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<title>Introduction to Open Data Science - Course Project</title>
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<hr />
<h1>Introduction to Open Data Science - Course Project</h1>
<h2>If you’re peer reviewing this after 13 Dec…</h2>
<p>..you might be wondering why it looks this crappy. I had major issues with knitr and had to revert to knit2html, which apparently uses an old version of Rmarkdown, and I ran horribly out of time while troubleshooting. Sorry!</p>
<hr />
<h1>Chapter 1</h1>
<p><a href="https://www.youtube.com/watch?v=bhlD1XfiEJE">Now playing</a><br />
<a href="https://github.com/voikukas/IODS-project">My GitHub IODS repository</a>\</p>
<h2><strong>How am I feeling right now?</strong><br />
5 minutes after switching from my UH computer to my personal computer, I finally got the environment working (after struggling with my work computer for 6 hours)! Feeling slightly annoyed now.</h2>
<p><strong>Impressions from R for health data science & Exercise set 1</strong><br />
I’m already slightly familiar with programming and R, so I didn’t go through everything in great detail.<br />
Many of the practical examples and recommendations, such as the one about equivalence & rounding, seem very useful and probably will have saved me from a big headache. On the other hand, I skimmed through the import data section as it had nothing new for me. Everything else will serve as a great reminder.</p>
<pre><code class="language-r"># This is a so-called "R chunk" where you can write R code.
date()
</code></pre>
<pre><code>## [1] "Tue Dec 13 02:32:39 2022"
</code></pre>
<hr />
<h1>Regression and model validation</h1>
<p><em>Describe the work you have done this week and summarize your learning.</em></p>
<p>This week, I worked with the exercise set and read through R for Health Data Science to be able to answer the stats questions. I learned something new about plotting (ggpairs is super nifty) and statistical analysis with R. I don’t want to touch SPSS ever again.</p>
<pre><code class="language-r">date()
</code></pre>
<pre><code>## [1] "Tue Dec 13 02:32:39 2022"
</code></pre>
<pre><code class="language-r">library(ggplot2)
library(GGally)
library(dplyr)
learning2014 <- read.csv("data/learning2014.csv")
</code></pre>
<h2>1.</h2>
<p>The data contain a condensed version of a full questionnaire dataset (details at <a href="https://www.mv.helsinki.fi/home/kvehkala/JYTmooc/JYTOPKYS2-meta.txt">https://www.mv.helsinki.fi/home/kvehkala/JYTmooc/JYTOPKYS2-meta.txt</a>). Students in an introductory statistics course have answered a questionnaire regarding their approaches and attitudes towards learning and statistics; additionally, their exam points and other background variables have been collected.</p>
<p>Questionnaire variables:
Respondents have given their answers on a 1-5 scale.
From the raw data, certain variables have been combined (and scaled back) in order to measure the respondents’ use of the following learning approaches: deep (variable name deep), strategic (stra), and surface (surf). The variable ‘attitude’ combines questions about respondents’ attitude towards statistics.</p>
<p>Other variables:
gender
age
points (note: respondents with 0 points have been removed)</p>
<pre><code class="language-r">dim(learning2014)
</code></pre>
<pre><code>## [1] 166 7
</code></pre>
<pre><code class="language-r">head(learning2014)
</code></pre>
<pre><code>## gender age attitude deep stra surf points
## 1 F 53 3.7 3.583333 3.375 2.583333 25
## 2 M 55 3.1 2.916667 2.750 3.166667 12
## 3 F 49 2.5 3.500000 3.625 2.250000 24
## 4 M 53 3.5 3.500000 3.125 2.250000 10
## 5 M 49 3.7 3.666667 3.625 2.833333 22
## 6 F 38 3.8 4.750000 3.625 2.416667 21
</code></pre>
<p>There are 166 respondents (rows) and 7 variables (columns).</p>
<h2>2.</h2>
<pre><code class="language-r"># Checking number of female respondents
nrow(filter(learning2014, gender =="F"))
</code></pre>
<pre><code>## [1] 110
</code></pre>
<pre><code class="language-r"># Graphical overview & variable summaries
p <- ggpairs(learning2014, mapping = aes(col=gender, alpha=.3), lower = list(combo = wrap("facethist", bins = 20)))
p
</code></pre>
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</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-10" /></p>
<p>There are 110 female respondents and 56 male respondents, which may bias the data towards female respondents. Thus, it makes sense to explore the data grouped by gender.<br />
By looking at the data densities grouped by gender, we can see that the distributions are somewhat similar in all variables. Largest gender differences seem to show in attitude (male respondents report a more neutral/positive attitude).</p>
<p>Most respondents are under 30 years old, but ages range from 17 to 55.
There are no significant interactions between age and other variables.</p>
<p>The strongest correlation can be found between attitude and points (.437, p < .001).
In males, there is a negative correlation between attitude and surface approach (r = -.374, p < .01). Males also show a strong negative correlation between deep and surface approaches (-.622, p < .001).</p>
<p>While there is a negative correlation between strategic and surface approaches (-.16, p < .05), it is not present in any of the genders separately.</p>
<h2>3. & 4.</h2>
<p>Chosen explanatory variables: attitude, deep, and surface approach</p>
<pre><code class="language-r">model <- lm(points ~ attitude + deep + surf, data = learning2014)
summary(model)
</code></pre>
<pre><code>##
## Call:
## lm(formula = points ~ attitude + deep + surf, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.9168 -3.1487 0.3667 3.8326 11.3519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.3551 4.7124 3.895 0.000143 ***
## attitude 3.4661 0.5766 6.011 1.18e-08 ***
## deep -0.9485 0.7903 -1.200 0.231815
## surf -1.0911 0.8360 -1.305 0.193669
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.313 on 162 degrees of freedom
## Multiple R-squared: 0.2024, Adjusted R-squared: 0.1876
## F-statistic: 13.7 on 3 and 162 DF, p-value: 5.217e-08
</code></pre>
<p>Variables deep and surf do not have a statistically significant relationship with points; adjusting the model.</p>
<pre><code class="language-r">model <- lm(points ~ attitude + stra, data = learning2014)
summary(model)
</code></pre>
<pre><code>##
## Call:
## lm(formula = points ~ attitude + stra, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.6436 -3.3113 0.5575 3.7928 10.9295
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.9729 2.3959 3.745 0.00025 ***
## attitude 3.4658 0.5652 6.132 6.31e-09 ***
## stra 0.9137 0.5345 1.709 0.08927 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.289 on 163 degrees of freedom
## Multiple R-squared: 0.2048, Adjusted R-squared: 0.1951
## F-statistic: 20.99 on 2 and 163 DF, p-value: 7.734e-09
</code></pre>
<p>We’re looking at the relationship between two variables; we’d like to see how “attitude” explains the obtained course points. Using ordinary least squares, simple linear regression fits a line to the observed data (where y is the dependent variable and x is the explanatory variable).
