classList.add("bi");
+            toggleIcon.classList.add("bi-caret-down-fill");
+
+            const toggleTitle = window.document.createElement("div");
+            const titleEl = window.document.body.querySelector(
+              placeholderDescriptor.titleSelector
+            );
+            if (titleEl) {
+              toggleTitle.append(
+                titleEl.textContent || titleEl.innerText,
+                toggleIcon
+              );
+            }
+            toggleTitle.classList.add("zindex-over-content");
+            toggleTitle.classList.add("quarto-sidebar-toggle-title");
+            toggleContainer.append(toggleTitle);
+
+            const toggleContents = window.document.createElement("div");
+            toggleContents.classList = el.classList;
+            toggleContents.classList.add("zindex-over-content");
+            toggleContents.classList.add("quarto-sidebar-toggle-contents");
+            for (const child of el.children) {
+              if (child.id === "toc-title") {
+                continue;
+              }
+
+              const clone = child.cloneNode(true);
+              clone.style.opacity = 1;
+              clone.style.display = null;
+              toggleContents.append(clone);
+            }
+            toggleContents.style.height = "0px";
+            const positionToggle = () => {
+              // position the element (top left of parent, same width as parent)
+              if (!elRect) {
+                elRect = el.getBoundingClientRect();
+              }
+              toggleContainer.style.left = `${elRect.left}px`;
+              toggleContainer.style.top = `${elRect.top}px`;
+              toggleContainer.style.width = `${elRect.width}px`;
+            };
+            positionToggle();
+
+            toggleContainer.append(toggleContents);
+            el.parentElement.prepend(toggleContainer);
+
+            // Process clicks
+            let tocShowing = false;
+            // Allow the caller to control whether this is dismissed
+            // when it is clicked (e.g. sidebar navigation supports
+            // opening and closing the nav tree, so don't dismiss on click)
+            const clickEl = placeholderDescriptor.dismissOnClick
+              ? toggleContainer
+              : toggleTitle;
+
+            const closeToggle = () => {
+              if (tocShowing) {
+                toggleContainer.classList.remove("expanded");
+                toggleContents.style.height = "0px";
+                tocShowing = false;
+              }
+            };
+
+            // Get rid of any expanded toggle if the user scrolls
+            window.document.addEventListener(
+              "scroll",
+              throttle(() => {
+                closeToggle();
+              }, 50)
+            );
+
+            // Handle positioning of the toggle
+            window.addEventListener(
+              "resize",
+              throttle(() => {
+                elRect = undefined;
+                positionToggle();
+              }, 50)
+            );
+
+            window.addEventListener("quarto-hrChanged", () => {
+              elRect = undefined;
+            });
+
+            // Process the click
+            clickEl.onclick = () => {
+              if (!tocShowing) {
+                toggleContainer.classList.add("expanded");
+                toggleContents.style.height = null;
+                tocShowing = true;
+              } else {
+                closeToggle();
+              }
+            };
+          });
+        };
+
+        // Converts a sidebar from a menu back to a sidebar
+        const convertToSidebar = () => {
+          for (const child of el.children) {
+            child.style.opacity = 1;
+            child.style.overflow = null;
+          }
+
+          const placeholderEl = window.document.getElementById(
+            placeholderDescriptor.id
+          );
+          if (placeholderEl) {
+            placeholderEl.remove();
+          }
+
+          el.classList.remove("rollup");
+        };
+
+        if (isReaderMode()) {
+          convertToMenu();
+          isVisible = false;
+        } else {
+          // Find the top and bottom o the element that is being managed
+          const elTop = el.offsetTop;
+          const elBottom =
+            elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight;
+
+          if (!isVisible) {
+            // If the element is current not visible reveal if there are
+            // no conflicts with overlay regions
+            if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) {
+              convertToSidebar();
+              isVisible = true;
+            }
+          } else {
+            // If the element is visible, hide it if it conflicts with overlay regions
+            // and insert a placeholder toggle (or if we're in reader mode)
+            if (inHiddenRegion(elTop, elBottom, hiddenRegions)) {
+              convertToMenu();
+              isVisible = false;
+            }
+          }
+        }
+      }
+    };
+  };
+
+  const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]');
+  for (const tabEl of tabEls) {
+    const id = tabEl.getAttribute("data-bs-target");
+    if (id) {
+      const columnEl = document.querySelector(
+        `${id} .column-margin, .tabset-margin-content`
+      );
+      if (columnEl)
+        tabEl.addEventListener("shown.bs.tab", function (event) {
+          const el = event.srcElement;
+          if (el) {
+            const visibleCls = `${el.id}-margin-content`;
+            // walk up until we find a parent tabset
+            let panelTabsetEl = el.parentElement;
+            while (panelTabsetEl) {
+              if (panelTabsetEl.classList.contains("panel-tabset")) {
+                break;
+              }
+              panelTabsetEl = panelTabsetEl.parentElement;
+            }
+
+            if (panelTabsetEl) {
+              const prevSib = panelTabsetEl.previousElementSibling;
+              if (
+                prevSib &&
+                prevSib.classList.contains("tabset-margin-container")
+              ) {
+                const childNodes = prevSib.querySelectorAll(
+                  ".tabset-margin-content"
+                );
+                for (const childEl of childNodes) {
+                  if (childEl.classList.contains(visibleCls)) {
+                    childEl.classList.remove("collapse");
+                  } else {
+                    childEl.classList.add("collapse");
+                  }
+                }
+              }
+            }
+          }
+
+          layoutMarginEls();
+        });
+    }
+  }
+
+  // Manage the visibility of the toc and the sidebar
+  const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, {
+    id: "quarto-toc-toggle",
+    titleSelector: "#toc-title",
+    dismissOnClick: true,
+  });
+  const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, {
+    id: "quarto-sidebarnav-toggle",
+    titleSelector: ".title",
+    dismissOnClick: false,
+  });
+  let tocLeftScrollVisibility;
+  if (leftTocEl) {
+    tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, {
+      id: "quarto-lefttoc-toggle",
+      titleSelector: "#toc-title",
+      dismissOnClick: true,
+    });
+  }
+
+  // Find the first element that uses formatting in special columns
+  const conflictingEls = window.document.body.querySelectorAll(
+    '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]'
+  );
+
+  // Filter all the possibly conflicting elements into ones
+  // the do conflict on the left or ride side
+  const arrConflictingEls = Array.from(conflictingEls);
+  const leftSideConflictEls = arrConflictingEls.filter((el) => {
+    if (el.tagName === "ASIDE") {
+      return false;
+    }
+    return Array.from(el.classList).find((className) => {
+      return (
+        className !== "column-body" &&
+        className.startsWith("column-") &&
+        !className.endsWith("right") &&
+        !className.endsWith("container") &&
+        className !== "column-margin"
+      );
+    });
+  });
+  const rightSideConflictEls = arrConflictingEls.filter((el) => {
+    if (el.tagName === "ASIDE") {
+      return true;
+    }
+
+    const hasMarginCaption = Array.from(el.classList).find((className) => {
+      return className == "margin-caption";
+    });
+    if (hasMarginCaption) {
+      return true;
+    }
+
+    return Array.from(el.classList).find((className) => {
+      return (
+        className !== "column-body" &&
+        !className.endsWith("container") &&
+        className.startsWith("column-") &&
+        !className.endsWith("left")
+      );
+    });
+  });
+
+  const kOverlapPaddingSize = 10;
+  function toRegions(els) {
+    return els.map((el) => {
+      const boundRect = el.getBoundingClientRect();
+      const top =
+        boundRect.top +
+        document.documentElement.scrollTop -
+        kOverlapPaddingSize;
+      return {
+        top,
+        bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize,
+      };
+    });
+  }
+
+  let hasObserved = false;
+  const visibleItemObserver = (els) => {
+    let visibleElements = [...els];
+    const intersectionObserver = new IntersectionObserver(
+      (entries, _observer) => {
+        entries.forEach((entry) => {
+          if (entry.isIntersecting) {
+            if (visibleElements.indexOf(entry.target) === -1) {
+              visibleElements.push(entry.target);
+            }
+          } else {
+            visibleElements = visibleElements.filter((visibleEntry) => {
+              return visibleEntry !== entry;
+            });
+          }
+        });
+
+        if (!hasObserved) {
+          hideOverlappedSidebars();
+        }
+        hasObserved = true;
+      },
+      {}
+    );
+    els.forEach((el) => {
+      intersectionObserver.observe(el);
+    });
+
+    return {
+      getVisibleEntries: () => {
+        return visibleElements;
+      },
+    };
+  };
+
+  const rightElementObserver = visibleItemObserver(rightSideConflictEls);
+  const leftElementObserver = visibleItemObserver(leftSideConflictEls);
+
+  const hideOverlappedSidebars = () => {
+    marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries()));
+    sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries()));
+    if (tocLeftScrollVisibility) {
+      tocLeftScrollVisibility(
+        toRegions(leftElementObserver.getVisibleEntries())
+      );
+    }
+  };
+
+  window.quartoToggleReader = () => {
+    // Applies a slow class (or removes it)
+    // to update the transition speed
+    const slowTransition = (slow) => {
+      const manageTransition = (id, slow) => {
+        const el = document.getElementById(id);
+        if (el) {
+          if (slow) {
+            el.classList.add("slow");
+          } else {
+            el.classList.remove("slow");
+          }
+        }
+      };
+
+      manageTransition("TOC", slow);
+      manageTransition("quarto-sidebar", slow);
+    };
+    const readerMode = !isReaderMode();
+    setReaderModeValue(readerMode);
+
+    // If we're entering reader mode, slow the transition
+    if (readerMode) {
+      slowTransition(readerMode);
+    }
+    highlightReaderToggle(readerMode);
+    hideOverlappedSidebars();
+
+    // If we're exiting reader mode, restore the non-slow transition
+    if (!readerMode) {
+      slowTransition(!readerMode);
+    }
+  };
+
+  const highlightReaderToggle = (readerMode) => {
+    const els = document.querySelectorAll(".quarto-reader-toggle");
+    if (els) {
+      els.forEach((el) => {
+        if (readerMode) {
+          el.classList.add("reader");
+        } else {
+          el.classList.remove("reader");
+        }
+      });
+    }
+  };
+
+  const setReaderModeValue = (val) => {
+    if (window.location.protocol !== "file:") {
+      window.localStorage.setItem("quarto-reader-mode", val);
+    } else {
+      localReaderMode = val;
+    }
+  };
+
+  const isReaderMode = () => {
+    if (window.location.protocol !== "file:") {
+      return window.localStorage.getItem("quarto-reader-mode") === "true";
+    } else {
+      return localReaderMode;
+    }
+  };
+  let localReaderMode = null;
+
+  const tocOpenDepthStr = tocEl?.getAttribute("data-toc-expanded");
+  const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1;
+
+  // Walk the TOC and collapse/expand nodes
+  // Nodes are expanded if:
+  // - they are top level
+  // - they have children that are 'active' links
+  // - they are directly below an link that is 'active'
+  const walk = (el, depth) => {
+    // Tick depth when we enter a UL
+    if (el.tagName === "UL") {
+      depth = depth + 1;
+    }
+
+    // It this is active link
+    let isActiveNode = false;
+    if (el.tagName === "A" && el.classList.contains("active")) {
+      isActiveNode = true;
+    }
+
+    // See if there is an active child to this element
+    let hasActiveChild = false;
+    for (child of el.children) {
+      hasActiveChild = walk(child, depth) || hasActiveChild;
+    }
+
+    // Process the collapse state if this is an UL
+    if (el.tagName === "UL") {
+      if (tocOpenDepth === -1 && depth > 1) {
+        el.classList.add("collapse");
+      } else if (
+        depth <= tocOpenDepth ||
+        hasActiveChild ||
+        prevSiblingIsActiveLink(el)
+      ) {
+        el.classList.remove("collapse");
+      } else {
+        el.classList.add("collapse");
+      }
+
+      // untick depth when we leave a UL
+      depth = depth - 1;
+    }
+    return hasActiveChild || isActiveNode;
+  };
+
+  // walk the TOC and expand / collapse any items that should be shown
+
+  if (tocEl) {
+    walk(tocEl, 0);
+    updateActiveLink();
+  }
+
+  // Throttle the scroll event and walk peridiocally
+  window.document.addEventListener(
+    "scroll",
+    throttle(() => {
+      if (tocEl) {
+        updateActiveLink();
+        walk(tocEl, 0);
+      }
+      if (!isReaderMode()) {
+        hideOverlappedSidebars();
+      }
+    }, 5)
+  );
+  window.addEventListener(
+    "resize",
+    throttle(() => {
+      if (!isReaderMode()) {
+        hideOverlappedSidebars();
+      }
+    }, 10)
+  );
+  hideOverlappedSidebars();
+  highlightReaderToggle(isReaderMode());
+});
+
+// grouped tabsets
+window.addEventListener("pageshow", (_event) => {
+  function getTabSettings() {
+    const data = localStorage.getItem("quarto-persistent-tabsets-data");
+    if (!data) {
+      localStorage.setItem("quarto-persistent-tabsets-data", "{}");
+      return {};
+    }
+    if (data) {
+      return JSON.parse(data);
+    }
+  }
+
+  function setTabSettings(data) {
+    localStorage.setItem(
+      "quarto-persistent-tabsets-data",
+      JSON.stringify(data)
+    );
+  }
+
+  function setTabState(groupName, groupValue) {
+    const data = getTabSettings();
+    data[groupName] = groupValue;
+    setTabSettings(data);
+  }
+
+  function toggleTab(tab, active) {
+    const tabPanelId = tab.getAttribute("aria-controls");
+    const tabPanel = document.getElementById(tabPanelId);
+    if (active) {
+      tab.classList.add("active");
+      tabPanel.classList.add("active");
+    } else {
+      tab.classList.remove("active");
+      tabPanel.classList.remove("active");
+    }
+  }
+
+  function toggleAll(selectedGroup, selectorsToSync) {
+    for (const [thisGroup, tabs] of Object.entries(selectorsToSync)) {
+      const active = selectedGroup === thisGroup;
+      for (const tab of tabs) {
+        toggleTab(tab, active);
+      }
+    }
+  }
+
+  function findSelectorsToSyncByLanguage() {
+    const result = {};
+    const tabs = Array.from(
+      document.querySelectorAll(`div[data-group] a[id^='tabset-']`)
+    );
+    for (const item of tabs) {
+      const div = item.parentElement.parentElement.parentElement;
+      const group = div.getAttribute("data-group");
+      if (!result[group]) {
+        result[group] = {};
+      }
+      const selectorsToSync = result[group];
+      const value = item.innerHTML;
+      if (!selectorsToSync[value]) {
+        selectorsToSync[value] = [];
+      }
+      selectorsToSync[value].push(item);
+    }
+    return result;
+  }
+
+  function setupSelectorSync() {
+    const selectorsToSync = findSelectorsToSyncByLanguage();
+    Object.entries(selectorsToSync).forEach(([group, tabSetsByValue]) => {
+      Object.entries(tabSetsByValue).forEach(([value, items]) => {
+        items.forEach((item) => {
+          item.addEventListener("click", (_event) => {
+            setTabState(group, value);
+            toggleAll(value, selectorsToSync[group]);
+          });
+        });
+      });
+    });
+    return selectorsToSync;
+  }
+
+  const selectorsToSync = setupSelectorSync();
+  for (const [group, selectedName] of Object.entries(getTabSettings())) {
+    const selectors = selectorsToSync[group];
+    // it's possible that stale state gives us empty selections, so we explicitly check here.
+    if (selectors) {
+      toggleAll(selectedName, selectors);
+    }
+  }
+});
+
+function throttle(func, wait) {
+  let waiting = false;
+  return function () {
+    if (!waiting) {
+      func.apply(this, arguments);
+      waiting = true;
+      setTimeout(function () {
+        waiting = false;
+      }, wait);
+    }
+  };
+}
+
+function nexttick(func) {
+  return setTimeout(func, 0);
+}
diff --git a/_book/site_libs/quarto-html/tippy.css b/_book/site_libs/quarto-html/tippy.css
new file mode 100644
index 0000000..e6ae635
--- /dev/null
+++ b/_book/site_libs/quarto-html/tippy.css
@@ -0,0 +1 @@
+.tippy-box[data-animation=fade][data-state=hidden]{opacity:0}[data-tippy-root]{max-width:calc(100vw - 10px)}.tippy-box{position:relative;background-color:#333;color:#fff;border-radius:4px;font-size:14px;line-height:1.4;white-space:normal;outline:0;transition-property:transform,visibility,opacity}.tippy-box[data-placement^=top]>.tippy-arrow{bottom:0}.tippy-box[data-placement^=top]>.tippy-arrow:before{bottom:-7px;left:0;border-width:8px 8px 0;border-top-color:initial;transform-origin:center top}.tippy-box[data-placement^=bottom]>.tippy-arrow{top:0}.tippy-box[data-placement^=bottom]>.tippy-arrow:before{top:-7px;left:0;border-width:0 8px 8px;border-bottom-color:initial;transform-origin:center bottom}.tippy-box[data-placement^=left]>.tippy-arrow{right:0}.tippy-box[data-placement^=left]>.tippy-arrow:before{border-width:8px 0 8px 8px;border-left-color:initial;right:-7px;transform-origin:center left}.tippy-box[data-placement^=right]>.tippy-arrow{left:0}.tippy-box[data-placement^=right]>.tippy-arrow:before{left:-7px;border-width:8px 8px 8px 0;border-right-color:initial;transform-origin:center right}.tippy-box[data-inertia][data-state=visible]{transition-timing-function:cubic-bezier(.54,1.5,.38,1.11)}.tippy-arrow{width:16px;height:16px;color:#333}.tippy-arrow:before{content:"";position:absolute;border-color:transparent;border-style:solid}.tippy-content{position:relative;padding:5px 9px;z-index:1}
\ No newline at end of file
diff --git a/_book/site_libs/quarto-html/tippy.umd.min.js b/_book/site_libs/quarto-html/tippy.umd.min.js
new file mode 100644
index 0000000..ca292be
--- /dev/null
+++ b/_book/site_libs/quarto-html/tippy.umd.min.js
@@ -0,0 +1,2 @@