Residuals are the differences between observed values and the fitted line(s). The median of residuals is .56, which suggests that the data fits the model quite nicely (but further analyses show whether this is true or not).</p>
<p>The coefficient intercept estimates: when attitude+stra = 0, points are at ~9 (p < .001 at null hypothesis, so when slope is at 0). The coefficient estimate of the explanatory variables are the slopes of the regression line (p < .001 for attitude, p < .1 for stra).</p>
<p>The adjusted R-squared stands for the coefficient of determination and is an indicator of how much of the variability is explained by the explanatory variable. It is at .1951, which is not that great. Thus, attitude and stra are not the only factors explaining the scores.</p>
<h2>5.</h2>
<pre><code class="language-r"># Scatter plots
qplot(attitude, points, data = learning2014) + geom_smooth(method = "lm")
</code></pre>
<pre><code>## `geom_smooth()` using formula = 'y ~ x'
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-13" /></p>
<pre><code class="language-r">qplot(stra, points, data = learning2014) + geom_smooth(method = "lm")
</code></pre>
<pre><code>## `geom_smooth()` using formula = 'y ~ x'
</code></pre>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAH4CAMAAACR9g9NAAAA0lBMVEUAAAAAADoAAGYAOpAAZmYAZrYzMzMzZv86AAA6ADo6OmY6OpA6kNs9PT1NTU1NTW5NTY5NbqtNjshmAABmADpmAGZmOgBmOpBmtv9uTU1uTY5ubqtuq6tuq+SOTU2OTY6ObquOjsiOq+SOyP+QOgCQOjqQOmaQ2/+rbk2rbo6r5P+2ZgC2/7a2///Ijk3Ijm7IyP/I///KysrW1tbbkDrb25Db/7bb///kq27kq47k/8jk///r6+v/tmb/yI7/25D/5Kv//7b//8j//9v//+T///+Zi7y7AAAACXBIWXMAAAsSAAALEgHS3X78AAARyElEQVR4nO2dcX8TNxqEfXCYuytxIbR3hV6grXtHGkpoEnqEo4TEZL//V+raCcR2drWSVq92ZjXvH+EX27Oj0YO0iuVdTypVkTUZugGqYUrgCy2BL7QEvtDyAP9HaIUr+umyG3IHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHiXbjLx1TlfmUYn8NkMJxMXl3Wd+5VpdAKfzVDgCwWvqb5U8FA6gQcx5A4o8DQ6gQcx5A4o8DQ6gQcx5A7oDV41xtKIJ9Bpqgcx5A4o8DQ6gQcx5A4o8DQ6ge8r3NoYSbJJ418h2zJJDAX+ura3QlNsy/pX0EZsCkOB/1wCv3qwPPCa6lcPFgieVCfwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRlcU+K2tLNfOVuyuV/QxXQ11HCWgnZbbiNjgtzavXXvZsfvc8cd0NNRxlIB2mn5wQOAFHhC8pvpWQ+crN4sRPLIhd0CBp9EJPIghd0CBp9EJPIghd0CBp9EJPIghd0CBp9EJPIghd0CBp9EJPIghd0CBp9HlAn+5P9u9+oEK3rWH4b8xYn/Vsv9eS8hh/CsQ/Nle9fqg/nE4BwXv2rX03wqNv17dt6H+u6tBh/Gv4Kn+8pejdwfL/wDVdDrtPhnkrmVP+D3n/0qLSuRg0tDGIy6e7dZjfgW+Qhzxmuo9K3xxd7b3Dhn8wIbcAdvBn85r5sjn+KENuQO2g68X9I/eQ6/qBzbkDuic6tdr2GYiGnIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIHFHgancCDGHIH5AIfezdp55bN2ME3dxoV+Nj7x7t350cOvqXTBF7g8cFrqo+pEUz1WIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRjcC8NFf0uy/2RJwmaRFQx0VfUtjfvDRX8vuv70ackW8QUMdFX0Tc4FvO4zAh+g01WuqzwfeREezSMMIKPA0OoEHMeQOKPA0OoEHMeQOKPA0uoHAq8ZYGvEEOk31IIbcAQWeRifwIIbcAQWeRgcLfuBrEf03aRIZJtGNYJNm6KuPvbdlUxmm0Flvyx4vS+DTGsKDP74uTfVpDbGn+uOb0uKOWxciPD4W+NHovIXHWyXw3Dof4TZzgR+BrlPYSF3g6XVuYRt1gafXuYQO7ALPrmsVOqkLPL2uSdjFXOBHoLsl9KIu8PS6TaEvdYGn160LA7ALPLvuizCIusDT65bCUOZg4E1uJp0bhCuETcCTdZo7O3zgbW4fnxm8K4RFwBrgOvidHX/yAp9Slxf8CiA9eE31YfUZIP1Ub6OjWaQF6DYBnjRzFfix6bYBCjyGoa2uAaDAYxia6doACjyGoY3OAVDgMQwNdG6AAo9hmFzXBVDgMQzT6jwACjyGYTKdL0CBxzBMowsAKPAYhgl0YQAFHsOwny4CYCbwi2ezh0eX+7OvD4zBx9/O2XEY/+fSNNS/2atXRgHMBP50Xp3uLX40H/E9buDefhj/59I01L/Z9Qv999UGAV/X2fz8yezR+6qaTqfdJ4PIWvZZ22/Rh/F/LtYhqtknJyfLjfSTvOXK1Pjo4of3Z3vV+U+rXzyHxdp/Kd8XFjPVX42/gI30gUb84vnR8p+avS34RDrwxV1/frnAnz89Wp3oz+YC30+XiF+M8P6yAsEfzmazvXpVv1sJfA9dEn4Rwvs3pb/js+v68wsU3t+q1YMCn1PXi1+EsBH5scBn1kXzixE24xb47LpIfjHgO5ALfCZdLD+/2hB2DfO1EnhjXQy/kPosDGC+KoG31IXzCyvH4q2rBN5IF4gwGHwP5qsS+OS6UASrCgC/SbukD2IEbNnE7u5Ebu44r2F0bsS4+N0IG0Z4QeADdudjN/Lj9vG3OWxetey+htnB70rYNqkLfFNlBN/AIRF494m8IPBoU307hz5Tve/irSTwOIbpOKzpwtbrAp/ZMDGHK13En2cCn83QhMNJ7F/kAp/D0IRDj3dh4gxXJfCeOhMO/ZhHGN6UwHfqUnNoXLyhf9iyHPAmHNoX7AKfVhcj7NWfrbqOSV3g0+qyf9zZ+YEYx4lc4NPqsn/4cVPnv3gT+LS67B+F+qILXK8LfFpdjv3xtQp7t7W/Xw/hkOBjv9y5XdfRL7GbJi7d59+amPvoPNqyWVsvJQQf8XXu18kDuinFNqlLV/+yQTtA592Wjdp+KTr4hmaGAIzVGYO/PauXDN5lF3t39Vid3VTfciIPPkV4tGWzcKd6l13y90WshLGfiKEJKPAhuu4FO01Age/UBf2NRhNQ4F268L/LaQIKfIsu5l2YPn6ROoFPJ4x6562HXy+dwCcR9mIe4ddfNxD4xsp8p75EdYN86JbYVADAAkZ8++Itd0MdusZOvhmk7qfDdCWA71iwZ2xoL34C7y/0OpHbNDQ9P4H3Evov3tI0tCcHS2Ex4APX6z0amo6DpRAVvGsPyrmVdVvYNsyd+2OOhjbbN/Vn+k+a3Kro+3qDgnftOjs3r7882fluq3tHvL2h669092fEJ01CddFf4TBG8J5vsPcE79GfAu/Tn7e6t13Xzv02bu8p22uqv+5s3/7UVN/Rn93VqWsb4ckM+/SnoW50i7sAnXNWT2DYvz8NdYWC7/4brZ9hov401JUE3nPx1tMwZX8a6goBH8Q81jB9fxrqRg8+iHa0oVF/GurGDD6WeZihZX8a6kYKvg9yb0P7/jTUjQ781jA3+iBGpv401I0EfOvizQR8tv401NGD71ivpwefsz8NdczgfRZvKcHn709DHQn47e2VdeSxF6+GbLZstDP2e6Cdr3RstqT59upUwqzg1/Y+bw3z2MvVA7ZXN5u5uaPp+s1f59pede+glgC+eWq3Bn+rmQLf8GB68N1vtppN9W3RNdXffjAp+PA32DvA+xfPIg0T/Id7F48n30WAv0U766dsk/cLoM4U/Kf/vHhz7+NXb0PAt4zwfOAt+gVQZwr+4ttXLx/UPzzBu2b1HODt+gVQZzvi//vrNy/8R7zrRG4P3rJfAHXG5/jJ3f998yLiHJ8bvHG/AOqQV/VZwGfpF0Cd9Tn++gcq+Ez9AqgzBP/p58mq7gat6jOCz9cvgDr7EQ851WfuF0Cd7Tn+zXLE30Gb6vP3C6DOdsQ3ruiHBT9IvwDqck31i2ezh0eX+7PddvCTyMvOQ8D3zNfYbMdmS6zO/4rG+MskTaf6l1/epz+dV6d7Z3vV4bwN/GQSd/WxP/j++Rqb3b69Gqvzv4a5x4XRpiP+8fo5/mz+7qCq2VfT6bRh9l+Cv7m72hL8MDdrC6xlwtQ6/2MGuMc2NKCaj7/44f3rK/BV5qk+3X/sxmZrqt8a8Rff/ro24hfPj6p3TvA2i7vIeDSLNMjF3VqdPz2qKuc5Pj34PvFoAGIE3Aa/PMlfDfjD2Wy2517VJwbfLx4NQIyAW+A//Vyv6j8M8ZZt73g0ADECboEfaJMmRTwagBgBAUZ8ong0ADECtp/jc4BPGY8GIEbAbfCt1XjIfuDTxqMBiBGwacQ3zfTJwSePRwMQI+AA53ijeDQAMQJugbdf1ZvFowGIEXB7qn/5YHk1jdVUbxmPBiBGwO0R//jqU3e3F/aNh/QG77oLdHQ8/z2M2IsYYy+29D9KSBGu6nd2dqLu6u0s/+3q2MuWYy+v9j9KULGB/yP+du7OEvg+OnPwVy+MvZ27szTV99DZgk/WTEshi44HfMJmWgpZdCTgyfsFUAcP3qKZlkIWHTh4m2ZaCll0yODNmmkpZNHhgjdspqWQRQcK3raZlkIWHRz4HM20FLLowMDnaaalkEWHBD5bMxENuQMKPI1O4EEMuQOOB3z0HtiGYeydrQNK4JPq4ne91w1j72UfUgKfVCfwYbrRgNdUH6YbD3iaRRpGQIGn0Qk8iCF3QIGn0Qk8iCF3QIGn0Q0EXjXG0ogn0GmqBzHkDijwNDqBBzHkDijwNLqRg4/e+7DfNEl01as9eJ/LiNHAR+922m+TprrO3Ry8140DBF7gIcBrqk8gZJzqUdY+gLqRL+5A+gVQJ/AghtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/A+Qotvd7b8cmdLYUngY+8mH/JKgc/QzFChwHfpRgpeU32XbqzgR6gTeBBD7oACT6MTeBBD7oACT6MTeBBD7oACT6MTeBBD7oACT6MTeBBD7oACT6MTeBBD7oAu8Kfz6nJ/9vWBwEPosoE/nM2rxY8a8Si6XOAXv9Uj/vzJ7NH7qppOp90nAxVftU71Z3vV+U+rX4b9/4loyB2wA3xdNXuBR9BlBb8c9HOBh9DlXtXvVgIPodPf8SCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkYn8CCG3AEFnkY3EHjVGEsjnkCnqR7EkDugwNPoBB7EkDugwNPoBL65XN8K7f9cwFG8G5roW6gFvrFc3wPv/1zIUXwbmup75wW+sQQ+TDca8Jrqw3TjAU+zSMMIKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0utGBT7SH4dpecdaGYcBRBL5fMxPtWro2VN21bhhyFIHv10yBH8RwePCa6gcxBACfSEezSMMIKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0OoEHMeQOKPA0unzgT+fV5f5styjw/pdQkgb88mA7+MPZvDrbqw7nBYH3v2iaNODNg63gF7/VI/7dwZJ9NZ1Ou08GY6gl6rbfxlitU/3rK/BVKSNeU/01+HelgQfWZQVf2jkeWadVPYghd0AX+I0atpmIhtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/AghtwBBZ5GJ/DhwjR3r/b3M9EJfLAwzf3q/f1sdAIfLBT4hgdLAK+pvuHBIsCPQifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAQWeRifwIIbcAb3Bq8ZYGvEEOk31IIbcAQWeRifwIIbcAQWeRifwIIbeukRfly3wIIa+uu1LrzECCrzAC7yRTlO9qQ4XfCKdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBqdwIMYcgcUeBrdQOCz1XTshkgBBX7EfgIPYogUEAm8KmMJfKEl8IWWwBdaMOAXz2YPj3IaXu7PdnP6VdX59+9z2tUBvz5ofRYG/Om8Ot3LaXi2V71u7xeDutx/lBX84kfXszDg6zqb5/W7/CXrFHP67x+ygj9/MnP8TwMCv8jbL/XJJetUf/79//MGrKe0859an8UBv3iedfwt6yznueV0NptlPZdVzoAw4M+fZuZeLyqygs8+pS0Dtp88YcAf5h4Q9aI372IrN3j3ny0w4FV5S+ALLYEvtAS+0BL4QkvgCy2BX9XFv94O3YTMJfCr+viVwBdWn36eTB7UP+7+/o9/3nn1ZjK5N3SL8lTx4D/cqy6+fVWP+I9/f7Ec+PUvQzcpSxUP/uPflmN8CX4529e//eXF0E3KUsWDX8H+7hr8hzuvLr4R+CLqzb2qevngM/h71QeN+ELq5WRy9+3F47u/1+AvHk/++vi7oVuUpQS+0BL4QkvgCy2BL7QEvtAS+EJL4AutPwH2Nqu1s2A1iwAAAABJRU5ErkJggg==" alt="plot of chunk unnamed-chunk-13" /></p>
<pre><code class="language-r"># Diagnostic plots
par(mfrow=c(2,2))
plot(model, which=c(1,2,5))
</code></pre>
<p><img 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09GkIFNC3yE9wb5a2EpcPct8YMnI0jBJmbqQz+WZV+HtIouvnxN/eAP66aQA6YkBH4sez+l9m9SjbuxNXbjLoWbvRKAHycq0nlPKn/8wQd4Jj21/MbqC2L/HUct2aBNShkE4NWSN+zIc4r10g2829ItowhMvVryN2XpDf/oHRfw99N4LtMRgFdLPgOHPpk8XNy2X8T4fmKFnQrAO4s+m3J7QJVWYacC8JGjmuQ1GQsBeI2UM3DsG7apcgfwGqln4FzpHk2K4APXlUbwA2fgJFvcy5mBD906NkU2cAZOytwBfHpRjaNZgR/b1OOa3Hu5s6SLezk38IGlT/CaDswc+03ESJ07gNcohW/LRlMY8BO/8uurWHV88sW9hBKv0e7GqvCagdPjnmaBmC/4APmpjeFwscL/pZMLnaJK8QlNOWPwIfJTGwFZ0PTO1rlVL5h5AB9Wkvx0tgH6Ev/gsjgpC8dWvaR6B1MfQrtX7q12X3tjJclP96Kl916ga5cby/cpkizUWs0NfPH2r8t3n3yiOH1Q8O5RzaE1X2lu4D9++6PXH3393VZbu/jKm5fEDoQ29e5RzYn77MB/st2/9u5lG/Hvt8WS2AEP+SW4QMffREe9hYHA1EdW8fU3Vjv0xqp1ro/vrYgd8IjMK8G40bc5FlaImWZB2gGaG/jqRM25PtnuXid2wC8ed2HkuLXf7+bJuafZoKeaDfjdC6xrLdTmxAaQH484/Uo8Xf+nKfGa4Wp6gzb9kKQ0F/C/ewsX6cdvbT1rc7n8Ekwm2LK1YExRUfCafsiUmgv4Etvy364ebz1rc7liTsQgNqBA6HL353/2l71+SBLyBD/+Gjj71w7funXrG561uVzeCTZPtqSFnXY4/urvST9k/3e+54okP/BO69yFEeX9eOtZm8sVGzztcPz1X/zp1anjo6xzN75im/oBHY7o8gQfZZ270RUafL9tP6DDEV2zqeNjKDB4Zt47/c50NZtWfQzFAB+l3xlB/iW+vSoEzLlrTH2MfmcE+bfqXVeFSFBRGncx+p0RNKBV77YqRIqKBL4M3u+MoAH9+NaqEOYQSSpmdy51edbxHqtCJCgA7+aiDDE7Dcm5K3vtplxRvGCkCKaKzfF4XO+RpD/bVK7ewQC8ra4YeLdgAD4115GCAfjUXEcKBuBTcx0pGIBPzTV0MNDcBeAzFYDPVAA+UwH4TAXgMxWAz1QAPlN5gKdf79mg/sK/9PC6/0r54ZwuG6k4zl0F7zj+E1k0/bOqYifrVS4lqYkn4Up60n3L0pBMXVDTadVyB08WjSkLnP/rpXj4eNtbR4h5VB7vR1MdKFAXvNa7NHacXeLxeBIzpOus+WyxIZm6oKbTauQM/vC3ZPbl5l6/7NHDuzvbQlwBfLPE5Vdy37IPmAqfMcUHdnd+edL3TaLpn5Udlp4Vn09+1niSfZCVieWOKpg2mdqghtPq5GHqSULWC+GENH2FxPBgKBvx233sbq1+dw+T0iqAx8clZ6XhJWddY5MhPWs8SW75RjrwhmQarkF7WrU8wZPs77GhhxfCFD1GS3JTrxfN7753MmnoRHJcPCs9LDkrOedoJX5N7JBwJR1X7xJvAq88rUGe4At5iRev4XBOfInVGDvOfguHS/GuYtH0z8oOi2cloTcnY9bxwpX03dX0TMnUgTedVi1P8KRQnoiHSSOzm5I1K7xCw5UdX/eLdn2gX7DZ8f5Z2WHxrMRhMWqrXriSnnT0DMnUB9WfVi3ox2cqAJ+pAHymAvCZCsBnKgCfqQB8pgLwmQrAZyoAn6kAfKYC8JkKwGcqAJ+pAHymAvCZCsBnqjHB766T6SJkltTjLflf61FvAsqoc2ODi6/5Tda3VunxtnuJfG9/ihRzqWmAoNkyKvgqK/Zn3S+6XS3wPP0a8MJSYuyC6fcBpN+5ZQFmDh4nf40WZOrpmk4XW6NrrxLwmP7uzpZOlsNeiF98hHophCl1iYuB//Ipe8uHXSS+rM2ta5drNgNxQbxsyFsw1QWX1TzD9bK59kW5u3WdelrwEh8sQ8Y29ddI8lmJZ3NmyTR6+iUMOv0eX/PhYlWDZ15wJiT3XS+tGPibl/hS6ovEQDcLPk+YXD++xDvbcvPl6oLL+gWTE3btLCvIx+2x+xk39eEyZJISz8Cz2fPkaqmp3999j5WCowY884JvGK+JpJOpNvXVFbAXAjYn/I0BxpEV8OqCy6rEb6oST13Ydg0+XIZMCJ5dJ76H2deuys29EzJFnpf4O1tsCKpJ1qRwzEgt8PVFkhJ/wtk2JZ68I1iX+P3pcn/6jTe37NpZVvTAh8uQacCfHj89pdUbrqvW6OgWBb+7sSK1wdGrS+zlcE6rfuplPc86vq6p6UWSOp5V9mhJrp9Zt2s/qy6YhjslBXrBrp1lBQdPA/A6PkyGQD8+UwH4TAXgMxWAz1QAPlMB+EwF4DMVgM9UAD5TAfhMBeAzFYDPVAA+UwH4TAXgMxWAz1QAPlMB+EwF4DMVgM9UAD5TAfhMBeAzFYDPVAA+UwH4TAXgMxWAz1QAPlMB+EwF4DMVgM9UAD5TAfhMBeAzFYDPVAA+UwH4TAXgMxWAz1QAPlMB+EwF4DMVgM9UAD5TAfhMBeAzFYDPVAA+UwH4TBUQPP2eoPjBvN1NeuRwvpQel0elcQMFUUjwlNbmWP6ZHACfloKDJ7/3p7TgF7T88wNfemlJtujPdfIxHbJVcAtBPqpEPtJWGYwKPI2IO7JId7dfwkdoBDTWl1fV2UBOilLi1yflhn0+Ef8hh9fk64gVePJ9QfyHbDEfJf0A2e7O02q3Bk8jYo5bFunu+rLkEdBYj1b8bCA3Ba/jMXcChnxk7EX2VTEGGJv6qsSX9ANd/BZgIt/iO2l2K18sotqRhSp5BDRWbAmYQ7jryEOBSzwpgezzaUfsI3JV4abfTK3Ar4lJ50b/iN0dd35zsWrt3my+w3a0oo7VNnVhEdRVAOLBQPYKberJx5Bb5a843golfn+6rO8G6qMktv7b7NuJbLexC2XlyLdZi2FZ25HqK40gR4UGfzhf0KoZAyQMGXhexxOjvOFF/QYpu9wHCbxBNEwXPI+IOvLtuoF4Y9Wq4wtFVwKkVPhW/fUTYqKJ7V3XrfrDOWnVk29qfpV9WpO38dd1v5+AbHZZc2FRRUQd2TYzKzQCcuRPLlaVJ5CTZj5yBx1+X80YPDYjUNS9NWPwoCEC8JkKwGcqd/BodoqQbfOXB3j6+/3QCYknAC8TgM9UvuBnpNkleBQB+EwFpj5TAfhMBaY+UwH4TAWmPlMB+EwFpj5TTQyeDKR/dO/lk3L3Qshou+eIFvOcNa2pR/T/4c3t7956LUiEipOABGlzpSAvrBwedGc3hQdfkLdiAPy40uUKeYVlvZSDdzmFJgR1e/cSwI8uXa7sz7Zl+eidGrzf421kynrKHMCPLFOJx79uDzP1RvCxBeBl0uYKnbzcn8HsXMdPPQUGwMvEc2VzsiZvqziEmI9ml+BRxHJlf/c9/M/u3YTZ5ePsEjyKKvA/o2+n24cwmfqp7XtL6aQkJfFcWaPl2snUC+C7pNstuqnvAQAvE8kV+oa5ZNkidQjpUeJQQW6Bh1Z9kgo1Vo8o8wZy0+EH8Ekq2Fg95ozkBR1MfYqq63hHUy+CZ/9Rdz8FJZKMxFR3586eWg6aqvKxP5iLmPWfsMDzMwN4mSrwTx48eTCsHy/adnqk1+obUVWCALxM1cjdYoMs14pT9eNr8N0NVDX0Ru/eAXidAk7EEJvx3NR3mvv8dhiDBph6jUJ15zo+6lJeh+jvjWkAALxMvI4/HTqAI3ii3btqrzuqp+j2xRKAl6nJFdupEFZj9Trw3SMAfhq1wA97SCN05mzZCuYgtAC8TC1T79SqlxxVZDBv3EmIyg5F4ATgZdLlivzhjSN4Oo7TqtWFVp5dNAME4GXS5sqOLSxc+21NtjSZ+tZh1G7Hd5p17XaAOpqqV+ZbCwB4mUiuqB/LbpbyEKbGXbtYd009apV0ZNWfb4b+UN9m2AnAy8Ryhcydp5OprUOYvHRa9G1UreEcu3GcPnjn2gDAy8Qbd3cvHVv1Ji+1PW82xGa+lLtY73dNPYAPIp4rBaKf97EPYWnqG7Nu6Ni3ozeQAlMfQu65ogXfh1LzlrbkFNEHJgXgZaKNu7OngYZsG2qo9Rf1B+/V4VEpNAoGC8DL5FvilW7dihjVrXplkHbDT+zzKf2aD9skOF8FN/WdpjeqLLzyNB03Q8Pd7XAvwaCueK44v0IlB9/02VHDvWO9xUZAG0zVDpCXYQAfUFV3LsgrVM3oDOPPCdYVN2r5qMMgIQJ1/GDqg6kC7/oKlcqposv+dlDXrhq8Hq06YxAALxPPleGvUDG3eqwFtUfoWROvqgXC9tgs+v3BznWVFKMf32LbnXDbuhHkIT1k7iYCeJl4rhRosXYauVO6oaYP13d41pEspIcAvJ/qOv6FoWP1TYO+XXrppoia3wWdWI11tUtT3yLBecsXvPIVqs54DdkWCjdzaO6IxqvpvC6jOv0Eg7qqTf3QhzRtK19zL9GzZwpaDa9+DaDqtHlXBl6hrrq0uVLQAty7IRQhOMqOqcfYn9mM21Thyv5d0KkOkMKDRuZLzFbc1EsnYdDlzhSrXonxVI/hUHMPEOzN7dD1352F0dqrOwSl9FZwvD5lgnMXBy99Osduh0NvgcP3sZV/H/9if6sfRP4i9oP4sWdku/VT9sKUsmNlE17l7vgD4GXS5cr+RXWJl0y2rF+SI6I2no3fdar9TjyqkdsqQstrMAjAyxSsjq8GaXiTriyr8Xnl83U92HDDewBeJt+RO7kDQ9205FFV5kvnoTkAH1chh2x5r/1Za1Zlq4Xveq5gs3AAvExhx+rFkdi6ehfBKx/OGlPgbDtAgkiuhFjnjkja16qBC11569cqVTHa+wcJYrkS4oUK1Rhdu9j3HWTbNgnQexYfEIEEVWP1ri9UaNbAoTvtTfnU6s7dENLU928MAC9TsLH6Zp4lqvO+rt6lc+qDzqHuJhDAGxWuO1cN1Na9+Xb1HguyIiXd3RFPPR8FBN8u7Lr59NqbIMIdAuBlqk294wwc6XJnzcTaqlEn86VDEW7YphMnSFDVuBs8EaMzWlN2TX0ndPMUTx55t34OQA3Ay+QLXjzcb7wjaS+uMgnSB7Vln3QQAwDgZfJt1UuOCpW6vPte8ZVNx5TFapcqjQC8TKGGbFFTmFvHlJZadJIbeTD1scRN/Ysr4Ruy+hDKxY96I/Dqzp/+SMBWHoCXiYN/+ealG3iNa7+Bx7fd8h/ARxYHf/arm+J69S7r3LVcu0VeetwmYVrvzQw9c6wAXqYK/HZ3+xWhxPfWuWuHUK6BoxikC9tBb8YELaIF8DLV4MvCuM6ddoHDqqXOUQj4gw7JAfjBIrkSZg2cpl2vGLvRxekKB0z9UPl25yTH20tYNluWUUakA+BlMuWKOD1DZeq7I3WN0bdLBIAfWdTUa6ZeOYAXmvT2eR71qS2Al4nlSpC1bCVDtpGR2mn6FKQo3qoPtJatMATvYcSD3yoAXiaeK8HWsu0Xeud8D1/fA3iZfFv1luA9OmoAfhQ1AzhuIdTOSLbpkiIw9WOIgw/+3Tn3QZxoSiIRySm0qed+kFM/Pq6SSERyigS+Hr51jVwRZIj9B/Ay8VxZBzX18nem7OIO/2wPwMtU9ePfO3v6mksIgw/PEgrgR1MF/skDcSKGLoTO1A/ABKZ+LPFc2Sw2bp8Y1dbxCYzTtpRUYpJRuMeyyWp2CR5F2lwpyDhufxKmJsTIL0daKsEkJSDdY1mywOF6KQcvXQNHMZ964rsBwMukeyxLjzx6Zyj4qQdyALxMuseydEnTw8Xt7sqWzqYewKco7WNZuqil3Vq22nOAqU9PcYZskxKAl8mUK/Zz7pIVgJfJNFavAj8jzS7Bo6hp3LmFmJFml+BR1HTn3EKAqZ+5fGfgAPiZC8bqMxWAz1S+M3DA1M9cvjNwpOBTfDYH4OXynYGjcEkxk1NM0/TynYGjcEkxk1NM0/QKOlYPpn4+4qb+bDt0nbt0BeBlormyps/Zj/uj8poQc9LsEjyKmhLvFmJGml2CR5FhsuXxN9HRShYCTP3MRXNld2NVSGbg4Fp/c7ztWwMAfyVEcuVwscL/xWUsMfLixGV6dctTQrmdUFISEp1efbbF1MVWPft+fFPijZMt27Gmk93ppCQl0RL/4BKX7EJs1ZN5luxb4r0Qdq9JyxwmoADgZaK5UqBrlxvLZzR2dbwC8CSWAMDL5DvZ0vtsAD4NjQueWoLiK29e7l65tzL7DiMAL1PUefVyg//7bbEs3v6184l9BeBligleZdg/vrf6+O2PXnc+s6cAvEwxp14pwH+y3b3+yXZvOe9juAC8TFHn3FFTv3uBjRTUtXrx9TdW5Mf5zJ4C8DJFf3fud2/hov34re2YtXpXAF6m+C9NYpv+29Xj7Zi1elcAXqb406v3rx2+devWN8as1bsC8DKNAR7/erwds1bvCsDLFNrUf/GDhw9/0jny/AP2U+vfPvzDP1N8UBsAAAM2SURBVP0n3fr3z5zP7iEAL1Ng8H/4xw/LP/5LG7MMfOX55wB+Mvmb+odE3b+YMC/tnz58+H3++/kHz7//vx9+/vDhB8zhu78gJZ7sf4pdqZcvfviDh9/7rHz+EP/+tG8xBgvAyxS4judF+3NC/QP2+/k//7ikxfy/mQM2Chg82ccl/osfl3/81w+/+NFn7Hf5/Iff79mH4QLwMhlzZd2fkaU19Z+T0vp//0HQff4T/puUfVL3EydyiNbxZJ+YelzKv/Mhxo+P0rDPif0IW+QBvEy6XNF9TVpbx/+kU+I/YJU6KdCkxOOyTRt3X/zof37+Ga4aSFmn4ImHz0Pb+RLAy6XNlc1CWeJV4q36Th1PiH5a1/Hf+SEBT/b/8