+!function(e,t){"object"==typeof exports&&"undefined"!=typeof module?module.exports=t(require("@popperjs/core")):"function"==typeof define&&define.amd?define(["@popperjs/core"],t):(e=e||self).tippy=t(e.Popper)}(this,(function(e){"use strict";var t={passive:!0,capture:!0},n=function(){return document.body};function r(e,t,n){if(Array.isArray(e)){var r=e[t];return null==r?Array.isArray(n)?n[t]:n:r}return e}function o(e,t){var n={}.toString.call(e);return 0===n.indexOf("[object")&&n.indexOf(t+"]")>-1}function i(e,t){return"function"==typeof e?e.apply(void 0,t):e}function a(e,t){return 0===t?e:function(r){clearTimeout(n),n=setTimeout((function(){e(r)}),t)};var n}function s(e,t){var n=Object.assign({},e);return t.forEach((function(e){delete n[e]})),n}function u(e){return[].concat(e)}function c(e,t){-1===e.indexOf(t)&&e.push(t)}function p(e){return e.split("-")[0]}function f(e){return[].slice.call(e)}function l(e){return Object.keys(e).reduce((function(t,n){return void 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G={name:"inlinePositioning",defaultValue:!1,fn:function(e){var t,n=e.reference;var r=-1,o=!1,i=[],a={name:"tippyInlinePositioning",enabled:!0,phase:"afterWrite",fn:function(o){var a=o.state;e.props.inlinePositioning&&(-1!==i.indexOf(a.placement)&&(i=[]),t!==a.placement&&-1===i.indexOf(a.placement)&&(i.push(a.placement),e.setProps({getReferenceClientRect:function(){return function(e){return function(e,t,n,r){if(n.length<2||null===e)return t;if(2===n.length&&r>=0&&n[0].left>n[1].right)return n[r]||t;switch(e){case"top":case"bottom":var o=n[0],i=n[n.length-1],a="top"===e,s=o.top,u=i.bottom,c=a?o.left:i.left,p=a?o.right:i.right;return{top:s,bottom:u,left:c,right:p,width:p-c,height:u-s};case"left":case"right":var f=Math.min.apply(Math,n.map((function(e){return e.left}))),l=Math.max.apply(Math,n.map((function(e){return e.right}))),d=n.filter((function(t){return"left"===e?t.left===f:t.right===l})),v=d[0].top,m=d[d.length-1].bottom;return{top:v,bottom:m,left:f,right:l,width:l-f,height:m-v};default:return t}}(p(e),n.getBoundingClientRect(),f(n.getClientRects()),r)}(a.placement)}})),t=a.placement)}};function s(){var t;o||(t=function(e,t){var n;return{popperOptions:Object.assign({},e.popperOptions,{modifiers:[].concat(((null==(n=e.popperOptions)?void 0:n.modifiers)||[]).filter((function(e){return e.name!==t.name})),[t])})}}(e.props,a),o=!0,e.setProps(t),o=!1)}return{onCreate:s,onAfterUpdate:s,onTrigger:function(t,n){if(m(n)){var o=f(e.reference.getClientRects()),i=o.find((function(e){return e.left-2<=n.clientX&&e.right+2>=n.clientX&&e.top-2<=n.clientY&&e.bottom+2>=n.clientY})),a=o.indexOf(i);r=a>-1?a:r}},onHidden:function(){r=-1}}}};var K={name:"sticky",defaultValue:!1,fn:function(e){var t=e.reference,n=e.popper;function r(t){return!0===e.props.sticky||e.props.sticky===t}var o=null,i=null;function a(){var s=r("reference")?(e.popperInstance?e.popperInstance.state.elements.reference:t).getBoundingClientRect():null,u=r("popper")?n.getBoundingClientRect():null;(s&&Q(o,s)||u&&Q(i,u))&&e.popperInstance&&e.popperInstance.update(),o=s,i=u,e.state.isMounted&&requestAnimationFrame(a)}return{onMount:function(){e.props.sticky&&a()}}}};function Q(e,t){return!e||!t||(e.top!==t.top||e.right!==t.right||e.bottom!==t.bottom||e.left!==t.left)}return F.setDefaultProps({plugins:[Y,J,G,K],render:N}),F.createSingleton=function(e,t){var n;void 0===t&&(t={});var r,o=e,i=[],a=[],c=t.overrides,p=[],f=!1;function l(){a=o.map((function(e){return u(e.props.triggerTarget||e.reference)})).reduce((function(e,t){return e.concat(t)}),[])}function v(){i=o.map((function(e){return e.reference}))}function m(e){o.forEach((function(t){e?t.enable():t.disable()}))}function g(e){return o.map((function(t){var n=t.setProps;return t.setProps=function(o){n(o),t.reference===r&&e.setProps(o)},function(){t.setProps=n}}))}function 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h(y,t)}return i.indexOf(e)>=0?h(y,e):void 0}},y.showNext=function(){var e=i[0];if(!r)return y.show(0);var t=i.indexOf(r);y.show(i[t+1]||e)},y.showPrevious=function(){var e=i[i.length-1];if(!r)return y.show(e);var t=i.indexOf(r),n=i[t-1]||e;y.show(n)};var E=y.setProps;return y.setProps=function(e){c=e.overrides||c,E(e)},y.setInstances=function(e){m(!0),p.forEach((function(e){return e()})),o=e,m(!1),v(),l(),p=g(y),y.setProps({triggerTarget:a})},p=g(y),y},F.delegate=function(e,n){var r=[],o=[],i=!1,a=n.target,c=s(n,["target"]),p=Object.assign({},c,{trigger:"manual",touch:!1}),f=Object.assign({touch:R.touch},c,{showOnCreate:!0}),l=F(e,p);function d(e){if(e.target&&!i){var t=e.target.closest(a);if(t){var r=t.getAttribute("data-tippy-trigger")||n.trigger||R.trigger;if(!t._tippy&&!("touchstart"===e.type&&"boolean"==typeof f.touch||"touchstart"!==e.type&&r.indexOf(X[e.type])<0)){var s=F(t,f);s&&(o=o.concat(s))}}}}function v(e,t,n,o){void 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+
diff --git a/_book/site_libs/quarto-nav/headroom.min.js b/_book/site_libs/quarto-nav/headroom.min.js
new file mode 100644
index 0000000..b08f1df
--- /dev/null
+++ b/_book/site_libs/quarto-nav/headroom.min.js
@@ -0,0 +1,7 @@
+/*!
+ * headroom.js v0.12.0 - Give your page some headroom. Hide your header until you need it
+ * Copyright (c) 2020 Nick Williams - http://wicky.nillia.ms/headroom.js
+ * License: MIT
+ */
+
+!function(t,n){"object"==typeof exports&&"undefined"!=typeof module?module.exports=n():"function"==typeof define&&define.amd?define(n):(t=t||self).Headroom=n()}(this,function(){"use strict";function t(){return"undefined"!=typeof window}function d(t){return function(t){return t&&t.document&&function(t){return 9===t.nodeType}(t.document)}(t)?function(t){var n=t.document,o=n.body,s=n.documentElement;return{scrollHeight:function(){return Math.max(o.scrollHeight,s.scrollHeight,o.offsetHeight,s.offsetHeight,o.clientHeight,s.clientHeight)},height:function(){return t.innerHeight||s.clientHeight||o.clientHeight},scrollY:function(){return void 0!==t.pageYOffset?t.pageYOffset:(s||o.parentNode||o).scrollTop}}}(t):function(t){return{scrollHeight:function(){return Math.max(t.scrollHeight,t.offsetHeight,t.clientHeight)},height:function(){return Math.max(t.offsetHeight,t.clientHeight)},scrollY:function(){return t.scrollTop}}}(t)}function n(t,s,e){var n,o=function(){var n=!1;try{var t={get passive(){n=!0}};window.addEventListener("test",t,t),window.removeEventListener("test",t,t)}catch(t){n=!1}return n}(),i=!1,r=d(t),l=r.scrollY(),a={};function c(){var t=Math.round(r.scrollY()),n=r.height(),o=r.scrollHeight();a.scrollY=t,a.lastScrollY=l,a.direction=l<t?"down":"up",a.distance=Math.abs(t-l),a.isOutOfBounds=t<0||o<t+n,a.top=t<=s.offset[a.direction],a.bottom=o<=t+n,a.toleranceExceeded=a.distance>s.tolerance[a.direction],e(a),l=t,i=!1}function h(){i||(i=!0,n=requestAnimationFrame(c))}var u=!!o&&{passive:!0,capture:!1};return t.addEventListener("scroll",h,u),c(),{destroy:function(){cancelAnimationFrame(n),t.removeEventListener("scroll",h,u)}}}function o(t){return t===Object(t)?t:{down:t,up:t}}function s(t,n){n=n||{},Object.assign(this,s.options,n),this.classes=Object.assign({},s.options.classes,n.classes),this.elem=t,this.tolerance=o(this.tolerance),this.offset=o(this.offset),this.initialised=!1,this.frozen=!1}return s.prototype={constructor:s,init:function(){return s.cutsTheMustard&&!this.initialised&&(this.addClass("initial"),this.initialised=!0,setTimeout(function(t){t.scrollTracker=n(t.scroller,{offset:t.offset,tolerance:t.tolerance},t.update.bind(t))},100,this)),this},destroy:function(){this.initialised=!1,Object.keys(this.classes).forEach(this.removeClass,this),this.scrollTracker.destroy()},unpin:function(){!this.hasClass("pinned")&&this.hasClass("unpinned")||(this.addClass("unpinned"),this.removeClass("pinned"),this.onUnpin&&this.onUnpin.call(this))},pin:function(){this.hasClass("unpinned")&&(this.addClass("pinned"),this.removeClass("unpinned"),this.onPin&&this.onPin.call(this))},freeze:function(){this.frozen=!0,this.addClass("frozen")},unfreeze:function(){this.frozen=!1,this.removeClass("frozen")},top:function(){this.hasClass("top")||(this.addClass("top"),this.removeClass("notTop"),this.onTop&&this.onTop.call(this))},notTop:function(){this.hasClass("notTop")||(this.addClass("notTop"),this.removeClass("top"),this.onNotTop&&this.onNotTop.call(this))},bottom:function(){this.hasClass("bottom")||(this.addClass("bottom"),this.removeClass("notBottom"),this.onBottom&&this.onBottom.call(this))},notBottom:function(){this.hasClass("notBottom")||(this.addClass("notBottom"),this.removeClass("bottom"),this.onNotBottom&&this.onNotBottom.call(this))},shouldUnpin:function(t){return"down"===t.direction&&!t.top&&t.toleranceExceeded},shouldPin:function(t){return"up"===t.direction&&t.toleranceExceeded||t.top},addClass:function(t){this.elem.classList.add.apply(this.elem.classList,this.classes[t].split(" "))},removeClass:function(t){this.elem.classList.remove.apply(this.elem.classList,this.classes[t].split(" "))},hasClass:function(t){return this.classes[t].split(" ").every(function(t){return this.classList.contains(t)},this.elem)},update:function(t){t.isOutOfBounds||!0!==this.frozen&&(t.top?this.top():this.notTop(),t.bottom?this.bottom():this.notBottom(),this.shouldUnpin(t)?this.unpin():this.shouldPin(t)&&this.pin())}},s.options={tolerance:{up:0,down:0},offset:0,scroller:t()?window:null,classes:{frozen:"headroom--frozen",pinned:"headroom--pinned",unpinned:"headroom--unpinned",top:"headroom--top",notTop:"headroom--not-top",bottom:"headroom--bottom",notBottom:"headroom--not-bottom",initial:"headroom"}},s.cutsTheMustard=!!(t()&&function(){}.bind&&"classList"in document.documentElement&&Object.assign&&Object.keys&&requestAnimationFrame),s});
diff --git a/_book/site_libs/quarto-nav/quarto-nav.js b/_book/site_libs/quarto-nav/quarto-nav.js
new file mode 100644
index 0000000..f6a53b1
--- /dev/null
+++ b/_book/site_libs/quarto-nav/quarto-nav.js
@@ -0,0 +1,289 @@
+const headroomChanged = new CustomEvent("quarto-hrChanged", {
+  detail: {},
+  bubbles: true,
+  cancelable: false,
+  composed: false,
+});
+
+window.document.addEventListener("DOMContentLoaded", function () {
+  let init = false;
+
+  // Manage the back to top button, if one is present.
+  let lastScrollTop = window.pageYOffset || document.documentElement.scrollTop;
+  const scrollDownBuffer = 5;
+  const scrollUpBuffer = 35;
+  const btn = document.getElementById("quarto-back-to-top");
+  const hideBackToTop = () => {
+    btn.style.display = "none";
+  };
+  const showBackToTop = () => {
+    btn.style.display = "inline-block";
+  };
+  if (btn) {
+    window.document.addEventListener(
+      "scroll",
+      function () {
+        const currentScrollTop =
+          window.pageYOffset || document.documentElement.scrollTop;
+
+        // Shows and hides the button 'intelligently' as the user scrolls
+        if (currentScrollTop - scrollDownBuffer > lastScrollTop) {
+          hideBackToTop();
+          lastScrollTop = currentScrollTop <= 0 ? 0 : currentScrollTop;
+        } else if (currentScrollTop < lastScrollTop - scrollUpBuffer) {
+          showBackToTop();
+          lastScrollTop = currentScrollTop <= 0 ? 0 : currentScrollTop;
+        }
+
+        // Show the button at the bottom, hides it at the top
+        if (currentScrollTop <= 0) {
+          hideBackToTop();
+        } else if (
+          window.innerHeight + currentScrollTop >=
+          document.body.offsetHeight
+        ) {
+          showBackToTop();
+        }
+      },
+      false
+    );
+  }
+
+  function throttle(func, wait) {
+    var timeout;
+    return function () {
+      const context = this;
+      const args = arguments;
+      const later = function () {
+        clearTimeout(timeout);
+        timeout = null;
+        func.apply(context, args);
+      };
+
+      if (!timeout) {
+        timeout = setTimeout(later, wait);
+      }
+    };
+  }
+
+  function headerOffset() {
+    // Set an offset if there is are fixed top navbar
+    const headerEl = window.document.querySelector("header.fixed-top");
+    if (headerEl) {
+      return headerEl.clientHeight;
+    } else {
+      return 0;
+    }
+  }
+
+  function footerOffset() {
+    const footerEl = window.document.querySelector("footer.footer");
+    if (footerEl) {
+      return footerEl.clientHeight;
+    } else {
+      return 0;
+    }
+  }
+
+  function dashboardOffset() {
+    const dashboardNavEl = window.document.getElementById(
+      "quarto-dashboard-header"
+    );
+    if (dashboardNavEl !== null) {
+      return dashboardNavEl.clientHeight;
+    } else {
+      return 0;
+    }
+  }
+
+  function updateDocumentOffsetWithoutAnimation() {
+    updateDocumentOffset(false);
+  }
+
+  function updateDocumentOffset(animated) {
+    // set body offset
+    const topOffset = headerOffset();
+    const bodyOffset = topOffset + footerOffset() + dashboardOffset();
+    const bodyEl = window.document.body;
+    bodyEl.setAttribute("data-bs-offset", topOffset);
+    bodyEl.style.paddingTop = topOffset + "px";
+
+    // deal with sidebar offsets
+    const sidebars = window.document.querySelectorAll(
+      ".sidebar, .headroom-target"
+    );
+    sidebars.forEach((sidebar) => {
+      if (!animated) {
+        sidebar.classList.add("notransition");
+        // Remove the no transition class after the animation has time to complete
+        setTimeout(function () {
+          sidebar.classList.remove("notransition");
+        }, 201);
+      }
+
+      if (window.Headroom && sidebar.classList.contains("sidebar-unpinned")) {
+        sidebar.style.top = "0";
+        sidebar.style.maxHeight = "100vh";
+      } else {
+        sidebar.style.top = topOffset + "px";
+        sidebar.style.maxHeight = "calc(100vh - " + topOffset + "px)";
+      }
+    });
+
+    // allow space for footer
+    const mainContainer = window.document.querySelector(".quarto-container");
+    if (mainContainer) {
+      mainContainer.style.minHeight = "calc(100vh - " + bodyOffset + "px)";
+    }
+
+    // link offset
+    let linkStyle = window.document.querySelector("#quarto-target-style");
+    if (!linkStyle) {
+      linkStyle = window.document.createElement("style");
+      linkStyle.setAttribute("id", "quarto-target-style");
+      window.document.head.appendChild(linkStyle);
+    }
+    while (linkStyle.firstChild) {
+      linkStyle.removeChild(linkStyle.firstChild);
+    }
+    if (topOffset > 0) {
+      linkStyle.appendChild(
+        window.document.createTextNode(`
+      section:target::before {
+        content: "";
+        display: block;
+        height: ${topOffset}px;
+        margin: -${topOffset}px 0 0;
+      }`)
+      );
+    }
+    if (init) {
+      window.dispatchEvent(headroomChanged);
+    }
+    init = true;
+  }
+
+  // initialize headroom
+  var header = window.document.querySelector("#quarto-header");
+  if (header && window.Headroom) {
+    const headroom = new window.Headroom(header, {
+      tolerance: 5,
+      onPin: function () {
+        const sidebars = window.document.querySelectorAll(
+          ".sidebar, .headroom-target"
+        );
+        sidebars.forEach((sidebar) => {
+          sidebar.classList.remove("sidebar-unpinned");
+        });
+        updateDocumentOffset();
+      },
+      onUnpin: function () {
+        const sidebars = window.document.querySelectorAll(
+          ".sidebar, .headroom-target"
+        );
+        sidebars.forEach((sidebar) => {
+          sidebar.classList.add("sidebar-unpinned");
+        });
+        updateDocumentOffset();
+      },
+    });
+    headroom.init();
+
+    let frozen = false;
+    window.quartoToggleHeadroom = function () {
+      if (frozen) {
+        headroom.unfreeze();
+        frozen = false;
+      } else {
+        headroom.freeze();
+        frozen = true;
+      }
+    };
+  }
+
+  window.addEventListener(
+    "hashchange",
+    function (e) {
+      if (
+        getComputedStyle(document.documentElement).scrollBehavior !== "smooth"
+      ) {
+        window.scrollTo(0, window.pageYOffset - headerOffset());
+      }
+    },
+    false
+  );
+
+  // Observe size changed for the header
+  const headerEl = window.document.querySelector("header.fixed-top");
+  if (headerEl && window.ResizeObserver) {
+    const observer = new window.ResizeObserver(() => {
+      setTimeout(updateDocumentOffsetWithoutAnimation, 0);
+    });
+    observer.observe(headerEl, {
+      attributes: true,
+      childList: true,
+      characterData: true,
+    });
+  } else {
+    window.addEventListener(
+      "resize",
+      throttle(updateDocumentOffsetWithoutAnimation, 50)
+    );
+  }
+  setTimeout(updateDocumentOffsetWithoutAnimation, 250);
+
+  // fixup index.html links if we aren't on the filesystem
+  if (window.location.protocol !== "file:") {
+    const links = window.document.querySelectorAll("a");
+    for (let i = 0; i < links.length; i++) {
+      if (links[i].href) {
+        links[i].dataset.originalHref = links[i].href;
+        links[i].href = links[i].href.replace(/\/index\.html/, "/");
+      }
+    }
+
+    // Fixup any sharing links that require urls
+    // Append url to any sharing urls
+    const sharingLinks = window.document.querySelectorAll(
+      "a.sidebar-tools-main-item, a.quarto-navigation-tool, a.quarto-navbar-tools, a.quarto-navbar-tools-item"
+    );
+    for (let i = 0; i < sharingLinks.length; i++) {
+      const sharingLink = sharingLinks[i];
+      const href = sharingLink.getAttribute("href");
+      if (href) {
+        sharingLink.setAttribute(
+          "href",
+          href.replace("|url|", window.location.href)
+        );
+      }
+    }
+
+    // Scroll the active navigation item into view, if necessary
+    const navSidebar = window.document.querySelector("nav#quarto-sidebar");
+    if (navSidebar) {
+      // Find the active item
+      const activeItem = navSidebar.querySelector("li.sidebar-item a.active");
+      if (activeItem) {
+        // Wait for the scroll height and height to resolve by observing size changes on the
+        // nav element that is scrollable
+        const resizeObserver = new ResizeObserver((_entries) => {
+          // The bottom of the element
+          const elBottom = activeItem.offsetTop;
+          const viewBottom = navSidebar.scrollTop + navSidebar.clientHeight;
+
+          // The element height and scroll height are the same, then we are still loading
+          if (viewBottom !== navSidebar.scrollHeight) {
+            // Determine if the item isn't visible and scroll to it
+            if (elBottom >= viewBottom) {
+              navSidebar.scrollTop = elBottom;
+            }
+
+            // stop observing now since we've completed the scroll
+            resizeObserver.unobserve(navSidebar);
+          }
+        });
+        resizeObserver.observe(navSidebar);
+      }
+    }
+  }
+});
diff --git a/_book/site_libs/quarto-search/autocomplete.umd.js b/_book/site_libs/quarto-search/autocomplete.umd.js
new file mode 100644
index 0000000..ae0063a
--- /dev/null
+++ b/_book/site_libs/quarto-search/autocomplete.umd.js
@@ -0,0 +1,3 @@
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diff --git a/_book/site_libs/quarto-search/fuse.min.js b/_book/site_libs/quarto-search/fuse.min.js
new file mode 100644
index 0000000..adc2835
--- /dev/null
+++ b/_book/site_libs/quarto-search/fuse.min.js
@@ -0,0 +1,9 @@
+/**
+ * Fuse.js v6.6.2 - Lightweight fuzzy-search (http://fusejs.io)
+ *
+ * Copyright (c) 2022 Kiro Risk (http://kiro.me)
+ * All Rights Reserved. Apache Software License 2.0
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ */
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B=q-1,J=n[e.charAt(B)];if(S&&(_[B]=+!!J),K[q]=(K[q+1]<<1|1)&J,F&&(K[q]|=(A[q+1]|A[q])<<1|1|A[q+1]),K[q]&$&&(C=R(t,{errors:F,currentLocation:B,expectedLocation:b,distance:a,ignoreLocation:p}))<=x){if(x=C,(L=B)<=b)break;z=Math.max(1,2*b-L)}}if(R(t,{errors:F+1,currentLocation:b,expectedLocation:b,distance:a,ignoreLocation:p})>x)break;A=K}var U={isMatch:L>=0,score:Math.max(.001,C)};if(S){var V=N(_,d);V.length?g&&(U.indices=V):U.isMatch=!1}return U}(e,n,i,{location:c+o,distance:a,threshold:s,findAllMatches:u,minMatchCharLength:h,includeMatches:r,ignoreLocation:l}),p=y.isMatch,m=y.score,k=y.indices;p&&(g=!0),v+=m,p&&k&&(d=[].concat(f(d),f(k)))}));var y={isMatch:g,score:g?v/this.chunks.length:1};return g&&r&&(y.indices=d),y}}]),e}(),z=function(){function e(t){r(this,e),this.pattern=t}return o(e,[{key:"search",value:function(){}}],[{key:"isMultiMatch",value:function(e){return D(e,this.multiRegex)}},{key:"isSingleMatch",value:function(e){return D(e,this.singleRegex)}}]),e}();function D(e,t){var n=e.match(t);return n?n[1]:null}var K=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=e===this.pattern;return{isMatch:t,score:t?0:1,indices:[0,this.pattern.length-1]}}}],[{key:"type",get:function(){return"exact"}},{key:"multiRegex",get:function(){return/^="(.*)"$/}},{key:"singleRegex",get:function(){return/^=(.*)$/}}]),n}(z),q=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=-1===e.indexOf(this.pattern);return{isMatch:t,score:t?0:1,indices:[0,e.length-1]}}}],[{key:"type",get:function(){return"inverse-exact"}},{key:"multiRegex",get:function(){return/^!"(.*)"$/}},{key:"singleRegex",get:function(){return/^!(.*)$/}}]),n}(z),B=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=e.startsWith(this.pattern);return{isMatch:t,score:t?0:1,indices:[0,this.pattern.length-1]}}}],[{key:"type",get:function(){return"prefix-exact"}},{key:"multiRegex",get:function(){return/^\^"(.*)"$/}},{key:"singleRegex",get:function(){return/^\^(.*)$/}}]),n}(z),J=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=!e.startsWith(this.pattern);return{isMatch:t,score:t?0:1,indices:[0,e.length-1]}}}],[{key:"type",get:function(){return"inverse-prefix-exact"}},{key:"multiRegex",get:function(){return/^!\^"(.*)"$/}},{key:"singleRegex",get:function(){return/^!\^(.*)$/}}]),n}(z),U=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=e.endsWith(this.pattern);return{isMatch:t,score:t?0:1,indices:[e.length-this.pattern.length,e.length-1]}}}],[{key:"type",get:function(){return"suffix-exact"}},{key:"multiRegex",get:function(){return/^"(.*)"\$$/}},{key:"singleRegex",get:function(){return/^(.*)\$$/}}]),n}(z),V=function(e){a(n,e);var t=l(n);function n(e){return r(this,n),t.call(this,e)}return o(n,[{key:"search",value:function(e){var t=!e.endsWith(this.pattern);return{isMatch:t,score:t?0:1,indices:[0,e.length-1]}}}],[{key:"type",get:function(){return"inverse-suffix-exact"}},{key:"multiRegex",get:function(){return/^!"(.*)"\$$/}},{key:"singleRegex",get:function(){return/^!(.*)\$$/}}]),n}(z),G=function(e){a(n,e);var t=l(n);function n(e){var i,o=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{},c=o.location,a=void 0===c?I.location:c,s=o.threshold,u=void 0===s?I.threshold:s,h=o.distance,l=void 0===h?I.distance:h,f=o.includeMatches,d=void 0===f?I.includeMatches:f,v=o.findAllMatches,g=void 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r&&(k.indices=o),k}}return{isMatch:!1,score:1}}}],[{key:"condition",value:function(e,t){return t.useExtendedSearch}}]),e}(),ne=[];function re(e,t){for(var n=0,r=ne.length;n<r;n+=1){var i=ne[n];if(i.condition(e,t))return new i(e,t)}return new T(e,t)}var ie="$and",oe="$or",ce="$path",ae="$val",se=function(e){return!(!e[ie]&&!e[oe])},ue=function(e){return!!e[ce]},he=function(e){return!v(e)&&m(e)&&!se(e)},le=function(e){return c({},ie,Object.keys(e).map((function(t){return c({},t,e[t])})))};function fe(e,t){var n=t.ignoreFieldNorm,r=void 0===n?I.ignoreFieldNorm:n;e.forEach((function(e){var t=1;e.matches.forEach((function(e){var n=e.key,i=e.norm,o=e.score,c=n?n.weight:null;t*=Math.pow(0===o&&c?Number.EPSILON:o,(c||1)*(r?1:i))})),e.score=t}))}function de(e,t){var n=e.matches;t.matches=[],k(n)&&n.forEach((function(e){if(k(e.indices)&&e.indices.length){var n={indices:e.indices,value:e.value};e.key&&(n.key=e.key.src),e.idx>-1&&(n.refIndex=e.idx),t.matches.push(n)}}))}function ve(e,t){t.score=e.score}function ge(e,t){var n=arguments.length>2&&void 0!==arguments[2]?arguments[2]:{},r=n.includeMatches,i=void 0===r?I.includeMatches:r,o=n.includeScore,c=void 0===o?I.includeScore:o,a=[];return i&&a.push(de),c&&a.push(ve),e.map((function(e){var n=e.idx,r={item:t[n],refIndex:n};return a.length&&a.forEach((function(t){t(e,r)})),r}))}var ye=function(){function e(n){var i=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{},o=arguments.length>2?arguments[2]:void 0;r(this,e),this.options=t(t({},I),i),this.options.useExtendedSearch,this._keyStore=new S(this.options.keys),this.setCollection(n,o)}return o(e,[{key:"setCollection",value:function(e,t){if(this._docs=e,t&&!(t instanceof $))throw new Error("Incorrect 'index' type");this._myIndex=t||F(this.options.keys,this._docs,{getFn:this.options.getFn,fieldNormWeight:this.options.fieldNormWeight})}},{key:"add",value:function(e){k(e)&&(this._docs.push(e),this._myIndex.add(e))}},{key:"remove",value:function(){for(var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:function(){return!1},t=[],n=0,r=this._docs.length;n<r;n+=1){var i=this._docs[n];e(i,n)&&(this.removeAt(n),n-=1,r-=1,t.push(i))}return t}},{key:"removeAt",value:function(e){this._docs.splice(e,1),this._myIndex.removeAt(e)}},{key:"getIndex",value:function(){return this._myIndex}},{key:"search",value:function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{},n=t.limit,r=void 0===n?-1:n,i=this.options,o=i.includeMatches,c=i.includeScore,a=i.shouldSort,s=i.sortFn,u=i.ignoreFieldNorm,h=g(e)?g(this._docs[0])?this._searchStringList(e):this._searchObjectList(e):this._searchLogical(e);return fe(h,{ignoreFieldNorm:u}),a&&h.sort(s),y(r)&&r>-1&&(h=h.slice(0,r)),ge(h,this._docs,{includeMatches:o,includeScore:c})}},{key:"_searchStringList",value:function(e){var t=re(e,this.options),n=this._myIndex.records,r=[];return n.forEach((function(e){var n=e.v,i=e.i,o=e.n;if(k(n)){var c=t.searchIn(n),a=c.isMatch,s=c.score,u=c.indices;a&&r.push({item:n,idx:i,matches:[{score:s,value:n,norm:o,indices:u}]})}})),r}},{key:"_searchLogical",value:function(e){var t=this,n=function(e,t){var n=(arguments.length>2&&void 0!==arguments[2]?arguments[2]:{}).auto,r=void 0===n||n,i=function e(n){var i=Object.keys(n),o=ue(n);if(!o&&i.length>1&&!se(n))return e(le(n));if(he(n)){var c=o?n[ce]:i[0],a=o?n[ae]:n[c];if(!g(a))throw new Error(x(c));var s={keyId:j(c),pattern:a};return r&&(s.searcher=re(a,t)),s}var u={children:[],operator:i[0]};return i.forEach((function(t){var r=n[t];v(r)&&r.forEach((function(t){u.children.push(e(t))}))})),u};return se(e)||(e=le(e)),i(e)}(e,this.options),r=function e(n,r,i){if(!n.children){var o=n.keyId,c=n.searcher,a=t._findMatches({key:t._keyStore.get(o),value:t._myIndex.getValueForItemAtKeyId(r,o),searcher:c});return a&&a.length?[{idx:i,item:r,matches:a}]:[]}for(var s=[],u=0,h=n.children.length;u<h;u+=1){var l=e(n.children[u],r,i);if(l.length)s.push.apply(s,f(l));else if(n.operator===ie)return[]}return s},i=this._myIndex.records,o={},c=[];return i.forEach((function(e){var t=e.$,i=e.i;if(k(t)){var a=r(n,t,i);a.length&&(o[i]||(o[i]={idx:i,item:t,matches:[]},c.push(o[i])),a.forEach((function(e){var t,n=e.matches;(t=o[i].matches).push.apply(t,f(n))})))}})),c}},{key:"_searchObjectList",value:function(e){var t=this,n=re(e,this.options),r=this._myIndex,i=r.keys,o=r.records,c=[];return o.forEach((function(e){var r=e.$,o=e.i;if(k(r)){var a=[];i.forEach((function(e,i){a.push.apply(a,f(t._findMatches({key:e,value:r[i],searcher:n})))})),a.length&&c.push({idx:o,item:r,matches:a})}})),c}},{key:"_findMatches",value:function(e){var t=e.key,n=e.value,r=e.searcher;if(!k(n))return[];var i=[];if(v(n))n.forEach((function(e){var n=e.v,o=e.i,c=e.n;if(k(n)){var a=r.searchIn(n),s=a.isMatch,u=a.score,h=a.indices;s&&i.push({score:u,key:t,value:n,idx:o,norm:c,indices:h})}}));else{var o=n.v,c=n.n,a=r.searchIn(o),s=a.isMatch,u=a.score,h=a.indices;s&&i.push({score:u,key:t,value:o,norm:c,indices:h})}return i}}]),e}();return ye.version="6.6.2",ye.createIndex=F,ye.parseIndex=function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{},n=t.getFn,r=void 0===n?I.getFn:n,i=t.fieldNormWeight,o=void 0===i?I.fieldNormWeight:i,c=e.keys,a=e.records,s=new $({getFn:r,fieldNormWeight:o});return s.setKeys(c),s.setIndexRecords(a),s},ye.config=I,function(){ne.push.apply(ne,arguments)}(te),ye},"object"==typeof exports&&"undefined"!=typeof module?module.exports=t():"function"==typeof define&&define.amd?define(t):(e="undefined"!=typeof globalThis?globalThis:e||self).Fuse=t();
\ No newline at end of file
diff --git a/_book/site_libs/quarto-search/quarto-search.js b/_book/site_libs/quarto-search/quarto-search.js
new file mode 100644
index 0000000..5f723d7
--- /dev/null
+++ b/_book/site_libs/quarto-search/quarto-search.js
@@ -0,0 +1,1286 @@
+const kQueryArg = "q";
+const kResultsArg = "show-results";
+
+// If items don't provide a URL, then both the navigator and the onSelect
+// function aren't called (and therefore, the default implementation is used)
+//
+// We're using this sentinel URL to signal to those handlers that this
+// item is a more item (along with the type) and can be handled appropriately
+const kItemTypeMoreHref = "0767FDFD-0422-4E5A-BC8A-3BE11E5BBA05";
+
+window.document.addEventListener("DOMContentLoaded", function (_event) {
+  // Ensure that search is available on this page. If it isn't,
+  // should return early and not do anything
+  var searchEl = window.document.getElementById("quarto-search");
+  if (!searchEl) return;
+
+  const { autocomplete } = window["@algolia/autocomplete-js"];
+
+  let quartoSearchOptions = {};
+  let language = {};
+  const searchOptionEl = window.document.getElementById(
+    "quarto-search-options"
+  );
+  if (searchOptionEl) {
+    const jsonStr = searchOptionEl.textContent;
+    quartoSearchOptions = JSON.parse(jsonStr);
+    language = quartoSearchOptions.language;
+  }
+
+  // note the search mode
+  if (quartoSearchOptions.type === "overlay") {
+    searchEl.classList.add("type-overlay");
+  } else {
+    searchEl.classList.add("type-textbox");
+  }
+
+  // Used to determine highlighting behavior for this page
+  // A `q` query param is expected when the user follows a search
+  // to this page
+  const currentUrl = new URL(window.location);
+  const query = currentUrl.searchParams.get(kQueryArg);
+  const showSearchResults = currentUrl.searchParams.get(kResultsArg);
+  const mainEl = window.document.querySelector("main");
+
+  // highlight matches on the page
+  if (query && mainEl) {
+    // perform any highlighting
+    highlight(escapeRegExp(query), mainEl);
+
+    // fix up the URL to remove the q query param
+    const replacementUrl = new URL(window.location);
+    replacementUrl.searchParams.delete(kQueryArg);
+    window.history.replaceState({}, "", replacementUrl);
+  }
+
+  // function to clear highlighting on the page when the search query changes
+  // (e.g. if the user edits the query or clears it)
+  let highlighting = true;
+  const resetHighlighting = (searchTerm) => {
+    if (mainEl && highlighting && query && searchTerm !== query) {
+      clearHighlight(query, mainEl);
+      highlighting = false;
+    }
+  };
+
+  // Clear search highlighting when the user scrolls sufficiently
+  const resetFn = () => {
+    resetHighlighting("");
+    window.removeEventListener("quarto-hrChanged", resetFn);
+    window.removeEventListener("quarto-sectionChanged", resetFn);
+  };
+
+  // Register this event after the initial scrolling and settling of events
+  // on the page
+  window.addEventListener("quarto-hrChanged", resetFn);
+  window.addEventListener("quarto-sectionChanged", resetFn);
+
+  // Responsively switch to overlay mode if the search is present on the navbar
+  // Note that switching the sidebar to overlay mode requires more coordinate (not just
+  // the media query since we generate different HTML for sidebar overlays than we do
+  // for sidebar input UI)
+  const detachedMediaQuery =
+    quartoSearchOptions.type === "overlay" ? "all" : "(max-width: 991px)";
+
+  // If configured, include the analytics client to send insights
+  const plugins = configurePlugins(quartoSearchOptions);
+
+  let lastState = null;
+  const { setIsOpen, setQuery, setCollections } = autocomplete({
+    container: searchEl,
+    detachedMediaQuery: detachedMediaQuery,
+    defaultActiveItemId: 0,
+    panelContainer: "#quarto-search-results",
+    panelPlacement: quartoSearchOptions["panel-placement"],
+    debug: false,
+    openOnFocus: true,
+    plugins,
+    classNames: {
+      form: "d-flex",
+    },
+    placeholder: language["search-text-placeholder"],
+    translations: {
+      clearButtonTitle: language["search-clear-button-title"],
+      detachedCancelButtonText: language["search-detached-cancel-button-title"],
+      submitButtonTitle: language["search-submit-button-title"],
+    },
+    initialState: {
+      query,
+    },
+    getItemUrl({ item }) {
+      return item.href;
+    },
+    onStateChange({ state }) {
+      // If this is a file URL, note that
+
+      // Perhaps reset highlighting
+      resetHighlighting(state.query);
+
+      // If the panel just opened, ensure the panel is positioned properly
+      if (state.isOpen) {
+        if (lastState && !lastState.isOpen) {
+          setTimeout(() => {
+            positionPanel(quartoSearchOptions["panel-placement"]);
+          }, 150);
+        }
+      }
+
+      // Perhaps show the copy link
+      showCopyLink(state.query, quartoSearchOptions);
+
+      lastState = state;
+    },
+    reshape({ sources, state }) {
+      return sources.map((source) => {
+        try {
+          const items = source.getItems();
+
+          // Validate the items
+          validateItems(items);
+
+          // group the items by document
+          const groupedItems = new Map();
+          items.forEach((item) => {
+            const hrefParts = item.href.split("#");
+            const baseHref = hrefParts[0];
+            const isDocumentItem = hrefParts.length === 1;
+
+            const items = groupedItems.get(baseHref);
+            if (!items) {
+              groupedItems.set(baseHref, [item]);
+            } else {
+              // If the href for this item matches the document
+              // exactly, place this item first as it is the item that represents
+              // the document itself
+              if (isDocumentItem) {
+                items.unshift(item);
+              } else {
+                items.push(item);
+              }
+              groupedItems.set(baseHref, items);
+            }
+          });
+
+          const reshapedItems = [];
+          let count = 1;
+          for (const [_key, value] of groupedItems) {
+            const firstItem = value[0];
+            reshapedItems.push({
+              ...firstItem,
+              type: kItemTypeDoc,
+            });
+
+            const collapseMatches = quartoSearchOptions["collapse-after"];
+            const collapseCount =
+              typeof collapseMatches === "number" ? collapseMatches : 1;
+
+            if (value.length > 1) {
+              const target = `search-more-${count}`;
+              const isExpanded =
+                state.context.expanded &&
+                state.context.expanded.includes(target);
+
+              const remainingCount = value.length - collapseCount;
+
+              for (let i = 1; i < value.length; i++) {
+                if (collapseMatches && i === collapseCount) {
+                  reshapedItems.push({
+                    target,
+                    title: isExpanded
+                      ? language["search-hide-matches-text"]
+                      : remainingCount === 1
+                      ? `${remainingCount} ${language["search-more-match-text"]}`
+                      : `${remainingCount} ${language["search-more-matches-text"]}`,
+                    type: kItemTypeMore,
+                    href: kItemTypeMoreHref,
+                  });
+                }
+
+                if (isExpanded || !collapseMatches || i < collapseCount) {
+                  reshapedItems.push({
+                    ...value[i],
+                    type: kItemTypeItem,
+                    target,
+                  });
+                }
+              }
+            }
+            count += 1;
+          }
+
+          return {
+            ...source,
+            getItems() {
+              return reshapedItems;
+            },
+          };
+        } catch (error) {
+          // Some form of error occurred
+          return {
+            ...source,
+            getItems() {
+              return [
+                {
+                  title: error.name || "An Error Occurred While Searching",
+                  text:
+                    error.message ||
+                    "An unknown error occurred while attempting to perform the requested search.",
+                  type: kItemTypeError,
+                },
+              ];
+            },
+          };
+        }
+      });
+    },
+    navigator: {
+      navigate({ itemUrl }) {
+        if (itemUrl !== offsetURL(kItemTypeMoreHref)) {
+          window.location.assign(itemUrl);
+        }
+      },
+      navigateNewTab({ itemUrl }) {
+        if (itemUrl !== offsetURL(kItemTypeMoreHref)) {
+          const windowReference = window.open(itemUrl, "_blank", "noopener");
+          if (windowReference) {
+            windowReference.focus();
+          }
+        }
+      },
+      navigateNewWindow({ itemUrl }) {
+        if (itemUrl !== offsetURL(kItemTypeMoreHref)) {
+          window.open(itemUrl, "_blank", "noopener");
+        }
+      },
+    },
+    getSources({ state, setContext, setActiveItemId, refresh }) {
+      return [
+        {
+          sourceId: "documents",
+          getItemUrl({ item }) {
+            if (item.href) {
+              return offsetURL(item.href);
+            } else {
+              return undefined;
+            }
+          },
+          onSelect({
+            item,
+            state,
+            setContext,
+            setIsOpen,
+            setActiveItemId,
+            refresh,
+          }) {
+            if (item.type === kItemTypeMore) {
+              toggleExpanded(item, state, setContext, setActiveItemId, refresh);
+
+              // Toggle more
+              setIsOpen(true);
+            }
+          },
+          getItems({ query }) {
+            if (query === null || query === "") {
+              return [];
+            }
+
+            const limit = quartoSearchOptions.limit;
+            if (quartoSearchOptions.algolia) {
+              return algoliaSearch(query, limit, quartoSearchOptions.algolia);
+            } else {
+              // Fuse search options
+              const fuseSearchOptions = {
+                isCaseSensitive: false,
+                shouldSort: true,
+                minMatchCharLength: 2,
+                limit: limit,
+              };
+
+              return readSearchData().then(function (fuse) {
+                return fuseSearch(query, fuse, fuseSearchOptions);
+              });
+            }
+          },
+          templates: {
+            noResults({ createElement }) {
+              const hasQuery = lastState.query;