A/f+68fPPzOLz5g4Elp/y5xeAimPr70uVIsXMEnqNkleBQZcqU4/mYD3vAZ8VQF4GUy5cruulDiqd5H81GsvJu1fHNFH07rOk1QUFfuc+5swgH45AXgMxWY+kwF4DMVgM9UkFmZCsBnKgCfqQB8pgLwmQrAZyoAn6kAfKZyA7+uVr1jG2thETzboIdz65U0hbOW5ebEJdEgmZzAF8dbtkQS26h3PYLKJnXZBSVL9gD4wXICj0sa+1AZ26h33YPSQ5bg+0F3d34J4AfLDXz1NXm2sRE/Lm8btKTz+byCYvYFgB+syUr82pa7cFYymwrID9VEdfzh3NLOi0HJBnAfLI9WPZmU49mqr4OuXYpt76wAPoSgH5+pAHymAvCZCsBnKgCfqQB8pgLwmQrAZyoAn6kAfKYC8JkKwGcqAJ+pAHymAvCZCsBnKgCfqaYAL363GjS6AHymmhD8msy6e7Qiu3Rzc+vaJd5YkNdsrr26Yu6gSJoOPJlXv1ni3/QX/r1ZkG/UHS5WZBr1iyt2cILk5aHpwLP58fu771VT5ckbcXjraEXerXq0gvnzUTVhiWdQN/dO+CYGj/83JR6gx9Qk4K8jUpWTufXLcneDTtDHm5g3djl6ddnU8QhMfSyl2I93eTUL5KkUwZOX58HOR1aK4EEjCMBnKgCfqQB8pgLwmQrAZyoAn6kAfKYC8JkKwGcqAJ+pAHymAvCZ6v8BK5uyCsHegbUAAAAASUVORK5CYII=" alt="plot of chunk unnamed-chunk-13" />
A simple regression model assumes</p>
<p><em>A linear relationship between predictors and outcome</em>
The scatter plots describe a somewhat linear pattern.</p>
<p><em>Independence of residuals</em>
The observations are independent (each data point represents an individual).</p>
<p><em>Normal distribution of residuals</em>
Q-Q plot looks normally distributed.</p>
<p><em>Equal variance of residuals</em>
Residuals vs fitted plot looks balanced.</p>
<hr />
<h1>Logistic regression</h1>
<pre><code class="language-r">date()
</code></pre>
<pre><code>## [1] "Tue Dec 13 02:32:45 2022"
</code></pre>
<pre><code class="language-r">library(ggplot2)
library(GGally)
library(dplyr)
alc <- read.csv("data/alc.csv")
</code></pre>
<h2>2.</h2>
<p>The data, gathered of students in secondary education in two Portuguese schools, describe student achievement in Portuguese and mathematics. Detailed description of the data set and all attributes can be found <a href="https://archive.ics.uci.edu/ml/datasets/Student+Performance">here</a>.</p>
<p>Our version is modified from the original as follows:
Only students with both Portuguese and maths grades available have been included.</p>
<p>Averaged grades:
G1 first period grade average of Math and Portuguese (0-20)
G2 second period grade average of Math and Portuguese (0-20)
G3 third period grade average of Math and Portuguese (0-20)</p>
<p>Variables on alcohol use:
alc_use average alcohol use based on workday and weekend alcohol consumption (from 1 - very low to 5 - very high)
high_use high use of alcohol: TRUE if alc_use is > 2; otherwise FALSE</p>
<pre><code class="language-r">head(alc)
</code></pre>
<pre><code>## school sex age address famsize Pstatus Medu Fedu Mjob Fjob reason guardian
## 1 GP F 18 U GT3 A 4 4 at_home teacher course mother
## 2 GP F 17 U GT3 T 1 1 at_home other course father
## 3 GP F 15 U LE3 T 1 1 at_home other other mother
## 4 GP F 15 U GT3 T 4 2 health services home mother
## 5 GP F 16 U GT3 T 3 3 other other home father
## 6 GP M 16 U LE3 T 4 3 services other reputation mother
## traveltime studytime schoolsup famsup activities nursery higher internet romantic famrel
## 1 2 2 yes no no yes yes no no 4
## 2 1 2 no yes no no yes yes no 5
## 3 1 2 yes no no yes yes yes no 4
## 4 1 3 no yes yes yes yes yes yes 3
## 5 1 2 no yes no yes yes no no 4
## 6 1 2 no yes yes yes yes yes no 5
## freetime goout Dalc Walc health failures paid absences G1 G2 G3 alc_use high_use
## 1 3 4 1 1 3 0 no 5 2 8 8 1.0 FALSE
## 2 3 3 1 1 3 0 no 3 7 8 8 1.0 FALSE
## 3 3 2 2 3 3 2 no 8 10 10 11 2.5 TRUE
## 4 2 2 1 1 5 0 no 1 14 14 14 1.0 FALSE
## 5 3 2 1 2 5 0 no 2 8 12 12 1.5 FALSE
## 6 4 2 1 2 5 0 no 8 14 14 14 1.5 FALSE
</code></pre>
<pre><code class="language-r">glimpse(alc)
</code></pre>
<pre><code>## Rows: 370
## Columns: 35
## $ school <chr> "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", "GP", …
## $ sex <chr> "F", "F", "F", "F", "F", "M", "M", "F", "M", "M", "F", "F", "M", "M", "M", "F"…
## $ age <int> 18, 17, 15, 15, 16, 16, 16, 17, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 16…
## $ address <chr> "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U", "U"…
## $ famsize <chr> "GT3", "GT3", "LE3", "GT3", "GT3", "LE3", "LE3", "GT3", "LE3", "GT3", "GT3", "…
## $ Pstatus <chr> "A", "T", "T", "T", "T", "T", "T", "A", "A", "T", "T", "T", "T", "T", "A", "T"…
## $ Medu <int> 4, 1, 1, 4, 3, 4, 2, 4, 3, 3, 4, 2, 4, 4, 2, 4, 4, 3, 3, 4, 4, 4, 4, 2, 2, 2, …
## $ Fedu <int> 4, 1, 1, 2, 3, 3, 2, 4, 2, 4, 4, 1, 4, 3, 2, 4, 4, 3, 2, 3, 3, 4, 2, 2, 4, 2, …
## $ Mjob <chr> "at_home", "at_home", "at_home", "health", "other", "services", "other", "othe…
## $ Fjob <chr> "teacher", "other", "other", "services", "other", "other", "other", "teacher",…
## $ reason <chr> "course", "course", "other", "home", "home", "reputation", "home", "home", "ho…
## $ guardian <chr> "mother", "father", "mother", "mother", "father", "mother", "mother", "mother"…
## $ traveltime <int> 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, …
## $ studytime <int> 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, 2, 1, 1, 2, 1, 2, 2, 3, 1, …
## $ schoolsup <chr> "yes", "no", "yes", "no", "no", "no", "no", "yes", "no", "no", "no", "no", "no…
## $ famsup <chr> "no", "yes", "no", "yes", "yes", "yes", "no", "yes", "yes", "yes", "yes", "yes…
## $ activities <chr> "no", "no", "no", "yes", "no", "yes", "no", "no", "no", "yes", "no", "yes", "y…
## $ nursery <chr> "yes", "no", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "y…
## $ higher <chr> "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "yes", "…
## $ internet <chr> "no", "yes", "yes", "yes", "no", "yes", "yes", "no", "yes", "yes", "yes", "yes…
## $ romantic <chr> "no", "no", "no", "yes", "no", "no", "no", "no", "no", "no", "no", "no", "no",…
## $ famrel <int> 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 4, 4, 3, 5, 5, 3, 4, 5, 4, 5, 4, 1, …
## $ freetime <int> 3, 3, 3, 2, 3, 4, 4, 1, 2, 5, 3, 2, 3, 4, 5, 4, 2, 3, 5, 1, 4, 4, 5, 4, 3, 2, …
## $ goout <int> 4, 3, 2, 2, 2, 2, 4, 4, 2, 1, 3, 2, 3, 3, 2, 4, 3, 2, 5, 3, 1, 2, 1, 4, 2, 2, …
## $ Dalc <int> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, …
## $ Walc <int> 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, 1, 4, 3, 1, 1, 3, 4, 1, 3, …
## $ health <int> 3, 3, 3, 5, 5, 5, 3, 1, 1, 5, 2, 4, 5, 3, 3, 2, 2, 4, 5, 5, 1, 5, 5, 5, 5, 5, …
## $ failures <int> 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, …
## $ paid <chr> "no", "no", "no", "no", "no", "no", "no", "no", "no", "no", "no", "no", "no", …
## $ absences <int> 5, 3, 8, 1, 2, 8, 0, 4, 0, 0, 1, 2, 1, 1, 0, 5, 8, 3, 9, 5, 0, 0, 1, 1, 2, 10,…
## $ G1 <int> 2, 7, 10, 14, 8, 14, 12, 8, 16, 13, 12, 10, 13, 11, 14, 16, 13, 10, 7, 10, 12,…
## $ G2 <int> 8, 8, 10, 14, 12, 14, 12, 9, 17, 14, 11, 12, 14, 11, 15, 16, 14, 12, 6, 11, 14…
## $ G3 <int> 8, 8, 11, 14, 12, 14, 12, 10, 18, 14, 12, 12, 13, 12, 16, 16, 14, 12, 6, 11, 1…
## $ alc_use <dbl> 1.0, 1.0, 2.5, 1.0, 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0, 2.0, 1.5, 1.0, 1.5…
## $ high_use <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FA…
</code></pre>
<p>There are 370 observations (students) and 35 attributes.</p>
<h2>3.</h2>
<p>Chosen variables and hypotheses:</p>
<ul>
<li>
<p>famrel (Quality of family relationships 1-5)
My suspicion is that poor family relationships might correlate with higher alcohol consumption, i.e., there could be a negative correlation.</p>
</li>
<li>
<p>G3 (Final grade 0-20)
Again, a possible negative correlation.</p>
</li>
<li>
<p>goout (Going out with friends 1-5)
Outgoing people might use more alcohol.</p>
</li>
<li>
<p>failures (Number of past class failures)
More failures might correlate with more alcohol consumption.</p>
</li>
</ul>
<h2>4.</h2>
<pre><code class="language-r">g1 <- ggplot(data = alc, aes(x = high_use))
g2 <- ggplot(data = alc, aes(x = alc_use))
# Plot bar plots grouped by family relations
g1 + geom_bar() + facet_wrap("famrel")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-16" /></p>
<pre><code class="language-r"># Most respondents report great relations with their parents. In fact, there are very few respondents who report worse relations (famrel <=2) to begin with.
# Those with worse relations do not report higher alcohol use relative to those with better relations.
# It's hard to tell counts from bar plots, so let's check cross-tabulations
alc %>% group_by(famrel, high_use) %>% summarise(count = n())
</code></pre>
<pre><code>## `summarise()` has grouped output by 'famrel'. You can override using the `.groups` argument.
</code></pre>
<pre><code>## # A tibble: 10 × 3
## # Groups: famrel [5]
## famrel high_use count
## <int> <lgl> <int>
## 1 1 FALSE 6
## 2 1 TRUE 2
## 3 2 FALSE 9
## 4 2 TRUE 9
## 5 3 FALSE 39
## 6 3 TRUE 25
## 7 4 FALSE 128
## 8 4 TRUE 52
## 9 5 FALSE 77
## 10 5 TRUE 23
</code></pre>
<pre><code class="language-r"># Here, my hypothesis seems wrong.
# Plot boxplots of grade and high use
g3 <- ggplot(alc, aes(x = high_use, y = G3))
g3 + geom_boxplot() + ylab("grade")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-16" /></p>
<pre><code class="language-r"># Non-high users seem to have slightly larger variation in their grades, and indeed better grades. There are some outliers among high users in both ends, though.
# Plot bar plots grouped by going out
g1 + geom_bar() + facet_wrap("goout")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-16" /></p>
<pre><code class="language-r"># Most people seem to be in the "moderately outgoing" category (goout value at 3).
# Very outgoing people are more likely to report higher use of alcohol than lower use of alcohol, which lends support to my hypothesis.
# Let's look at cross-tabulations, too
alc %>% group_by(goout, high_use) %>% summarise(count = n())
</code></pre>
<pre><code>## `summarise()` has grouped output by 'goout'. You can override using the `.groups` argument.