+
+              return createElement(
+                "div",
+                {
+                  class: `quarto-search-no-results${
+                    hasQuery ? "" : " no-query"
+                  }`,
+                },
+                language["search-no-results-text"]
+              );
+            },
+            header({ items, createElement }) {
+              // count the documents
+              const count = items.filter((item) => {
+                return item.type === kItemTypeDoc;
+              }).length;
+
+              if (count > 0) {
+                return createElement(
+                  "div",
+                  { class: "search-result-header" },
+                  `${count} ${language["search-matching-documents-text"]}`
+                );
+              } else {
+                return createElement(
+                  "div",
+                  { class: "search-result-header-no-results" },
+                  ``
+                );
+              }
+            },
+            footer({ _items, createElement }) {
+              if (
+                quartoSearchOptions.algolia &&
+                quartoSearchOptions.algolia["show-logo"]
+              ) {
+                const libDir = quartoSearchOptions.algolia["libDir"];
+                const logo = createElement("img", {
+                  src: offsetURL(
+                    `${libDir}/quarto-search/search-by-algolia.svg`
+                  ),
+                  class: "algolia-search-logo",
+                });
+                return createElement(
+                  "a",
+                  { href: "http://www.algolia.com/" },
+                  logo
+                );
+              }
+            },
+
+            item({ item, createElement }) {
+              return renderItem(
+                item,
+                createElement,
+                state,
+                setActiveItemId,
+                setContext,
+                refresh,
+                quartoSearchOptions
+              );
+            },
+          },
+        },
+      ];
+    },
+  });
+
+  window.quartoOpenSearch = () => {
+    setIsOpen(false);
+    setIsOpen(true);
+    focusSearchInput();
+  };
+
+  document.addEventListener("keyup", (event) => {
+    const { key } = event;
+    const kbds = quartoSearchOptions["keyboard-shortcut"];
+    const focusedEl = document.activeElement;
+
+    const isFormElFocused = [
+      "input",
+      "select",
+      "textarea",
+      "button",
+      "option",
+    ].find((tag) => {
+      return focusedEl.tagName.toLowerCase() === tag;
+    });
+
+    if (
+      kbds &&
+      kbds.includes(key) &&
+      !isFormElFocused &&
+      !document.activeElement.isContentEditable
+    ) {
+      event.preventDefault();
+      window.quartoOpenSearch();
+    }
+  });
+
+  // Remove the labeleledby attribute since it is pointing
+  // to a non-existent label
+  if (quartoSearchOptions.type === "overlay") {
+    const inputEl = window.document.querySelector(
+      "#quarto-search .aa-Autocomplete"
+    );
+    if (inputEl) {
+      inputEl.removeAttribute("aria-labelledby");
+    }
+  }
+
+  function throttle(func, wait) {
+    let waiting = false;
+    return function () {
+      if (!waiting) {
+        func.apply(this, arguments);
+        waiting = true;
+        setTimeout(function () {
+          waiting = false;
+        }, wait);
+      }
+    };
+  }
+
+  // If the main document scrolls dismiss the search results
+  // (otherwise, since they're floating in the document they can scroll with the document)
+  window.document.body.onscroll = throttle(() => {
+    // Only do this if we're not detached
+    // Bug #7117
+    // This will happen when the keyboard is shown on ios (resulting in a scroll)
+    // which then closed the search UI
+    if (!window.matchMedia(detachedMediaQuery).matches) {
+      setIsOpen(false);
+    }
+  }, 50);
+
+  if (showSearchResults) {
+    setIsOpen(true);
+    focusSearchInput();
+  }
+});
+
+function configurePlugins(quartoSearchOptions) {
+  const autocompletePlugins = [];
+  const algoliaOptions = quartoSearchOptions.algolia;
+  if (
+    algoliaOptions &&
+    algoliaOptions["analytics-events"] &&
+    algoliaOptions["search-only-api-key"] &&
+    algoliaOptions["application-id"]
+  ) {
+    const apiKey = algoliaOptions["search-only-api-key"];
+    const appId = algoliaOptions["application-id"];
+
+    // Aloglia insights may not be loaded because they require cookie consent
+    // Use deferred loading so events will start being recorded when/if consent
+    // is granted.
+    const algoliaInsightsDeferredPlugin = deferredLoadPlugin(() => {
+      if (
+        window.aa &&
+        window["@algolia/autocomplete-plugin-algolia-insights"]
+      ) {
+        window.aa("init", {
+          appId,
+          apiKey,
+          useCookie: true,
+        });
+
+        const { createAlgoliaInsightsPlugin } =
+          window["@algolia/autocomplete-plugin-algolia-insights"];
+        // Register the insights client
+        const algoliaInsightsPlugin = createAlgoliaInsightsPlugin({
+          insightsClient: window.aa,
+          onItemsChange({ insights, insightsEvents }) {
+            const events = insightsEvents.flatMap((event) => {
+              // This API limits the number of items per event to 20
+              const chunkSize = 20;
+              const itemChunks = [];
+              const eventItems = event.items;
+              for (let i = 0; i < eventItems.length; i += chunkSize) {
+                itemChunks.push(eventItems.slice(i, i + chunkSize));
+              }
+              // Split the items into multiple events that can be sent
+              const events = itemChunks.map((items) => {
+                return {
+                  ...event,
+                  items,
+                };
+              });
+              return events;
+            });
+
+            for (const event of events) {
+              insights.viewedObjectIDs(event);
+            }
+          },
+        });
+        return algoliaInsightsPlugin;
+      }
+    });
+
+    // Add the plugin
+    autocompletePlugins.push(algoliaInsightsDeferredPlugin);
+    return autocompletePlugins;
+  }
+}
+
+// For plugins that may not load immediately, create a wrapper
+// plugin and forward events and plugin data once the plugin
+// is initialized. This is useful for cases like cookie consent
+// which may prevent the analytics insights event plugin from initializing
+// immediately.
+function deferredLoadPlugin(createPlugin) {
+  let plugin = undefined;
+  let subscribeObj = undefined;
+  const wrappedPlugin = () => {
+    if (!plugin && subscribeObj) {
+      plugin = createPlugin();
+      if (plugin && plugin.subscribe) {
+        plugin.subscribe(subscribeObj);
+      }
+    }
+    return plugin;
+  };
+
+  return {
+    subscribe: (obj) => {
+      subscribeObj = obj;
+    },
+    onStateChange: (obj) => {
+      const plugin = wrappedPlugin();
+      if (plugin && plugin.onStateChange) {
+        plugin.onStateChange(obj);
+      }
+    },
+    onSubmit: (obj) => {
+      const plugin = wrappedPlugin();
+      if (plugin && plugin.onSubmit) {
+        plugin.onSubmit(obj);
+      }
+    },
+    onReset: (obj) => {
+      const plugin = wrappedPlugin();
+      if (plugin && plugin.onReset) {
+        plugin.onReset(obj);
+      }
+    },
+    getSources: (obj) => {
+      const plugin = wrappedPlugin();
+      if (plugin && plugin.getSources) {
+        return plugin.getSources(obj);
+      } else {
+        return Promise.resolve([]);
+      }
+    },
+    data: (obj) => {
+      const plugin = wrappedPlugin();
+      if (plugin && plugin.data) {
+        plugin.data(obj);
+      }
+    },
+  };
+}
+
+function validateItems(items) {
+  // Validate the first item
+  if (items.length > 0) {
+    const item = items[0];
+    const missingFields = [];
+    if (item.href == undefined) {
+      missingFields.push("href");
+    }
+    if (!item.title == undefined) {
+      missingFields.push("title");
+    }
+    if (!item.text == undefined) {
+      missingFields.push("text");
+    }
+
+    if (missingFields.length === 1) {
+      throw {
+        name: `Error: Search index is missing the <code>${missingFields[0]}</code> field.`,
+        message: `The items being returned for this search do not include all the required fields. Please ensure that your index items include the <code>${missingFields[0]}</code> field or use <code>index-fields</code> in your <code>_quarto.yml</code> file to specify the field names.`,
+      };
+    } else if (missingFields.length > 1) {
+      const missingFieldList = missingFields
+        .map((field) => {
+          return `<code>${field}</code>`;
+        })
+        .join(", ");
+
+      throw {
+        name: `Error: Search index is missing the following fields: ${missingFieldList}.`,
+        message: `The items being returned for this search do not include all the required fields. Please ensure that your index items includes the following fields: ${missingFieldList}, or use <code>index-fields</code> in your <code>_quarto.yml</code> file to specify the field names.`,
+      };
+    }
+  }
+}
+
+let lastQuery = null;
+function showCopyLink(query, options) {
+  const language = options.language;
+  lastQuery = query;
+  // Insert share icon
+  const inputSuffixEl = window.document.body.querySelector(
+    ".aa-Form .aa-InputWrapperSuffix"
+  );
+
+  if (inputSuffixEl) {
+    let copyButtonEl = window.document.body.querySelector(
+      ".aa-Form .aa-InputWrapperSuffix .aa-CopyButton"
+    );
+
+    if (copyButtonEl === null) {
+      copyButtonEl = window.document.createElement("button");
+      copyButtonEl.setAttribute("class", "aa-CopyButton");
+      copyButtonEl.setAttribute("type", "button");
+      copyButtonEl.setAttribute("title", language["search-copy-link-title"]);
+      copyButtonEl.onmousedown = (e) => {
+        e.preventDefault();
+        e.stopPropagation();
+      };
+
+      const linkIcon = "bi-clipboard";
+      const checkIcon = "bi-check2";
+
+      const shareIconEl = window.document.createElement("i");
+      shareIconEl.setAttribute("class", `bi ${linkIcon}`);
+      copyButtonEl.appendChild(shareIconEl);
+      inputSuffixEl.prepend(copyButtonEl);
+
+      const clipboard = new window.ClipboardJS(".aa-CopyButton", {
+        text: function (_trigger) {
+          const copyUrl = new URL(window.location);
+          copyUrl.searchParams.set(kQueryArg, lastQuery);
+          copyUrl.searchParams.set(kResultsArg, "1");
+          return copyUrl.toString();
+        },
+      });
+      clipboard.on("success", function (e) {
+        // Focus the input
+
+        // button target
+        const button = e.trigger;
+        const icon = button.querySelector("i.bi");
+
+        // flash "checked"
+        icon.classList.add(checkIcon);
+        icon.classList.remove(linkIcon);
+        setTimeout(function () {
+          icon.classList.remove(checkIcon);
+          icon.classList.add(linkIcon);
+        }, 1000);
+      });
+    }
+
+    // If there is a query, show the link icon
+    if (copyButtonEl) {
+      if (lastQuery && options["copy-button"]) {
+        copyButtonEl.style.display = "flex";
+      } else {
+        copyButtonEl.style.display = "none";
+      }
+    }
+  }
+}
+
+/* Search Index Handling */
+// create the index
+var fuseIndex = undefined;
+var shownWarning = false;
+
+// fuse index options
+const kFuseIndexOptions = {
+  keys: [
+    { name: "title", weight: 20 },
+    { name: "section", weight: 20 },
+    { name: "text", weight: 10 },
+  ],
+  ignoreLocation: true,
+  threshold: 0.1,
+};
+
+async function readSearchData() {
+  // Initialize the search index on demand
+  if (fuseIndex === undefined) {
+    if (window.location.protocol === "file:" && !shownWarning) {
+      window.alert(
+        "Search requires JavaScript features disabled when running in file://... URLs. In order to use search, please run this document in a web server."
+      );
+      shownWarning = true;
+      return;
+    }
+    const fuse = new window.Fuse([], kFuseIndexOptions);
+
+    // fetch the main search.json
+    const response = await fetch(offsetURL("search.json"));
+    if (response.status == 200) {
+      return response.json().then(function (searchDocs) {
+        searchDocs.forEach(function (searchDoc) {
+          fuse.add(searchDoc);
+        });
+        fuseIndex = fuse;
+        return fuseIndex;
+      });
+    } else {
+      return Promise.reject(
+        new Error(
+          "Unexpected status from search index request: " + response.status
+        )
+      );
+    }
+  }
+
+  return fuseIndex;
+}
+
+function inputElement() {
+  return window.document.body.querySelector(".aa-Form .aa-Input");
+}
+
+function focusSearchInput() {
+  setTimeout(() => {
+    const inputEl = inputElement();
+    if (inputEl) {
+      inputEl.focus();
+    }
+  }, 50);
+}
+
+/* Panels */
+const kItemTypeDoc = "document";
+const kItemTypeMore = "document-more";
+const kItemTypeItem = "document-item";
+const kItemTypeError = "error";
+
+function renderItem(
+  item,
+  createElement,
+  state,
+  setActiveItemId,
+  setContext,
+  refresh,
+  quartoSearchOptions
+) {
+  switch (item.type) {
+    case kItemTypeDoc:
+      return createDocumentCard(
+        createElement,
+        "file-richtext",
+        item.title,
+        item.section,
+        item.text,
+        item.href,
+        item.crumbs,
+        quartoSearchOptions
+      );
+    case kItemTypeMore:
+      return createMoreCard(
+        createElement,
+        item,
+        state,
+        setActiveItemId,
+        setContext,
+        refresh
+      );
+    case kItemTypeItem:
+      return createSectionCard(
+        createElement,
+        item.section,
+        item.text,
+        item.href
+      );
+    case kItemTypeError:
+      return createErrorCard(createElement, item.title, item.text);
+    default:
+      return undefined;
+  }
+}
+
+function createDocumentCard(
+  createElement,
+  icon,
+  title,
+  section,
+  text,
+  href,
+  crumbs,
+  quartoSearchOptions
+) {
+  const iconEl = createElement("i", {
+    class: `bi bi-${icon} search-result-icon`,
+  });
+  const titleEl = createElement("p", { class: "search-result-title" }, title);
+  const titleContents = [iconEl, titleEl];
+  const showParent = quartoSearchOptions["show-item-context"];
+  if (crumbs && showParent) {
+    let crumbsOut = undefined;
+    const crumbClz = ["search-result-crumbs"];
+    if (showParent === "root") {
+      crumbsOut = crumbs.length > 1 ? crumbs[0] : undefined;
+    } else if (showParent === "parent") {
+      crumbsOut = crumbs.length > 1 ? crumbs[crumbs.length - 2] : undefined;
+    } else {
+      crumbsOut = crumbs.length > 1 ? crumbs.join(" > ") : undefined;
+      crumbClz.push("search-result-crumbs-wrap");
+    }
+
+    const crumbEl = createElement(
+      "p",
+      { class: crumbClz.join(" ") },
+      crumbsOut
+    );
+    titleContents.push(crumbEl);
+  }
+
+  const titleContainerEl = createElement(
+    "div",
+    { class: "search-result-title-container" },
+    titleContents
+  );
+
+  const textEls = [];
+  if (section) {
+    const sectionEl = createElement(
+      "p",
+      { class: "search-result-section" },
+      section
+    );
+    textEls.push(sectionEl);
+  }
+  const descEl = createElement("p", {
+    class: "search-result-text",
+    dangerouslySetInnerHTML: {
+      __html: text,
+    },
+  });
+  textEls.push(descEl);
+
+  const textContainerEl = createElement(
+    "div",
+    { class: "search-result-text-container" },
+    textEls
+  );
+
+  const containerEl = createElement(
+    "div",
+    {
+      class: "search-result-container",
+    },
+    [titleContainerEl, textContainerEl]
+  );
+
+  const linkEl = createElement(
+    "a",
+    {
+      href: offsetURL(href),
+      class: "search-result-link",
+    },
+    containerEl
+  );
+
+  const classes = ["search-result-doc", "search-item"];
+  if (!section) {
+    classes.push("document-selectable");
+  }
+
+  return createElement(
+    "div",
+    {
+      class: classes.join(" "),
+    },
+    linkEl
+  );
+}
+
+function createMoreCard(
+  createElement,
+  item,
+  state,
+  setActiveItemId,
+  setContext,
+  refresh
+) {
+  const moreCardEl = createElement(
+    "div",
+    {
+      class: "search-result-more search-item",
+      onClick: (e) => {
+        // Handle expanding the sections by adding the expanded
+        // section to the list of expanded sections
+        toggleExpanded(item, state, setContext, setActiveItemId, refresh);
+        e.stopPropagation();
+      },
+    },
+    item.title
+  );
+
+  return moreCardEl;
+}
+
+function toggleExpanded(item, state, setContext, setActiveItemId, refresh) {
+  const expanded = state.context.expanded || [];
+  if (expanded.includes(item.target)) {
+    setContext({
+      expanded: expanded.filter((target) => target !== item.target),
+    });
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+  // means that long search terms mixed with large index gets very slow
+  //
+  // This injects a subIndex that will be used once the terms get long enough
+  // Usually making this subindex is cheap since there will typically be
+  // a subset of results matching the existing query
+  if (subSearchFuse !== undefined && query.startsWith(subSearchTerm)) {
+    // Use the existing subSearchFuse
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diff --git a/_quarto.yml b/_quarto.yml
new file mode 100644
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--- /dev/null
+++ b/_quarto.yml
@@ -0,0 +1,40 @@
+project:
+  type: book
+
+book:
+  title: "Introduction to R with Tidyverse"
+  author: "Sophie Lee"
+  date: "06/15/2024"
+  repo-url: https://github.com/sophie-a-lee/Introduction_R_Tidyverse_course
+  downloads: [pdf]
+  sharing: [twitter]
+  navbar:
+    right: 
+      - icon: github
+        href: https://github.com/sophie-a-lee/
+        aria-label: Github
+      - icon: book
+        href: https://scubed.rbind.io/
+        aria-label: Website
+      - icon: twitter
+        href: https://x.com/SophieStats10
+        aria-label: Twitter
+  chapters:
+    - index.qmd
+    - session1_notes.qmd
+    - session2_notes.qmd
+    - session3_notes.qmd
+    - session4_notes.qmd
+    - session5_notes.qmd
+appendices: 
+  - data_description.qmd
+  - exercise_solutions.qmd
+
+format:
+  html:
+    theme: cosmo
+  pdf:
+    documentclass: scrreprt
+
+
+
diff --git a/data_description.qmd b/data_description.qmd
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--- /dev/null
+++ b/data_description.qmd
@@ -0,0 +1,45 @@
+# Data description {.unnumbered}
+
+## What is 'CSP'?
+The data we will be using throughout this course relates to the Core Spending Power (CSP) of English local authorities between 2015 and 2020. This is a measure of the resources available to local authorities in England to fund service delivery. The CSP is broken down into several components, presented as variables in the data. These components include:
+
+- Settlement Funding Assessment (`sfa`)
+- Compensation for under-indexing the business rates multipler (`under_index`)
+- Income from council tax (`ct_total`)
+- New Homes Bonus (`nhb`)
+- Rural Services Delivery Grant (`rsdg`)
+
+Spending power is given in millions of pounds (£). The data were provided by the UK government's Department for Levelling Up, Housing and Communities. Full guidance on the data can be found on the [Department's website](https://www.gov.uk/government/publications/explanatory-note-on-core-spending-power-provisional-local-government-finance-settlement-2024-to-2025/explanatory-note-on-core-spending-power-provisional-local-government-finance-settlement-2024-to-2025). A brief description of the variables included in the data are given below.
+
+## Descriptions of variables
+
+### Identifier variables
+Each dataset contains a unique identifier code variable, `ons_code`. This is a code given by the Government's Office for National Statistics (ONS), and is used to join different datasets. There is also an `authority` variable which contains the local authority name (to see where each local authority lies on a map, you can visit the [Government's geoportal website](https://geoportal.statistics.gov.uk/documents/cb64eeb1b0a74e5ca277f9fac58500f4/explore)).
+
+### Regions of England
+In addition to each local authority's unique code and name, we are given the region that they lie within. England is separated into 9 regions (shown on [this map](https://geoportal.statistics.gov.uk/documents/bfe6f7099f9e4cc59f8064962959bfb5/explore)) which are given as acronyms in the data. These are:
+
+- `L` = London
+- `NW` = North West
+- `NE` = North East
+- `YH` = Yorkshire and the Humber
+- `WM` = West Midlands
+- `EM` = East Midlands
+- `EE` = East England
+- `SW` = South West
+- `SE` = South East
+
+### Settlement Funding Assessment (SFA)
+The Settlement Funding Assessment (`sfa` in the data) is the baseline funding level of local authorities, and includes the Revenue Support Grant (a central government grant given to local authorities).
+
+### Under-indexing business rate multipliers
+The `under_index` variable is given to compensate local authorities that under-indexed business rate multipliers in previous years (i.e. those that used a measure of inflation that was lower than that should have been used).
+
+### Council tax
+Council tax (`ct_total`) is the income made by each local authority from council tax. In England, the amount of council tax charged to residents is set by each local authority to make up additional revenue needed to cover planned spending.
+
+### New Homes Bonus
+The `nhb` variables is the funding received as part of the New Homes Bonus, a government inncentive to encourage local authorities to promote new housing delevopment.
+
+### Rural Services Delivery Grant 
+The `rsdg` variable is funding received as part of the Rural Services Delivery Grant, provided to rural councils to recognise additional costs in these areas.
diff --git a/exercise solutions.qmd b/exercise solutions.qmd
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--- /dev/null
+++ b/exercise solutions.qmd	
@@ -0,0 +1,353 @@
+# Exercise solutions {.unnumbered}
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE, collapse = TRUE, message = FALSE)
+
+pacman::p_load(tidyverse)
+
+csp_2020 <- read_csv("data/CSP_2020.csv")
+
+csp_long2 <- read_csv("data/CSP_long_201520.csv")
+```
+
+## Exercise 1
+1.	Open a new script file if you have not already done so.
+2.	Save this script file into an appropriate location.
+
+## Solutions
+1. To open a new R script, click the ![new file icon](images/open_shortcut.png) icon and select 'R script'.
+2. Save this file by following **File -> Save as...** from the drop-down menu, selecting the folder you are working from in this course, and giving the file an appropriate name.
+
+
+## Exercise 2
+1. Add your name and the date to the top of your script file (hint: comment this out so R does not try to run it)
+2.	Use R to calculate the following calculations. Add the result to the same line of the script file in a way that ensures there are no errors in the code.
+  a. $64^2$
+  b. $3432 \div 8$
+  c. $96 \times 72$
+
+When you have finished this exercise, select the entire script file (using `Ctrl + a` on windows or `Command + a` on Mac) and run it to ensure there are no errors in the code.
+
+## Solutions
+1. Add a `#` symbol to the script file before printing your name and the date, 
+
+2. After running the calculation, copy and paste the result after a `#` symbol to ensure there are no errors:
+
+```{r exercise 2 calcs}
+64 ^ 2 # 4096
+3432 / 8 # 429
+96 * 72 # 6912
+```
+
+
+## Exercise 3
+1. How many local authorities were included in the London region?
+
+2. Give three different ways that it would be possible to select all spend variables (sfa_2020, nhb_2020, etc.) from the CSP_2020 dataset.
+
+3. Create a new tibble, `em_2020`, that just includes local authorities from the East Midlands (EM) region.
+  a. How many local authorities in the East Midlands had an SFA of between £5 and 10 million?
+  b. Create a new variable with the total overall spend in 2020 for local authorities in the East Midlands.
+
+
+## Solutions
+1. First `filter` the data to return only rows which belong to the London region, then count the number of rows in this subgroup:
+
+```{r n local authorities in London}
+csp_2020 %>% 
+  filter(region == "L") %>% 
+  count()
+```
+
+2. There are many different ways to select variables from a dataset. For a list of selection helpers, check the helpfile `?tidyr_tidy_select`. Some example include:
+
+```{r selecting variables, eval = FALSE}
+# Using the : symbol to return consecutive columns
+
+# By variable name:
+select(csp_2020, sfa_2020:rsdg_2020)
+
+# Or by column number:
+select(csp_2020, 4:9)
+
+# Returning all variables with names ending "_2020"
+select(csp_2020, ends_with("_2020"))
+
+# Return all numeric variables
+select(csp_2020, where(is.numeric))
+
+# Return all variables that are not character 
+select(csp_2020, where(!is.character))
+```
+
+3. To create a new tibble, use `filter` to select the subgroup where region is "EM", and attach as an object using the `<-` symbol 
+
+```{r create em tibble}
+em_2020 <- filter(csp_2020, region == "EM")
+```
+
+a. Use `filter` to select the subgroup and then `count` the number of rows:
+
+```{r select em between 5 and 10}
+em_2020 %>% 
+  filter(between(sfa_2020, 5, 10)) %>% 
+  count()
+```
+
+b. Use the `mutate` function to create a new variable from the existing ones. **Hint:** If you are not sure of the variable names in the data, use the `names` function and copy them from the console:
+
+```{r em total spend}
+names(em_2020)
+
+
+em_2020 <- em_2020 %>% 
+  mutate(total_spend = sfa_2020 + under_index_2020 + ct_total_2020 + 
+           nhb_2020 + nhb_return_2020 + rsdg_2020)
+```
+
+## Exercise 4
+1.	Create a data frame with the minimum, maximum and median total spend per year for each region. 
+2.	Produce a frequency table containing the number and percentage of local authorities in each region.
+3.	Convert the data object `csp_long2` back into wide format, with one row per local authority and one variable per total spend per year (**HINT:** start by selecting only the variables you need from the long data frame). Use the help file `?pivot_wider` and `vignette("pivot")` for more hints.
+4.	Using your new wide data frame, calculate the difference in total spending for each local authority between 2015 and 2020. How many local authorities have had an overall reduction in spending since 2015?
+
+## Solutions
+1. Use the `summarise` function after grouping by the `year` and `region` variables:
+
+```{r summarise total spend per region per year}
+csp_long2 %>% 
+  group_by(region, year) %>% 
+  summarise(min_spend = min(total_spend),
+            max_spend = max(total_spend),
+            median_spend = median(total_spend)) %>% 
+  ungroup()
+```
+
+2. To calculate the percentage of local authorities in each region, we need the total number in each region and the overall number of local authorities:
+
+```{r frequency table regions}
+# Use the csp_2020 data as only require one row per local authority
+csp_2020 %>% 
+  # Begin by calculating number of local authorities per region
+  group_by(region) %>% 
+  # Count number of rows in each group
+  summarise(n_la_region = n()) %>% 
+  ungroup() %>% 
+  # Create a new variable with the total number of local authorities (the sum)
+  mutate(n_la_overall = sum(n_la_region),
+         # Calculate the percentage (and round to make easier to read)
+         perc_la_region = round((n_la_region / n_la_overall) * 100, 2)) %>% 
+  # Remove the total local authority column
+  select(-n_la_overall)
+```
+
+3. Use the `pivot_wider` function, use the year to set the new variable names suffix (`names_from = `), add a prefix to avoid variable names beginning with a number (`names_prefix = `), and take the `values_from` the current `total_spend` column:
+
+```{r pivot csp wider}
+csp_total_wide <- csp_long2 %>% 
+  # Select variables to keep
+  select(ons_code:year, total_spend) %>% 
+  pivot_wider(names_from = year,
+              names_prefix = "total_spend_",
+              values_from = total_spend)
+```
+
+4. Begin by using `mutate` to create a variable with the difference between total spend 2015 - 2020. Use `filter` to return rows where there is a reduction in spend, `count` the number of rows:
+
+```{r number of local authorities with reduction}
+csp_total_wide %>% 
+  mutate(total_diff = total_spend_2020 - total_spend_2015) %>% 
+  filter(total_diff < 0) %>% 
+  count()
+```
+
+
+## Exercise 5
+1.	Create a new data object containing the 2020 CSP data without the Greater London Authority observation. Name this data frame `csp_nolon_2020`.
+2.	Using the `csp_nolon_2020` data, create a data visualisation to check the distribution (or shape) of the SFA variable.
+3.	Based on the visualisation above, create a summary table for the SFA variable containing the minimum and maximum, and appropriate measures of the centre/average and spread.
+
+## Solutions
+1. Create a new object using the `<-` symbol, use `filter` to remove the duplicate row:
+
+```{r csp_nolon_2020}
+csp_nolon_2020 <- filter(csp_2020, authority != "Greater London Authority")
+```
+
+2. Histograms are used to check the distribution of numeric variables:
+
+```{r sfa histogram}
+ggplot(data = csp_nolon_2020) +
+  geom_histogram(aes(x = sfa_2020))
+```
+
+3.	The histogram shows that the `sfa_2020` variable is very skewed, therefore the `median` and `IQR` are the most appropriate measures of centre and spread:
+
+```{r sfa_2020 summary table}
+summarise(csp_nolon_2020,
+          min_sfa = min(sfa_2020),
+          max_sfa = max(sfa_2020),
+          median_sfa = median(sfa_2020),
+          iqr_sfa = IQR(sfa_2020))
+```
+
+## Exercise 6
+1. What is the problem with the following code? Fix the code to change the shape of all the points.
+
+```{r aesthetic exercise, eval = FALSE}
+ggplot(csp_nolon_2020) + 
+  geom_point(aes(x = sfa_2020, y = ct_total_2020, shape = "*"))
+```
+
+2. Add a line of best fit to the scatterplot showing the relationship between SFA and council tax total (hint: use ```?geom_smooth```).
+
+3.	Add a line of best fit for each region (hint: make each line a different colour).
+
+## Solutions
+1. Only aesthetics determined by variables in the data should lie inside the `aes` function, the `shape` argument should be outside of this:
+
+```{r aesthetic solution}
+ggplot(csp_nolon_2020) + 
+  geom_point(aes(x = sfa_2020, y = ct_total_2020), shape = "*")
+```
+
+2. The function `geom_smooth` adds a line of best fit, make sure to set `method = lm` to fit a linear trend:
+
+```{r scatter with line of best fit}
+ggplot(data = csp_nolon_2020, aes(x = ct_total_2020, y = sfa_2020)) +
+  geom_point() +
+  geom_smooth(method = "lm")
+```
+
+**Hint:** To reduce repetitive coding, setting `aes` in the `ggplot` function applies these to the entire object.
+
+3. A line of best fit for each group simply requires adding this to the `aes` function as a colour:
+
+```{r scatter with line of best fit by region}
+ggplot(data = csp_nolon_2020, 
+       aes(x = ct_total_2020, y = sfa_2020, colour = region)) +
+  geom_point() +
+  geom_smooth(method = "lm")
+```
+
+
+## Exercise 7
+Use an appropriate data visualisation to show how the total spend in each local authority has changed over the years between 2015 and 2020. Choose a visualisation that shows these trends over time and allows us to compare them between regions.  
+
+## Solution
+The most appropriate plot to show a change in variable over time is a line graph (with year on the x-axis and spend on the y-axis). To compare these between regions, we could set the colour of these lines, but as there are so many local authorities, this would overload the graph and make it hard to compare. As an alternative, we can facet this graph by region to show the line graphs on the same scale on the same output.
+
+Be sure to set appropriate axis labels, font sizes, etc. 
+
+```{r region total spend line graph}
+# Remove the Greater London Authority duplicate
+csp_long2 %>% 
+  filter(authority != "Greater London Authority") %>% 
+  ggplot() + 
+  # Need to add a group to know what each line represents
+  geom_line(aes(x = year, y = total_spend, group = ons_code,
+                # OPTIONAL: colour by region to make it prettier!
+                colour = region)) +
+  facet_wrap( ~ region) + 
+  labs(x = "Year", y = "Total core spending power (millions)") +
+  # Add theme_light to make the background a nicer colour
+  theme_light() + 
+  # Rotate the x-axis labels to avoid overlap
+  theme(axis.text.x.bottom = element_text(angle = 45),
+        # Remove the legend (not needed, we have labels on the facets)
+        legend.position = "none")
+
+```
+
+
+## Exercise 8 
+Create an RMarkdown file that creates a html report describing the trends in core spending power in English local authorities between 2015 and 2020. Your report should include:
+
+- A summary table of the total spending per year per region
+- A suitable visualisation showing how the total annual spending has changed over this period, compared between regions
+- A short interpretation of the table and visualisation
+
+**Note:** You are not expected to be an expert in this data! Interpret these outputs as you would any other numeric variable measured over time.
+
+## Solutions
+There are many different correct solutions to this exercise. All RMarkdown files should begin with a YAML header similar to the one below:
+
+````{verbatim}
+---
+title: "Core spending power in English local authorities, 2015 - 2020"
+author: Sophie Lee
+output: html_document
+---  
+````
+
+Next, you may have a code chunk that sets up the global chunk options, loads any packages you needed, and loads the data that we will be using for the report. For example:
+
+```` {verbatim}
+```{r setup, include = FALSE}
+# Set global chunk options to not show R code or messages
+knitr::opts_chunk$set(echo = FALSE, message = FALSE)
+
+# Load the tidyverse package
+library(tidyverse)
+
+# Load the long dataset
+csp_long2 <- read_csv("data/CSP_long_201520.csv")
+```
+````
+You may have began with an introduction using RMarkdown syntax:
+
+````{verbatim}
+# Introduction
+The following report will investigate the trends in core spending power 
+across England between 2015 and 2020. All values are give in millions 
+of pounds. 
+
+The core spending power was made up of the following provisions:
+
+- Settlement funding assessment (SFA)
+- Compensation for under-indexing the business rates multipliers
+- council tax 
+- New homes bonus
+- New homes bonus returned funding
+- Rural Services Delivery Grant (RSDG)
+````
+
+Followed by a summary table, created using `summarise` and displayed using `kable`:
+
+````{verbatim}
+# Total core spending power by region
+Below is a summary table containing the total core spending power per year 
+per region, given in millions of £:
+
+```{r csp total summary table}
+csp_long2 %>% 
+  group_by(region, year) %>% 
+  summarise(min_spend = min(total_spend),
+            max_spend = max(total_spend),
+            median_spend = median(total_spend),
+            iqr_spend = IQR(total_spend)) %>% 
+  ungroup() %>% 
+  knitr::kable(.,
+               col.names = c("Region", "Year", "Minimum", 
+                             "Maximum", "Median", "IQR"))
+```
+````
+
+Then an additional code chunk producing a faceted line chart, similar to the one in Exercise 7:
+
+````{verbatim}
+```{r}
+csp_long2 %>% 
+  filter(authority != "Greater London Authority") %>% 
+  ggplot() + 
+  geom_line(aes(x = year, y = total_spend, group = ons_code,
+                colour = region)) +
+  facet_wrap( ~ region) + 
+  labs(x = "Year", y = "Total core spending power (millions)") +
+  theme_light() + 
+  theme(axis.text.x.bottom = element_text(angle = 45),
+        legend.position = "none")
+
+```
+````
+
diff --git a/index.qmd b/index.qmd
new file mode 100644
index 0000000..800bebc
--- /dev/null
+++ b/index.qmd
@@ -0,0 +1,23 @@
+# Welcome!
+
+Welcome to the course materials for the **Introduction to R with Tidyverse** course. 
+
+This course is designed to equip you with the essential skills to leverage the power of R and Tidyverse for their work. The course begins with a gentle introduction to the user-friendly RStudio interface and the basics of the R coding language, or syntax. This makes it ideal for anyone with little or no prior coding experience, or those looking for a refresher of the basics.
+
+Through this course, you will learn how to manipulate, transform, and clean data efficiently, and how to create compelling visualisations to communicate your findings effectively. Throughout the course, we will discuss best practices for reproducible coding. 
+
+:::{.callout-tip}
+# Style tip
+
+Throughout these notes, you will also see boxes like this containing 'style tips'. These ensure that your code follows the [Tidyverse style guide](https://style.tidyverse.org/), making it as consistent and readable as possible.
+:::
+
+## Data used for the course
+The examples and exercises in these materials are based on real world data. This data relates to the Core Spending Power (CSP) of English local authorities between 2015 and 2020.
+
+Data for this course can be downloaded from the `data` folder of this course's [repository](https://github.com/sophie-a-lee/Introduction_R_Tidyverse_course).
+
+For more information about this data, including variable descriptions and sources, see [the appendix](data_description.qmd).
+
+## License
+I believe that science should not be behind a paywall, that is why these materials are available for free online, licensed under a [CC BY-SA licence](https://creativecommons.org/licenses/by-sa/4.0/).
\ No newline at end of file
diff --git a/session1_notes.Rmd b/session1_notes.qmd
similarity index 80%
rename from session1_notes.Rmd
rename to session1_notes.qmd
index 595ce98..7bcbf67 100644
--- a/session1_notes.Rmd
+++ b/session1_notes.qmd
@@ -1,33 +1,10 @@
----
-title: "Introduction to R with Tidyverse"
-subtitle: "Session 1: Introduction to R and RStudio"
-author: Sophie Lee
-fontfamily: lmodern
-output:   
-  pdf_document:
-    highlight: tango
-    toc: TRUE
-    latex_engine: xelatex
-    fig_height: 4
-    fig_width: 6
-    fig_caption: FALSE
-header-includes:
-    - \usepackage{setspace}\onehalfspacing
-    - \setlength{\parskip}{12pt}
-fontsize: 12pt    
-mainfont: Cambria
-sansfont: Cambria
-linkcolor: blue
-url_color: blue
----
+# Session 1: Introduction to R and RStudio
 
 ```{r setup, include=FALSE}
 knitr::opts_chunk$set(echo = TRUE, collapse = TRUE)
 ```
 