</code></pre>
<pre><code>## # A tibble: 10 × 3
## # Groups: goout [5]
## goout high_use count
## <int> <lgl> <int>
## 1 1 FALSE 19
## 2 1 TRUE 3
## 3 2 FALSE 82
## 4 2 TRUE 15
## 5 3 FALSE 97
## 6 3 TRUE 23
## 7 4 FALSE 40
## 8 4 TRUE 38
## 9 5 FALSE 21
## 10 5 TRUE 32
</code></pre>
<pre><code class="language-r"># Check cross-tabulations of failures and high use
alc %>% group_by(high_use, failures) %>% summarise(count = n())
</code></pre>
<pre><code>## `summarise()` has grouped output by 'high_use'. You can override using the `.groups` argument.
</code></pre>
<pre><code>## # A tibble: 8 × 3
## # Groups: high_use [2]
## high_use failures count
## <lgl> <int> <int>
## 1 FALSE 0 238
## 2 FALSE 1 12
## 3 FALSE 2 8
## 4 FALSE 3 1
## 5 TRUE 0 87
## 6 TRUE 1 12
## 7 TRUE 2 9
## 8 TRUE 3 3
</code></pre>
<pre><code class="language-r"># Can't really say that the data lend support to my hypothesis here: there are very few failures in total and they seem to be somewhat evenly distributed between high and non-high users. However, considering the proportions of high vs. non-high users, there are proportionally considerably more non-high users with zero failures.
</code></pre>
<h2>5.</h2>
<pre><code class="language-r">m <- glm(high_use ~ famrel + G3 + goout + failures, data = alc, family = "binomial")
# view summary
summary(m)
</code></pre>
<pre><code>##
## Call:
## glm(formula = high_use ~ famrel + G3 + goout + failures, family = "binomial",
## data = alc)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8046 -0.7672 -0.5733 0.9947 2.3416
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.68968 0.80944 -2.087 0.0368 *
## famrel -0.37266 0.13616 -2.737 0.0062 **
## G3 -0.02464 0.04099 -0.601 0.5478
## goout 0.75188 0.12022 6.254 4e-10 ***
## failures 0.48924 0.22963 2.131 0.0331 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 452.04 on 369 degrees of freedom
## Residual deviance: 388.05 on 365 degrees of freedom
## AIC: 398.05
##
## Number of Fisher Scoring iterations: 4
</code></pre>
<p>Going out is the strongest predictor of high alcohol use (p < .001). Family relations also have a significance level of < .01. Failures are significant at p < .05.</p>
<p>Final grade does not have a significant correlation with high use.</p>
<p>In terms of my hypotheses, famrel, goout and failures are supported. G3 is not.</p>
<pre><code class="language-r"># compute odds ratios (OR)
OR <- coef(m) %>% exp
# compute confidence intervals (CI)
CI <- confint(m) %>% exp
</code></pre>
<pre><code>## Waiting for profiling to be done...
</code></pre>
<pre><code class="language-r"># print out the odds ratios with their confidence intervals
cbind(OR, CI)
</code></pre>
<pre><code>## OR 2.5 % 97.5 %
## (Intercept) 0.1845781 0.03639237 0.8771040
## famrel 0.6888964 0.52587985 0.8985892
## G3 0.9756601 0.90036973 1.0578228
## goout 2.1209922 1.68623053 2.7043570
## failures 1.6310777 1.04644221 2.5883902
</code></pre>
<p>The odds ratio here is the change in the odds of high/low alcohol use.</p>
<hr />
<h1>Clustering and classification</h1>
<pre><code class="language-r">date()
</code></pre>
<pre><code>## [1] "Tue Dec 13 02:32:47 2022"
</code></pre>
<pre><code class="language-r">#library(GGally)
#library(dplyr)
library(MASS)
library(tidyr)
library(corrplot)
library(ggplot2)
data("Boston")
</code></pre>
<h2>2.</h2>
<p>The data set describes housing value in suburbs of Boston, Massachusetts. The data set has been put together and analyzed by Harrison & Rubinfeld (1978). The raw data has been collected in ~1970 (Harrison & Rubinfeld, 1978).</p>
<p>Listing of its variables are available <a href="https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/Boston.html">here</a>, for instance. Definitions of how the variables have been collected and calculated can be found in Harrison, D. and Rubinfeld, D.L. (1978) Hedonic prices and the demand for clean air. J. Environ. Economics and Management 5, 81–102.</p>
<pre><code class="language-r">str(Boston)
</code></pre>
<pre><code>## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
</code></pre>
<p>There are 506 observations and 14 variables. Each observation represents one neighborhood/town.</p>
<p>In summary, the variables include median values of homes, variables describing housing, infrastructural, environmental and industrial structure, and demographic information on the neighborhood (Harrison & Rubinfeld, 1978).</p>
<pre><code class="language-r">summary(Boston)
</code></pre>
<pre><code>## crim zn indus chas nox
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000 Min. :0.3850
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000 1st Qu.:0.4490
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000 Median :0.5380
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917 Mean :0.5547
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000 3rd Qu.:0.6240
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000 Max. :0.8710
## rm age dis rad tax
## Min. :3.561 Min. : 2.90 Min. : 1.130 Min. : 1.000 Min. :187.0
## 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100 1st Qu.: 4.000 1st Qu.:279.0
## Median :6.208 Median : 77.50 Median : 3.207 Median : 5.000 Median :330.0
## Mean :6.285 Mean : 68.57 Mean : 3.795 Mean : 9.549 Mean :408.2
## 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188 3rd Qu.:24.000 3rd Qu.:666.0
## Max. :8.780 Max. :100.00 Max. :12.127 Max. :24.000 Max. :711.0
## ptratio black lstat medv
## Min. :12.60 Min. : 0.32 Min. : 1.73 Min. : 5.00
## 1st Qu.:17.40 1st Qu.:375.38 1st Qu.: 6.95 1st Qu.:17.02
## Median :19.05 Median :391.44 Median :11.36 Median :21.20
## Mean :18.46 Mean :356.67 Mean :12.65 Mean :22.53
## 3rd Qu.:20.20 3rd Qu.:396.23 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :22.00 Max. :396.90 Max. :37.97 Max. :50.00
</code></pre>
<p>The median value of housing seems to be capped at $50.000, which looks like an artificial decision.</p>
<p>Let’s visualize the data set.</p>
<h2>3.</h2>
<pre><code class="language-r"># Create scatterplot matrix
pairs(Boston)
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-22" /></p>
<h3>Commenting on median value plotted against other factors:</h3>
<p>Not surprisingly, higher-value areas have lower crime rates. The density of residential areas (var zn) and whether tract bounds river (chas [this is not surprising as this is a dummy variable anyway]) do not have a clear effect on housing value. Prices seem to be lower where industrial density is very high, but low industrial density has both high and low-value areas. The situation looks fairly similar with highly polluted areas (one might ask how independent nox and indus are). As average number of rooms in units (rm) grows, so does value – again, not surprisingly.
Newest areas are not cheap, but the priciest areas are not new. Both the cheapest and the most expensive area seem to have a short distance to Boston employment centers. Rad – index of accessibility to radial highways – seems to have a very binary distribution despite its values varying from 1 to 24. I am not sure how to interpret how tax and value are related (the highest taxes seem to be in cheapest areas, which seems odd from someone coming from a progressive tax state). Pupil-teacher ratio is generally lower in more valuable neighborhoods, as one would expect. Towns with a lower proportion of African-Americans are not among the most expensive areas. There is a high correlation between the price of housing and lower percentage of “lower-status” population (i.e., male workers classified as laborers and adults with no high school education).</p>
<pre><code class="language-r"># Look at correlations
corbos = cor(Boston)
corrplot(corbos)
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-23" />
The strongest correlation seems to be between radial highway accessibility and property tax rate. Looking at the scatterplot matrix, there is a highly taxed highly accessible outlier, which may confound the results.
Distance and pollution have a strong negative correlation: far-away areas have lower pollution.