-\newpage
-
-# Chapter 1: The RStudio interface
+## The RStudio interface
 
 There are a number of software packages based on the R programming language aimed at making writing and running analyses easier for users. They all run R in the background but look different and contain different features. 
 
@@ -37,22 +14,37 @@ Before installing RStudio, we must ensure that R is downloaded onto the machine.
 
 Rstudio is also free to download from the [**Posit**](https://posit.co/) website.
 
-### 1.1 The RStudio console window
+#### The RStudio console window
 The screenshot below shows the RStudio interface which comprises of four windows: 
 
 ![RStudio interface](images/rstudio_ide.png)
-\newpage
 
 **Window A: R script files**
 
 All analysis and actions in R are carried out using the R syntax language. R script files allow you to write and edit code before running it in the console window. 
 
+:::{.callout-tip}
+### Style tip
+
+Limit script files to 80 characters per line to ensure it is readable. 
+
+RStudio has an option to add a margin that makes this easier to adhere to. Under the *Tools* drop-down menu, select *Global options*. Select *Code* from the list on the right, then under the *Display* tab, tick the *Show margin* box.
+:::
+
 If this window is not visible, create a new script file using *File -> New File -> R Script* from the drop-down menus or clicking the ![New file icon](images/new_file_shortcut.png) icon above the console and selecting *R Script*. This will open a new, blank script file. More than one script file can be open at the same time.
 
 Code entered into the script file does not run automatically. To run commands from the script, highlight the code and click the ![Run icon](images/run_shortcut.png) icon above the top right corner of the script window (this can be carried out by pressing `Ctrl + Enter` in Windows or `Command + Enter` on a Mac computer). More than one command can be run at the same time by highlighting all of them.
 
 The main advantage of using the script file rather than entering the code directly into the console is that it can be saved, edited and shared. To save a script file, use *File -> Save As…* from the drop down menu, or click the ![save icon](images/save_shortcut.png) icon at the top of the window. It is important to save the script files at regular intervals to avoid losing work. Once the script file has been saved, we can also use the keyboard shortcuts `Ctrl + s` on Windows and `Command + s` on Mac to save the latest script file.
 
+:::{.callout-tip}
+### Style tip
+
+Script file names should be meaningful, lower case, and end in `.R`. Avoid using special characters in file names, including spaces. Use `_` instead of spaces.
+
+Where files should be run in a specific order, prefix the file name with numbers.
+:::
+
 Past script files can be opened using *File -> Open File…* from the drop-down menu or by clicking the ![open icon](images/open_shortcut.png) icon and selecting a `.R` file. The keyboard shortcut to open an existing script file is `Ctrl + o` on Windows, and `Command + o` on Macs.
 
 
@@ -62,7 +54,6 @@ The R console window is where all commands run from the script file, results (ot
 
 Every time a new R session is opened, details about version and citations of R will be given by default. To clear text from the console window, use the keyboard shortcut `control + l` (this is the same for both Windows and Mac users). Be aware that this clears all text from the console, including any results. Before running this command, check that any results can be replicated within the script file. 
 
-\newpage
 
 **Window C: Environment and history**
 
@@ -73,32 +64,38 @@ This window lists all data and objects currently loaded into R. More details on
 This window has many potential uses: graphics are displayed and can be saved from here, and R help files will appear here. This window is only available in the RStudio interface and not in the basic R package.
 
 
-## Exercise 1
+### Exercise 1 {.unnumbered}
 1.	Open a new script file if you have not already done so.
 2.	Save this script file into an appropriate location.
 
-\newpage
 
-# Chapter 2: R syntax
+## R syntax
 All analyses within R are carried out using **syntax**, the R programming language. It is important to note that R is case-sensitive, so always ensure that you use the correct combination of upper and lower case letters when running functions or calling objects.
 
 Any text written in the R console or script file can be treated the same as text from other documents or programmes: text can be highlighted, copied and pasted to make coding more efficient. 
 
 When creating script files, it is important to ensure they are clear and easy to read. Comments can be added to script files using the `#` symbol. R will ignore any text following the `#` on the same line. 
 
-**Hash tip 1:** Combining `#` and `-` creates sections within a script file, making them easier to navigate and organise. 
+::: {.callout-tip}
+### Style tip
+
+Combining `#` and `-` creates sections within a script file, making them easier to navigate and organise. 
 
 For example:
 
-```{r section style, eval = FALSE}
+```{r section style}
 # Load data ----------
 
 # Tidy data ----------
 ```
+:::
+
 
-These section headings will be listed at the bottom of the script file window. Selecting one of these headings from the list will send your cursor to the section heading.
+:::{.callout-note}
+### Helpful hint
 
-**Hash tip 2:** To comment out chunks of code, highlight the rows and use the keyboard shortcut `ctrl + shift + c` on Windows, and `Command + shift + c` on Mac.
+To comment out chunks of code, highlight the rows and use the keyboard shortcut *ctrl + shift + c* on Windows, and *Command + shift + c* on Mac
+:::
 
 The choice of brackets in R coding is particularly important as they all have different functions:
 
@@ -108,7 +105,25 @@ The choice of brackets in R coding is particularly important as they all have di
 
 All standard notation for mathematical calculations (`+`, `-`, `*`, `/`, `^`, etc.) are compatible with R. At its simplest level, R is just a very powerful calculator!
 
-## Exercise 2
+::: {.callout-tip}
+### Style tip
+
+Although R will work whether a space is added before/after a mathematical operator, the [style guide](https://style.tidyverse.org/syntax.html) recommends to add them surrounding most mathematical operations (`+`, `-`, `*`, `/`), but not around `^`. 
+
+For example:
+
+```{r space style, eval = FALSE}
+# Stylish code
+1959 - 683
+(351 + 457)^2 - (213 + 169)^2
+
+# Un-stylish code
+1959-683
+(351+457)^2 - (213 + 169) ^ 2
+```
+:::
+
+### Exercise 2 {.unnumbered}
 1.	Add your name and the date to the top of your script file (hint: comment this out so R does not try to run it)
 2.	Use R to calculate the following calculations. Add the result to the same line of the script file in a way that ensures there are no errors in the code.
   a. $64^2$
@@ -117,14 +132,18 @@ All standard notation for mathematical calculations (`+`, `-`, `*`, `/`, `^`, et
   
 When you have finished this exercise, select the entire script file (using `ctrl + a` on windows or `Command + a` on Mac) and run it to ensure there are no errors in the code.
 
-\newpage
-
-# Chapter 3: R objects and functions
+## R objects and functions
 
-## 3.1 Objects
+### Objects
 One of the main advantages to using R over other software packages such as SPSS is that more than one dataset can be accessed at the same time. A collection of data stored in any format within the R session is known as an **object**. Objects can include single numbers, single variables, entire datasets, lists of datasets, or even tables and graphs.
 
-Objects are defined in R using the `<-` symbol. For example, 
+:::{.callout-tip}
+### Style tip
+
+Object names should only contain lower case letters, numbers and `_` (instead of a space to separate words). The should be meaningful and concise.
+:::
+
+Objects are defined in R using the `<-` or `=` symbols. For example, 
 
 ```{r assign qone}
 object_1 <- 81
@@ -132,6 +151,12 @@ object_1 <- 81
 
 Creates an object in the environment named `object_1`, which takes the value `81`. This will appear in the environment window of the console (window C from the interface shown earlier).
 
+:::{.callout-tip}
+### Style tip
+
+Although both work, use `<-` for assignment, not `=`.
+:::
+
 To retrieve an object, type its name into the script or console and run it. This object can then be included in functions or operations in place of the value assigned to it:
 
 ```{r qone, collapse = TRUE}
@@ -150,11 +175,11 @@ The `[1]` that appears at the beginning of each output line indicates that this
 
 For example, if we had an object with 6 elements and when called the first line contained the first 5 elements, each line would begin with `[1]` and `[6]` respectively.
 
-## 3.2 Functions
+### Functions
 
 **Functions** are built-in commands that allow R users to run analyses. All functions require the definition of arguments within round brackets `()`. Each function requires different information and has different arguments that can be used to customise the analysis. A detailed list of these arguments and a description of the function can be found in the function's associated **help file**.
 
-## 3.3 Help files
+### Help files
 
 Each function that exists within R has an associated help file. RStudio does not require an internet connection to access these help files if the function is available in the current session of R.
 
@@ -171,7 +196,7 @@ Help files contain the following information:
 -	Examples: example code with applications of the function
  
 
-## 3.4 Error and warning messages
+### Error and warning messages
 Where a function or object has not been correctly specified, or their is some mistake in the syntax that has been sent to the console, R will return an error message. These messages are generally informative and include the location of the error.
 
 The most common errors include misspelling functions or objects:
@@ -197,30 +222,37 @@ When working within the R console, if an incomplete command is run, a `+` symbol
 One of the benefits of using RStudio rather than the basic R package is that it will suggest object or function names after typing the first few letters. This avoids spelling mistakes and accidental errors when running code. To accept the suggestion, either click the correct choice with your mouse or use the `tab` button on your keyboard.
 
 
-## 3.5 Cleaning the environment
+### Cleaning the environment
 To remove objects from the RStudio environment, we can use the `rm` function. This can be combined with the `ls()` function, which lists all objects in the environment, to remove all objects currently loaded:
 
 ```{r remove everything, eval = FALSE}
 rm(list = ls())
 ```
 
-**WARNING!** There are no undo and redo buttons for R syntax. The `rm` function will permanently delete objects from the environment. The only way to reverse this is to re-run the code that created the objects originally from the script file.
+:::{.callout-warning} 
+There are no undo and redo buttons for R syntax. The `rm` function will permanently delete objects from the environment. The only way to reverse this is to re-run the code that created the objects originally from the script file.
+:::
 
-
-## 3.6 R packages
+### R packages
 R packages are a collection of functions and datasets developed by R users that expand existing R capabilities or add completely new ones. Packages allow users to apply the most up-to-date methods shortly after they are developed, unlike other statistical software packages that require an entirely new version. 
 
 
-### 3.6.1 Installing packages from CRAN
+#### Installing packages from CRAN
 The quickest way to install a package in R is by using the `install.packages` function. This sends RStudio to the online repository of tested and verified R packages (known as [CRAN](https://cran.r-project.org/)) and downloads the package files onto the machine you are currently working from in temporary files. Ensure that the package you wish to install is spelled correctly and surrounded by `''`.
 
-**WARNING:** The `install.packages` function requires an internet connection, and can take a long time if the package has a lot of dependent packages that also need downloading. 
+:::{.callout-warning} 
+The `install.packages` function requires an internet connection, and can take a long time if the package has a lot of dependent packages that also need downloading. 
 
 This process should only be carried out the first time a package is used on a machine, or when a substantial update has taken place, to download the latest version of the package.
+:::
 
-### 3.6.2 Loading packages to an R session
+#### Loading packages to an R session
 Every time a new session of RStudio is opened, packages must be reloaded. To load a package into R (and gain access to the associated functions and data), use the `library` function. 
 
 Loading a package does not require an internet connection, but will only work if the package has already been installed and saved onto the computer you are working from. If you are unsure, use the function `installed.packages` to return a list of all packages that are loaded onto the machine you are working from.
 
-**Top tip:** Add your `library` function at the beginning of your script file. This reminds you to re-load packages when opening a new R session, and reduces the chance of error messages from functions requiring these packages.
+:::{.callout-tip}
+### Style tip
+
+Add your `library` function at the beginning of your script file. This reminds you to re-load packages when opening a new R session, and reduces the chance of error messages from functions requiring these packages.
+:::
\ No newline at end of file
diff --git a/session2_notes.Rmd b/session2_notes.qmd
similarity index 88%
rename from session2_notes.Rmd
rename to session2_notes.qmd
index 6c6a644..ef439db 100644
--- a/session2_notes.Rmd
+++ b/session2_notes.qmd
@@ -1,34 +1,14 @@
----
-title: "Introduction to R with Tidyverse"
-subtitle: "Session 2: Introduction to tidyverse and data wrangling"
-author: "Sophie Lee"
-fontfamily: lmodern
-output:   
-  pdf_document:
-    highlight: tango
-    toc: TRUE
-    latex_engine: xelatex
-    fig_caption: FALSE
-header-includes:
-    - \usepackage{setspace}\onehalfspacing
-    - \setlength{\parskip}{12pt}
-fontsize: 12pt    
-mainfont: Cambria
-sansfont: Cambria
-linkcolor: blue
-url_color: blue
----
+# Session 2: Introduction to tidyverse and data wrangling
 
 ```{r setup, include=FALSE}
 knitr::opts_chunk$set(echo = TRUE, collapse = TRUE, message = FALSE)
 
 library(tidyverse)
 ```
-\newpage
 
-# Chapter 4: Opening and exploring data
+## Opening and exploring data
 
-## 4.1 Styles of R coding
+### Styles of R coding
 Up to this point, we have not thought about the style of R coding we will be using. There are different approaches to R coding that we can use, they can be thought of as different dialects of the R programming language. 
 
 The choice of R 'dialect' depends on personal preference. Some prefer to use the 'base R' approach that does not rely on any packages that may need updating, making it a more stable approach. However, base R can be difficult to read for those not comfortable with coding. 
@@ -45,7 +25,9 @@ If you have not done so already, install the tidyverse packages to your machine
 install.packages('tidyverse')
 ```
 
-**WARNING:** This can take a long time if you have never downloaded the tidyverse packages before as there are many dependencies that are required. Do not stress if you get a lot of text in the console! This is normal, but watch out for any error messages.
+:::{.callout-warning}
+This can take a long time if you have never downloaded the tidyverse packages before as there are many dependencies that are required. Do not stress if you get a lot of text in the console! This is normal, but watch out for any error messages.
+:::
 
 Once the tidyverse package is installed, we must load it into the current working session. At the beginning of your script file add the following syntax:
 
@@ -53,15 +35,20 @@ Once the tidyverse package is installed, we must load it into the current workin
 library(tidyverse)
 ```
 
+:::{.callout-tip}
+### Style tip
 
-## 4.2 The working directory
+Begin every script file with the `library` command, loading packages in before any data. This avoids any potential errors arising where functions are called before the necessary package has been loaded into the current session.
+:::
+
+### The working directory
 The working directory is a file path on your computer that R sets as the default location when opening, saving, or exporting documents, files, and graphics. This file path can be specified manually but setting the working directory saves time and makes code more efficient. 
 
 The working directory can be set manually by using the *Session -> Set Working Directory -> Change Directory…* option from the drop-down menu, or the `setwd` function. Both options require the directory to be specified each time R is restarted, are sensitive to changes in folders within the file path, and cannot be used when script files are shared between colleagues.
 
 An alternative approach that overcomes these issues is to create an R project.
 
-### 4.2.1 R projects
+#### R projects
 
 R projects are files (saved with the `.Rproj` extension) that keep associated files (including scripts, data, and outputs) grouped together. An R project automatically sets the working directory relative to its current location, which makes collaborative work easier, and avoids issues when a file path is changed.
 
@@ -69,6 +56,12 @@ Projects are created by using the *File -> New project* option from the drop-dow
 
 When creating a new project, we must choose whether we want to create a new directory or use an existing one. Usually, we will have already set up a folder containing data or other documents related to the analysis we plan to carry out. If this is the case, we are using an existing directory and selecting the analysis folder as the project directory.
 
+:::{.callout-tip}
+### Style tip
+
+Have a clear order to your analysis folder. Consider creating separate folders within a project for input and output data, documentation, and outputs such as graphs or tables.
+:::
+
 ## 4.3 Data input
 
 To ensure our code is collaborative and reproducible, we should strive to store data in formats that can be used across multiple platforms. One of the best ways to do this is to store data as a comma-delimited file (.csv). CSV files can be opened by a range of different softwares (including R, SPSS, STATA and excel), and base R can be used to open these files without requiring additional packages. 
@@ -96,6 +89,12 @@ Other useful functions that help explore a dataset include:
 names(csp_2020)
 ```
 
+:::{.callout-tip}
+### Style tip
+
+Variable names should follow the same style rules as object names: only contain lower case letters, numbers, and use `_` to separate words. They should be meaningful and concise.
+:::
+
 ```{r structure}
 # Display information about the structure of an object
 str(csp_2020)
@@ -117,7 +116,7 @@ tail(csp_2020)
 ```
 
 
-## 4.4 Selecting variables
+### Selecting variables
 Often, our analysis will not require every variable in a downloaded dataset, and we may wish to create a smaller analysis tibble. We may also wish to select individual variables from the tibble to apply functions to them without including the entire dataset. 
 
 To select one or more variable and return them as a new tibble, we can use the `select` function from tidyverse's `dplyr` package.
@@ -177,10 +176,11 @@ It is important to save any changes made to the existing dataset. This can be do
 write_csv(csp_2020, file = "data/csp_2020_new.csv")
 ```
 
+:::{.callout-warning}
 When saving updated tibbles as files, use a different file name to the original raw data. Using the same name will overwrite the original file. We always want a copy of the raw data in case of any errors or issues.
+:::
 
-
-## 4.5 Filtering data
+### Filtering data
 
 The `filter` function, from tidyverse's `dplyr` package allows us to return subgroups of the data based on conditional statements. These conditional statements can include mathematical operators, e.g.  `<=` (less than or equal to), `==` (is equal to), and `!=` (is not equal to), or can be based on conditional functions, e.g. `is.na(variable)` (is missing), `between(a, b)` (number lies between a and b). 
 
@@ -199,12 +199,16 @@ Multiple conditional statements can be added to the same function by separating
 filter(csp_2020, region == "NW", sfa_2020 > 40)
 ```
 
-## 4.6 Pipes
+### Pipes
 When creating an analysis-ready dataset, we often want to combine functions such as `select` and `filter`. Previously, these would need to be carried out separately and a new object would need to be created or overwritten at each step, clogging up the environment. 
 
 In tidyverse, we combine multiple functions into a single process by using the 'pipe' symbol `%>%`, which is read as 'and then' within the code.
 
-**Piping hint:** To save time when piping, use the keyboard shortcut *ctrl + shift + m* for Windows and *Command + shift + m* for Mac to create a pipe.
+:::{.callout-note}
+### Helpful hint
+
+ To save time when piping, use the keyboard shortcut *ctrl + shift + m* for Windows, and *Command + shift + m* for Mac to create a pipe.
+:::
 
 For example, we can return a list of local authority names from the North West region:
 
@@ -217,6 +221,12 @@ csp_2020 %>%
   select(authority)
 ```
 
+:::{.callout-tip}
+### Style tips
+
+When combining multiple functions within a process using pipes, it is good practice to start the code with the data and pipe that into the functions, rather than including it in the function itself.
+:::
+
 The pipe can also be combined with the `filter` function to `count` the number of observations that lie within a subgroup:
 
 ```{r Count NW region}
@@ -228,7 +238,7 @@ csp_2020 %>%
   count()
 ```
 
-## 4.7 Creating new variables
+### Creating new variables
 The function `mutate` from tidyverse's `dplyr` package allows us to add new variables to a dataset, either by manually specifying them or by creating them from existing variables. We can add multiple variables within the same function, separating each with a comma `,`. 
 
 For example, we can create a new variables with the squared settlement funding assessment (`sfa_2020`), and another that recodes the council tax variable (`ct_total_2020`) into a categorical variable with three levels (low: below £5 million, medium: between £5 million and £15 million, and high: above £15 million):
@@ -248,6 +258,12 @@ csp_2020_new <- csp_2020 %>%
                            include_lowest = TRUE))
 ```
 
+:::{.callout-note}
+### Helpful hint
+
+The `c` function takes a list of values separated by commas and returns them as a `vector`. This is useful when a function argument requires multiple values (and we don't want R to move onto the next argument, which is what a comma inside functions usually means).
+:::
+
 The `mutate` function is also useful for reclassifying variables when R did not correctly choose the variable type. In this example, the `region` variable is a grouping variable, but `str(csp_2020)` shows it is recognised by R as a `character`. Grouping variables in R are known as `factors`. To convert the `region` variable to a `factor`, we use the `factor` function inside `mutate`:
 
 ```{r region as factor}
@@ -273,8 +289,7 @@ str(csp_2020_new)
 
 Although there is no real ordering to the regions in England, attaching this order allows us to control how the are displayed in outputs. By default, character variables are displayed in alphabetical order. By adding the order to this variable, we will produce output where the reference region (London) will be displayed first, followed by regions from north to south.
 
-
-## Exercise 3
+### Exercise 3 {.unnumbered}
 
 1. How many local authorities were included in the London region?
 
diff --git a/session3_notes.Rmd b/session3_notes.qmd
similarity index 92%
rename from session3_notes.Rmd
rename to session3_notes.qmd
index 947d180..dc2507a 100644
--- a/session3_notes.Rmd
+++ b/session3_notes.qmd
@@ -1,35 +1,13 @@
----
-title: "Introduction to R with Tidyverse"
-subtitle: "Session 3: Data preparation and manipulation"
-author: "Sophie Lee"
-fontfamily: lmodern
-output:   
-  pdf_document:
-    highlight: tango
-    toc: TRUE
-    latex_engine: xelatex
-    fig_height: 4
-    fig_width: 6
-    fig_caption: FALSE
-header-includes:
-    - \usepackage{setspace}\onehalfspacing
-    - \setlength{\parskip}{12pt}
-fontsize: 12pt    
-mainfont: Cambria
-sansfont: Cambria
-linkcolor: blue
-url_color: blue
----
+# Session 3: Data preparation and manipulation
 
 ```{r setup, include=FALSE}
 knitr::opts_chunk$set(echo = TRUE, collapse = FALSE, message = FALSE)
 library(tidyverse)
 ```
-\newpage
 
-# Chapter 5: Data wrangling and summarising
+## Data wrangling and summarising
 
-## 5.1 Combining two datasets
+### Combining two datasets
 We may need to combine data from different files within R to perform an analysis. For example, in our case we have the core spending power for each year between 2015 and 2020. If our analysis required comparing this spending over the time period, we would need to combine these files together.
 
 Before the data can be combined, it must be loaded into R. We will begin combining data from 2015 and 2016, then extend this to the entire period. 
@@ -58,7 +36,7 @@ csp_201516 <- full_join(CSP_2015, CSP_2016,
                         by = c("ons_code", "authority", "region"))
 ```
 
-## 5.2 Joining multiple datasets
+### Joining multiple datasets
 R's joining functions can only be applied to two datasets at a time. To combine all 6 core spending power datasets from 2015 to 2020 in this way would require a lot of repetitive coding (which we want to avoid where necessary). 
 
 An alternative approach would be to automate this process by using **functional programming**, implemented using tidyverse's `purrr` package.
@@ -93,7 +71,7 @@ csp_201520 <- list.files(path = "data", pattern = "CSP_20") %>%
   reduce(full_join, by = c("ons_code", "authority", "region"))
 ```
 
-## 5.3 Transforming data
+### Transforming data
 
 The dataset containing core spending power in England between 2015 and 2020 is currently in what is known as **wide format**. This means there is a variable per measure per year, making the object very wide. 
 
@@ -148,7 +126,7 @@ write_csv(csp_long2, file = "data/CSP_long_201520.csv")
 ```
 
 
-## 5.4 Summary tables
+### Summary tables
 Summary tables can be created using the `summarise` function. This returns tables in a tibble format, meaning they can easily be customised and exported as CSV files (using the `write_csv` function). 
 
 The `summarise` function is set up similarly to the `mutate` function: summaries are listed and given variable names, separated by a comma. The difference between these functions is that `summarise` collapses the tibble into a single summary row, and the new variables must be created using a summary function.
@@ -204,10 +182,11 @@ csp_long2 %>%
 
 ```
 
-**WARNING:** Whenever using `group_by`, make sure to `ungroup` the data before proceeding. The grouping structure can be large and slow analysis down, or may interact with other functions to produce unexpected analyses.
+:::{.callout-warning}
+Whenever using `group_by`, make sure to `ungroup` the data before proceeding. The grouping structure can be large and slow analysis down, or may interact with other functions to produce unexpected analyses.
+:::
 
-
-## Exercise 4
+### Exercise 4 {.unnumbered}
 
 1.	Create a data frame with the minimum, maximum and median total spend per year for each region. 
 2.	Produce a frequency table containing the number and percentage of local authorities in each region.
diff --git a/session4_notes.Rmd b/session4_notes.qmd
similarity index 91%
rename from session4_notes.Rmd
rename to session4_notes.qmd
index c8558fd..2ced6f8 100644
--- a/session4_notes.Rmd
+++ b/session4_notes.qmd
@@ -1,26 +1,4 @@
----
-title: "Introduction to R with Tidyverse"
-subtitle: "Session 4: Data visualisation with ggplot2"
-author: "Sophie Lee"
-fontfamily: lmodern
-output:   
-  pdf_document:
-    highlight: tango
-    toc: TRUE
-    latex_engine: xelatex
-    fig_height: 4
-    fig_width: 6
-    fig_caption: FALSE
-header-includes:
-    - \usepackage{setspace}\onehalfspacing
-    - \setlength{\parskip}{12pt}
-fontsize: 12pt    
-mainfont: Cambria
-sansfont: Cambria
-linkcolor: blue
-url_color: blue
----
-
+# Session 4: Data visualisation with ggplot2
 
 ```{r setup, include=FALSE}
 pacman::p_load(flextable, tidyverse)
@@ -30,13 +8,12 @@ knitr::opts_chunk$set(echo = TRUE, collapse = TRUE, message = FALSE)
 csp_2020 <- read_csv("data/CSP_2020.csv")
 csp_long2 <- read_csv("data/CSP_long_201520.csv")
 ```
-\newpage
 
-# Chapter 6: Data visualisation with ggplot2
+## Data visualisation with ggplot2
 
 Data visualisation is a powerful tool with multiple important uses. First, visualisations allow us to explore the data, identify potential outliers and errors, or check that the variables behave in the way we would expect them to if they had been recorded correctly. Visualisations can also be used as an analysis tool, allowing us to identify trends in the data or differences between groups. Finally, visualisations can help to convey messages to an audience in a clear, concise way that is often more powerful than presenting them using numbers or text. In some cases, data visualisations can show results so clearly that further analysis is arguably unnecessary. 
 
-## 6.1 Choosing the most appropriate visualisation
+### Choosing the most appropriate visualisation
 
 The most appropriate choice of visualisation will depend on the type of variable(s) we wish to display, the number of variables and the message we are trying to disseminate. Common plots used to display combinations of different types of data are given in following table: 
 
@@ -83,6 +60,8 @@ flextable(vis_tab) %>%
 
 R is very flexible when it comes to visualising data and contains a wide variety of options to customise graphs. This section will focus on the Tidyverse package `ggplot2` and introduce some of the more commonly used graphical functions and parameters but is by no means comprehensive. 
 
+### The ggplot2 package
+
 The `ggplot2` package implements the ‘grammar of graphics’, a system that aims to describe all statistical graphics in terms of their components or layers. All graphics can be broken down into the same components: the data, a coordinate system (or plot area) and some visual markings of the data. More complex plots may have additional layers but all must contain these three. 
 
 For example, in the `csp_2020` dataset, we may wish to explore the relationship between the settlement funding assessment (`sfa_2020`) and council tax total (`ct_total_2020`) spending for each local authority. To visualise the relationship between two continuous numeric variables, a **scatterplot** would be most appropriate. 
@@ -97,6 +76,10 @@ To add information to this graph, we add a **geom** layer: a visual representati
 
 Each geom object must contain a mapping argument, coupled with the `aes` function which defines how the variables in the dataset are visualised. In this case, we use the `aes` function to specify the variables on the x and y axes but it can also be used to set the colour, size or symbol based on variable values. 
 
+:::{.callout-warning} 
+Although `ggplot2` is a tidyverse package, it uses a different method of piping to the  other packages. Use the `+` symbol to add an extra layer when working in `ggplot`.
+:::
+
 ```{r Scatterplot SFA and CT total 2020}
 # Generate the chart area and specify the data
 ggplot(data = csp_2020) + 
@@ -104,8 +87,6 @@ ggplot(data = csp_2020) +
   geom_point(mapping = aes(x = sfa_2020, y = ct_total_2020))
 ```
 
-**NOTE:** Although `ggplot2` is a tidyverse package, it uses a different method of piping to the  other packages. Use the `+` symbol to add an extra layer when working in `ggplot`.
-
 The resulting scatterplot shows a positive association between the SFA and council tax spending in English local authorities during 2020. We can identify an outlier in the top right corner of the graph. Before proceding, we want to ensure that this observation is an outlier and not an error to be removed from the data. We can use the `filter` function to return the name of the local authority that matches these values:
 
 ```{r Find outlier}
@@ -151,7 +132,7 @@ sfa_ct_plot <- csp_2020 %>%
 ggsave(sfa_ct_plot, filename = "sfa_ct_plot.png")
 ```
 
-## Exercise 5
+### Exercise 5 {.unnumbered}
 1.	Create a new data object containing the 2020 CSP data without the Greater London Authority observation. Name this data frame `csp_nolon_2020`.
 2.	Using the `csp_nolon_2020` data, create a data visualisation to check the distribution (or shape) of the SFA variable.
 3.	Based on the visualisation above, create a summary table for the SFA variable containing the minimum and maximum, and appropriate measures of the centre/average and spread.
@@ -162,7 +143,7 @@ csp_nolon_2020 <- csp_2020 %>%
 ```
 
 
-## 6.2 Customising visualisations
+### Customising visualisations
 Additional variables can be included into a visualisation within the mapping argument of a `geom` function. For example, we could explore the relationship between SFA and council tax across regions by colouring points based on the region:
 
 ```{r Scatterplot, SFA and council tax by region}
@@ -183,9 +164,19 @@ ggplot(data = csp_nolon_2020_new) +
   geom_point(aes(x = sfa_2020, y = ct_total_2020, colour = region_fct))
 ```
 
-Other aesthetic mapping options that can be used to visualise other variable(s) within the same plot include `shape`, which changes the symbol based on a category, `size`, which sets the size of each point to the numerical value of a variable, and `alpha`, which sets the transparency of each point based on a numerical value. These can be combined to visualise more than three variables in the same graph.
+Arguments that can be adjusted within geoms include:
+
+- `colour`: change the colour (if point or line) or outline (if bar or histogram) of the markings
+- `size`: change the size of the markings (if point used)
+- `shape`: change the shape of markings (for points)
+- `fill`: Change the colour of bars in bar charts or histograms
+- `linewidth`: Change the line width
+- `linetype`: Choose the type of line (e.g. `dotted`)
+- `alpha`: Change the transparency of a visualisation
 
-**WARNING:** Although it may be tempting to add many variables to the same visualisation, be sure that you are not overcomplicating the graph and losing important messages. It is better to have multiple, clear but simpler visualisations, than fewer confusing ones.
+:::{.callout-warning}
+Although it may be tempting to add many variables to the same visualisation, be sure that you are not overcomplicating the graph and losing important messages. It is better to have multiple, clear but simpler visualisations, than fewer confusing ones.
+:::
 
 Aesthetic properties of the geom object may also be set manually, outside of the `aes` function, using the same argument but with a shared value rather than a variable. For example:
 
@@ -197,7 +188,8 @@ ggplot(csp_nolon_2020_new) +
              colour = "blue")
 ```
 
-## Exercise 6
+### Exercise 6 {.unnumbered}
+
 1. What is the problem with the following code? Fix the code to change the shape of all the points.
 
 ```{r aesthetic exercise, eval = FALSE}
@@ -209,9 +201,10 @@ ggplot(csp_nolon_2020) +
 
 3.	Add a line of best fit for each region (hint: make each line a different colour).
 
-## 6.3 Scale functions
 
-### 6.3.1 Customising axes
+### Scale functions
+
+#### Customising axes
 Scale functions allow us to customise aesthetics defined in geom objects such as colours and axes labels. They take the form `scale_'aesthetic to customise'_'scale of variable’`. For example, `scale_x_continuous` customises the x axis when the variable is continuous, and `scale_x_discrete` can be used where the variable is discrete or categorical. Arguments to customise the x or y axes include:
 
 - `name = ` to change the axis title
@@ -250,12 +243,17 @@ ggplot(csp_nolon_2020_new) +
 
 We can now clearly see the strong positive association between SFA and council tax spending in local authorities with lower values of this without losing any information. 
 
-### 6.3.2 Customising colour scales
+#### 6.3.2 Customising colour scales
 There are a wide range of options for customising the colour aesthetics of geoms. These include pre-defined colour palettes, such as `scale_colour_viridis_c` for continuous variables, or `scale_colour_viridis_d` for discrete or categorical variables. Viridis colour palettes are designed to be colourblind friendly and print well in grey scale. There are also many R packages containing colour palettes for different scenarios. 
 
 Colour palettes can be created manually for categorical variables using the `scale_colour_manual` function. Here, the argument `values` allows us to specify a colour per category. 
 
-R contains a list of 657 pre-programmed colours that can be used to create palettes (run `colours()` in the console for a full list). Hexadecimal codes can also be included instead in the form ```#rrggbb``` (where rr (red), gg (green), and bb (blue) are numbers between 00 and 99 giving the level of intensity of each colour). 
+:::{.callout-tip}
+### Style tip
+R contains a list of 657 pre-programmed colours that can be used to create palettes (run `colours()` in the console for a full list). 
+
+Hexadecimal codes can also be included instead in the form ```#rrggbb``` (where rr (red), gg (green), and bb (blue) are numbers between 00 and 99 giving the level of intensity of each colour). 
+:::
 
 Where a colour palette will be used across multiple plots, defining this list of colours as a vector and then entering this into `scale_colour_manual` will reduce repetition:
 
@@ -273,7 +271,7 @@ ggplot(csp_nolon_2020_new) +
 
 Palettes can also be created using gradients with the `scale_colour_gradient` function, that specifies a two colour gradient from low to high, `scale_colour_gradient2` that creates a diverging gradient using low, medium, and high colours, and `scale_colour_gradientn` that creates an n-colour gradient.
 
-## 6.4 Other labelling functions
+### Other labelling functions
 
 Although axis and legend labels can be updated within scale functions, the `labs` function exist as an alternative. This function also allows us to add titles and subtitles to visualisations:
 
@@ -297,10 +295,14 @@ annotate(“rect”, xmin = 0, xmax = 10, ymin = 20, ymax = 50, alpha = 0.2)
 
 adds a rectangle to the graph. 
 
-## 6.5 Theme functions
+### Theme functions
 
 The `theme` function modifies non-data components of the visualisation. For example, the legend position, label fonts, the graph background, and gridlines. There are many options that exist within the `theme` function (use `?theme` to list them all). 
 
+:::{.callout-note}
+Many of the elements that can be customised within the `theme` function require an `element` wrapper. This wrapper is determined by the type of object we are customising (e.g. `element_text` when customising text, `element_rect` when customising a background, `element_blank` to remove something). Check `?theme` for more information.
+:::
+
 One of the most common theme options is `legend.position` which can be used to move the legend to the top or bottom of the graph space (`legend.position = “top”` or `legend.position = “bottom”`) or remove the legend completely (`legend.position = “none”`). 
 
 `ggplot` also contains a number of pre-defined ‘complete themes’ which change all non-data elements of the plot to a programmed default. For example `theme_void` removes all gridlines and axes, `theme_light` changes the graph background white and the gridlines and axes light grey:
@@ -345,7 +347,7 @@ ggplot(csp_nolon_2020_new) +
 
 Creating a custom theme is useful to ensure all visualisations are formatted consistently. 
 
-## 6.6 Facet functions
+### Facet functions
 
 Faceting allows us to divide a plot into subplots based on some grouping variable within the data. This allows us to show multiple variables in the same visualisation without risking overloading the plot and losing the intended message. 
 
@@ -370,6 +372,6 @@ csp_long2 %>%
   theme_intro_course()
 ```
 
-## Exercise 7
+### Exercise 7 {.unnumbered}
 
 Use an appropriate data visualisation to show how the total spend in each local authority has changed over the years between 2015 and 2020. Choose a visualisation that shows these trends over time and allows us to compare them between regions.  
\ No newline at end of file
diff --git a/session5_notes.qmd b/session5_notes.qmd
new file mode 100644
index 0000000..d61bfb6
--- /dev/null
+++ b/session5_notes.qmd
@@ -0,0 +1,304 @@
+# Reproducible research with RMarkdown
+
+```{r setup, include=FALSE}
+pacman::p_load(tidyverse)
+
+knitr::opts_chunk$set(echo = TRUE, collapse = TRUE, message = FALSE)
+
+csp_2020 <- read_csv("data/CSP_2020.csv")
+
+csp_long2 <- read_csv("data/CSP_long_201520.csv")
+```
+
+## Introduction to RMarkdown
+RMarkdown is a tool that is used to author high-quality documents, making it easy to communicate results efficiently. One of the main appeals of RMarkdown is that it is easy to integrate R code and output seamlessly into a document, encouraging openness and reproducibility in research.
+
+There are a number of ways we can use RMarkdown to enhance the research process, such as:
+
+- Generating reports to show the latest findings in a project, combining research output with interpretations. Reports can be automated within RMarkdown, to ensure outputs show the latest data.
+- Keeping track of projects as an alternative to a notebook. Documents can include R code and visualisations alongside thoughts and comments on findings so far.
+- Creating a collaborative document that can be shared with colleagues. The inclusion of R code in documents provides an audit trail, making it easy to carry out quality assurance and resolve discrepancies in results.
+
+Before we begin working with RMarkdown in RStudio, we must first download and install the `rmarkdown` package as we would any other package:
+
+```{r install and load rmarkdown, eval = FALSE}
+install.packages("rmarkdown")
+
+library(rmarkdown)
+```
+
+### Creating an RMarkdown files
+RMarkdown files (`.Rmd`) are created and saved separately to the script files we have been using up to now on the course. To create a new RMarkdown file, either use the drop-down menu, following the *File -> New File -> R Markdown...* options, or using the ![new file icon](images/new_file_shortcut.png) icon and selecting *R Markdown...*.
+
+![Rmarkdown new file](images/rmarkdown_new.png)
+
+When creating a new RMarkdown file, we are given the option to set the title, author and date of the new document. We are also given options to select the type of document, presentation, or Shiny app we would like to create. This does not give a comprehensive list of documents available within RMarkdown and can be changed later. We will discuss output document types in more detail later in the session.
+
+Clicking 'OK' on this window will produce an RMarkdown file (`.Rmd`) with some example code. If we do not want this, there is an option to 'Create Empty Document' on the bottom left of the window.
+
+### Rmarkdown content
+RMarkdown files contain three main types of content:
+
+- A YAML header (this sets the global options for the document)
+- Text, or syntax (this includes headings and comments)
+- Code chunks containing R code
+
+#### The YAML header
+The first part of an RMarkdown script, surrounded by '`---`' is known as the **YAML header**. This sets global options for the document that will be produced by the script. YAML headers can include the title, author and date of a document, the output document type, table of contents options, and can include code to edit the appearance of text and figures.
+
+For this course, we will just use the YAML to define the `title`, `author`, `date`, and `output` of our document:
+
+````markdown
+---
+title: "Introduction to R with Tidyverse"
+author: My name
+date: 2024-07-15
+output: html_document
+---
+````
+
+There are many output document types that can be produced using RMarkdown. Some of the most common include:
+
+- `html_document`:HTML document,`.html`
+- `pdf_document`: PDF document,`.pdf`, created using a LaTeX template 
+- `word_document`: Microsoft word document (`.docx`)
+- `odt_document`: OpenDocument text document (`.odt`), similar to Microsoft Word/Google Docs but compatible with free word processors)
+- `github_document`: Github document (`.md`, markdown files that are compatible with Github and are converted to HTML when viewed there)
+- `powerpoint_presentation`: Powerpoint presentation (`.pptx`)
+
+RMarkdown can also be combined with other R packages to create books (via `bookdown`), websites (via `blogdown`) and interactive dashboards (via `flexdashboard`).
+
+
+#### RMarkdown syntax
+RMarkdown text, or syntax, will generally make up the majority of a RMarkdown file. This can include headers and subheadings, equations, and any other text or comments in the document. Text is formatted using **markdown syntax**. A detailed list of syntax commands are given in the RMarkdown [cheatsheet](https://rstudio.github.io/cheatsheets/html/rmarkdown.html#write-with-markdown). Common syntax commands that may be used in an RMarkdown document include:
+
+- `*italic*`
+- `**bold**`
+- Add ``` `code` ``` into text
+- ```# Header 1```
+- ```## Header 2```
+- ...
+- ```###### Header 6```
+- ``` [This is a link](link url)```
+- ``` ![caption](image.png) ```
+
+```
+- Unordered list
+  - List with indent
+```
+
+```
+1. Ordered list
+  - With indent
+2. Second item
+```
+
+```Equation: $r^2 = (x - a)^2 + (y - b)^2$```
+
+*RMarkdown equations are built using the same language as LaTeX. [See here](https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols) for a list of mathematical symbols that can be used in these equations.*
+
+#### Code chunks
+Code chunks allow us to embed R code and outputs into our documents. This is one of the main draw of RMarkdown as it removes the need to copy and paste or import results from R into another document.
+
+Code chunks are pieces of code that begin ` ```{r} ` 
+and end ` ``` `. For example, 
+
+````{verbatim}
+```{r}
+ 1 + 1
+``` 
+````
+Code chunks can be created by manually typing these wrappers, by clicking the ![code chunk icon](images/code_chunk_icon.png) icon and selecting 'R', or using the keyboard shortcut `ctrl + alt + i` on Windows, and `Command + Option + i` on Mac.
+
+Code chunks can be given titles to make an RMarkdown script easier to navigate (these will appear under the script window where lists of subheadings appear in script files). These are added inside the opening of the code chunk: ` ```{r chunk title} `.
+
+There are a number of chunk options to customise which code/output to display in the document. These are included in the opening of a chunk, after the title, separated by commas `,`. Some of the most common, include:
+
+- `echo = TRUE/FALSE`: whether to display code in the output document
+- `eval = TRUE/FALSE`: whether to run the code in the chunk or not
+- `include = TRUE/FALSE`: whether to include anything from the chunk (code or output) in the document
+- `error/warning/message = TRUE/FALSE`: whether to display error/warning/other messages in the document
+
+**Top tip:** It may be useful to add a setup code chunk at the beginning of an RMarkdown file that loads any packages and datasets that are required for the rest of the document. These can also include universal options for future code chunks to avoid repeating the code, using the `knitr::opts_chunk$set` function. 
+
+For example:
+
+````{verbatim}
+```{r setup, include = FALSE} 
+# Set global options for code chunks 
+
+# Do not show any R code or messages unless specified 
+knitr::opts_chunk$set(echo = FALSE, message = FALSE) 
+
+# Load in the tidyverse package
+library(tidyverse)
+```
+````
+
+### Compiling RMarkdown documents
+Compiling RMarkdown actually requires multiple steps and programmes. Luckily for us, this process takes place in the background so we don't need to be aware of these steps happening!
+
+Generating an output file from RMarkdown is know **knitting** a document. This process sends the `.Rmd` file to another R package `knitr` (which is installed alongside `rmarkdown`), which executes all the code chunks in the document and creates a markdown `.md` file including the code and output. This markdown file is then processed by another programme **pandoc** which converts markdown code into the finished document. 
+
+![RMarkdown to document process](images/rmarkdown_pipe.png)
+
+To **knit** an RMarkdown file in RStudio is very simple. Either click the ![knit icon](images/knit_icon.png) icon above the RMarkdown script, or use the keyboard shortcut `ctrl + shift + k` on Windows or `Command + shift + k` on Mac. This initiates the process above and will return an output document (if there are no errors!) in the requested format to the working directory.
+
+### Data visualisation in RMarkdown
+Output such as graphs and tables can be embedded in code chunks, the code used to create them will be the same as it would be in any other R script. 
+
+:::{.callout-note} 
+Often, when providing output in RMarkdown, we often do not want to show the code that was used to create this. Make sure to add `echo = FALSE` to the opening of the code chunk.
+:::
+
+#### Graphs in RMarkdown
+`ggplot` can be used to create graphs that are embedded within code chunks and included in an output document. For example, we could use the data from previous sections to show the relationship between Settlement Funding Assessment (SFA) and council tax total in English local authorities in 2020, colour code by regions in a scatterplot:
+
+````{verbatim}
+```{r scatterplot sfa_2020 and ct_total_2020 by region, message = FALSE}
+# Load and tidy the 2020 data
+read_csv("data/CSP_2020.csv") %>% 
+  # Remove the Greater London Authority row
+  filter(authority != "Greater London Authority") %>% 
+  # Convert region variable to factor
+  mutate(region_fct = factor(region, 
+                             levels = c("L", "NW", "NE", "YH", "WM",
+                                        "EM", "EE", "SW", "SE"))) %>% 
+  # Create a ggplot 
+  ggplot() +
+  # Scatterplot definition
+  geom_point(aes(x = ct_total_2020, y = sfa_2020, colour = region_fct)) +
+  # Add colour palette for region
+  scale_colour_manual(values = c("aquamarine2", "blue", "chartreuse2", 
+                                 "coral", "orchid", "firebrick", 
+                                 "gold3", "violetred", "grey50")) +
+  # Change axis/label titles
+  labs(x = "Council tax total (£millions)", 
+       y = "Settlement funding assessment (£milliongs)",
+       colour = "Region") +
+  theme_light()
+```
+````
+
+```{r scatterplot sfa_2020 and ct_total_2020 by region, echo = FALSE, message = FALSE}
+# Load and tidy the 2020 data
+read_csv("data/CSP_2020.csv") %>% 
+  # Remove the Greater London Authority row
+  filter(authority != "Greater London Authority") %>% 
+  # Convert region variable to factor
+  mutate(region_fct = factor(region, 
+                             levels = c("L", "NW", "NE", "YH", "WM",
+                                        "EM", "EE", "SW", "SE"))) %>% 
+  # Create a ggplot 
+  ggplot() +
+  # Scatterplot definition
+  geom_point(aes(x = ct_total_2020, y = sfa_2020, colour = region_fct)) +
+  # Add colour palette for region
+  scale_colour_manual(values = c("aquamarine2", "blue", "chartreuse2", 
+                                 "coral", "orchid", "firebrick", 
+                                 "gold3", "violetred", "grey50")) +
+  # Change axis/label titles
+  labs(x = "Council tax total (£millions)", 
+       y = "Settlement funding assessment (£milliongs)",
+       colour = "Region") +
+  theme_light()
+```
+
+#### Tables in RMarkdown
+There are a number of ways to include tables within RMarkdown which can either be entered manually, or generated using an R package. The choice of approach to creating tables depends on the format and size of the data, the amount of flexibility you would like to customise the output, the type of output document you are creating, and personal preference of how it should look.
+
+In this course, we will look at how tables can be created using RMarkdown syntax (without the need for additional packages), and using the `kable` function within the `knitr` package.
+
+**Manually creating tables** 
+
+Tables can be created in RMarkdown syntax, using the `|` symbol to separate columns, and dashes `-` to separate column headings from the body of the table. These are created outside of code chunks within the text. For example, 
+
+```` {verbatim}
+ Header 1 | Header 2 | Header 3 |
+|----------|----------|----------|
+| This     | Is       | A        |
+| Very     | Simple   | Table    |
+````
+
+produces the following output:
+
+| Header 1 | Header 2 | Header 3 |
+|----------|----------|----------|
+| This     | Is       | A        |
+| Very     | Simple   | Table    |
+
+Colons can be added to the header/body separator row of the table to control the justification of the text in each column. For example,
+
+```` {verbatim}
+| Left | Right | Center  | Default   |
+|:-----|------:|:-------:|-----------|
+| This | Is    | Another | Simple    |
+| Table | But   | It is  | Justified |
+````
+
+produces the following output:
+
+| Left | Right | Center  | Default   |
+|:-----|------:|:-------:|-----------|
+| This | Is    | Another | Simple    |
+| Table | But   | It is  | Justified |
+
+
+**Creating tables from data frames**
+
+The `knitr` package that compiles RMarkdown files contains the `kable` function that can be used to create simple data tables. The `kable` function requires data to be stored as a matrix, data frame, or tibble object (although these can be easily created using the `matrix`, `data.frame` or `tibble` functions). Accessing the help file `?knitr::kable` gives a list of arguments that can be used to customise these tables.
+
+:::{.callout-note} 
+As these tables are created using R functions, they must be generated within a code chunk.
+:::
+
+For example, we can create a simple data table using `kable` showing the first 6 rows of the `mtcars` dataset (a dataset pre-loaded into base R):
+
+````{verbatim}
+```{r mtcars table, echo = FALSE} 
+knitr::kable(head(mtcars))
+``` 
+````
+
+which produces the following output:
+
+```{r mtcars table, echo = FALSE}
+knitr::kable(head(mtcars))
+```
+
+Where data are not already saved as an object, we need to create them first before generating a table. For example, the table we created manually earlier can be recreated using the `kable` function, by first creating a data frame with the information, and then piping it through to the function:
+
+````{verbatim}
+```{r kable table}
+# Create a data frame with the table information
+data.frame(col1 = c("This", "Very"),
+           col2 = c("Is", "Simple"),
+           col3 = c("A", "Table")) %>% 
+  knitr::kable(., col.names = c("Header 1", "Header 2", "Header 3"))
+``` 
+````
+
+```{r kable table run, echo = FALSE}
+# Create a data frame with the table information
+data.frame(col1 = c("This", "Very"),
+           col2 = c("Is", "Simple"),
+           col3 = c("A", "Table")) %>% 
+  knitr::kable(., col.names = c("Header 1", "Header 2", "Header 3"))
+```
+
+**Other ways to create tables**
+
+Although the `kable` function and RMarkdown syntax tables do not require additional R packages to be installed, they are fairly simple and do not give many options to customise the tables. For a more flexible alternative, I would recommend looking at the `flextable` package, which gives a much wider range of customisible features. The `flextable` user manual can be accessed for free from [this website](https://ardata-fr.github.io/flextable-book/).
+
+
+
+### Exercise 8 {.unnumbered} 
+Create an RMarkdown file that creates a html report describing the trends in core spending power in English local authorities between 2015 and 2020. Your report should include:
+
+- A summary table of the total spending per year per region
+- A suitable visualisation showing how the total annual spending has changed over this period, compared between regions
+- A short interpretation of the table and visualisation
+
+:::{.callout-note}
+You are not expected to be an expert in this data! Interpret these outputs as you would any other numeric variable measured over time.
+:::
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