Nox and indus are also strongly correlated.</p>
<h2>4.</h2>
<pre><code class="language-r"># Standardize the dataset and print out summaries of the scaled data. How did the variables change? Create a categorical variable of the crime rate in the Boston dataset (from the scaled crime rate). Use the quantiles as the break points in the categorical variable. Drop the old crime rate variable from the dataset. Divide the dataset to train and test sets, so that 80% of the data belongs to the train set. (0-2 points)
boston_scaled <- scale(Boston)
summary(boston_scaled)
</code></pre>
<pre><code>## crim zn indus chas nox
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563 Min. :-0.2723 Min. :-1.4644
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668 1st Qu.:-0.2723 1st Qu.:-0.9121
## Median :-0.390280 Median :-0.48724 Median :-0.2109 Median :-0.2723 Median :-0.1441
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150 3rd Qu.:-0.2723 3rd Qu.: 0.5981
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202 Max. : 3.6648 Max. : 2.7296
## rm age dis rad tax
## Min. :-3.8764 Min. :-2.3331 Min. :-1.2658 Min. :-0.9819 Min. :-1.3127
## 1st Qu.:-0.5681 1st Qu.:-0.8366 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668
## Median :-0.1084 Median : 0.3171 Median :-0.2790 Median :-0.5225 Median :-0.4642
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4823 3rd Qu.: 0.9059 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294
## Max. : 3.5515 Max. : 1.1164 Max. : 3.9566 Max. : 1.6596 Max. : 1.7964
## ptratio black lstat medv
## Min. :-2.7047 Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.:-0.4876 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.2746 Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.8058 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 1.6372 Max. : 0.4406 Max. : 3.5453 Max. : 2.9865
</code></pre>
<p>Columns are scaled by first subtracting column values by the corresponding column mean, and then dividing the difference by standard deviation. This way, the mean for all variables is at 0, and we can compare variables in a more meaningful way.</p>
<pre><code class="language-r">boston_scaled<-as.data.frame(boston_scaled)
boston_scaled$crim <- as.numeric(boston_scaled$crim)
# create a quantile vector of crim and print it
bins <- quantile(boston_scaled$crim)
bins
</code></pre>
<pre><code>## 0% 25% 50% 75% 100%
## -0.419366929 -0.410563278 -0.390280295 0.007389247 9.924109610
</code></pre>
<pre><code class="language-r"># create a categorical variable 'crime'
crime <- cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label=c("low","med_low","med_high","high"))
# look at the table of the new factor crime
table(crime)
</code></pre>
<pre><code>## crime
## low med_low med_high high
## 127 126 126 127
</code></pre>
<pre><code class="language-r"># remove original crim from the dataset
boston_scaled <- dplyr::select(boston_scaled, -crim)
# add the new categorical value to scaled data
boston_scaled <- data.frame(boston_scaled, crime)
# number of rows in the Boston dataset
n <- nrow(boston_scaled)
# choose randomly 80% of the rows
ind <- sample(n, size = n * 0.8)
# create train set
train <- boston_scaled[ind,]
# create test set
test <- boston_scaled[-ind,]
</code></pre>
<h2>5.</h2>
<pre><code class="language-r"># Fit the linear discriminant analysis on the train set. Use the categorical crime rate as the target variable and all the other variables in the dataset as predictor variables. Draw the LDA (bi)plot. (0-3 points)
# linear discriminant analysis
lda.fit <- lda(crime ~ ., data = train)
# print the lda.fit object
lda.fit
</code></pre>
<pre><code>## Call:
## lda(crime ~ ., data = train)
##
## Prior probabilities of groups:
## low med_low med_high high
## 0.2623762 0.2623762 0.2301980 0.2450495
##
## Group means:
## zn indus chas nox rm age dis rad
## low 1.0077966 -0.9013763 -0.08661679 -0.8911379 0.45085821 -0.8903606 0.8851931 -0.6947544
## med_low -0.1320881 -0.2552932 -0.04947434 -0.5300626 -0.16156904 -0.2934666 0.3206352 -0.5409032
## med_high -0.4033301 0.2702447 0.19334945 0.4181606 0.01553335 0.4386564 -0.4093262 -0.4520945
## high -0.4872402 1.0171737 -0.07348562 1.0794376 -0.38004812 0.8082157 -0.8388567 1.6375616
## tax ptratio black lstat medv
## low -0.7195738 -0.44659523 0.37096288 -0.75369946 0.53649222
## med_low -0.4615823 -0.01301423 0.34853814 -0.11935320 -0.03567311
## med_high -0.3154313 -0.25660396 0.01487736 0.07564177 0.09078245
## high 1.5136504 0.78011702 -0.87620173 0.85077290 -0.74897074
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3
## zn 0.088258721 0.65837316 -0.88806054
## indus 0.093040787 -0.25358910 0.21574553
## chas -0.110019905 -0.04817162 0.06112401
## nox 0.349907616 -0.74229932 -1.31086088
## rm -0.196730284 -0.04478351 -0.22896315
## age 0.170060613 -0.29252053 -0.10113863
## dis -0.026360903 -0.21139852 0.15396380
## rad 3.699395868 0.90128195 0.13610207
## tax -0.001425383 0.09251606 0.37290789
## ptratio 0.107397040 -0.03809865 -0.17966173
## black -0.123001318 0.06853286 0.22237406
## lstat 0.222069923 -0.25010923 0.29858207
## medv 0.223316232 -0.41990591 -0.23586695
##
## Proportion of trace:
## LD1 LD2 LD3
## 0.9572 0.0322 0.0106
</code></pre>
<pre><code class="language-r"># the function for lda biplot arrows
lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){
heads <- coef(x)
arrows(x0 = 0, y0 = 0,
x1 = myscale * heads[,choices[1]],
y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads)
text(myscale * heads[,choices], labels = row.names(heads),
cex = tex, col=color, pos=3)
}
# target classes as numeric
classes <- as.numeric(train$crime)
# plot the lda results
plot(lda.fit, dimen = 2, col = classes, pch = classes)
lda.arrows(lda.fit, myscale = 2.5)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-26" /></p>
<h2>6.</h2>
<pre><code class="language-r"># Save the crime categories from the test set and then remove the categorical crime variable from the test dataset. Then predict the classes with the LDA model on the test data. Cross tabulate the results with the crime categories from the test set. Comment on the results. (0-3 points)
# save the correct classes from test data
correct_classes <- test$crime
# remove the crime variable from test data
test <- dplyr::select(test, -crime)
# predict classes with test data
lda.pred <- predict(lda.fit, newdata = test)
</code></pre>
<pre><code class="language-r"># cross tabulate the results
results <- table(correct = correct_classes, predicted = lda.pred$class)
# calculate model precision & sensitivity
table(correct = correct_classes, predicted = lda.pred$class)
</code></pre>
<pre><code>## predicted
## correct low med_low med_high high
## low 15 5 1 0
## med_low 6 12 2 0
## med_high 0 15 15 3
## high 0 0 0 28
</code></pre>
<pre><code class="language-r">1-diag(results)/colSums(results) # Precision: fraction of false positives
</code></pre>
<pre><code>## low med_low med_high high
## 0.28571429 0.62500000 0.16666667 0.09677419
</code></pre>
<pre><code class="language-r">1-diag(results)/rowSums(results) # Sensitivity: fraction of false negatives
</code></pre>
<pre><code>## low med_low med_high high
## 0.2857143 0.4000000 0.5454545 0.0000000
</code></pre>
<p>The model is best at predicting high crime areas. No areas were misclassified as high, although one high area was falsely classified as med_high. The model had more difficulties with classes med_high and med_low; many med_high classes were incorrectly classified as med_low, making 45% of med_low classifications incorrect and greatly reducing the sensitivity of med_high classification. Areas with a low crime rate were better classified, with about 80% precision and 26% sensitivity.</p>
<h2>7.</h2>
<pre><code class="language-r"># Make another scaled Boston data set
boston_scaled <- scale(Boston)
# Distances between observations
summary(dist(boston_scaled))
</code></pre>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1343 3.4625 4.8241 4.9111 6.1863 14.3970
</code></pre>
<p>An ideal grouping has a minimal within-group sum of squares (“WGSS”) over all variables. Let’s plot these for one to ten-group solutions to see which solution has the smallest WGSS.</p>
<pre><code class="language-r">set.seed(123)
# determine the number of clusters
k_max <- 10
# calculate the total within sum of squares
twcss <- sapply(1:k_max, function(k){kmeans(Boston, k)$tot.withinss})
# visualize the results
df<- data.frame(wgss=c(twcss),groups=1:k_max)
ggplot(data = df, aes(x=groups, y=wgss)) + geom_line() + scale_x_continuous(breaks = 1:10)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-30" />
There are two “elbows” in the plot, at 3 and 8 groups. Let’s investigate those further.</p>
<pre><code class="language-r">set.seed(123)
# k-means clustering
km3 <- kmeans(boston_scaled, centers = 3)
# plot the Boston dataset with clusters
pairs(boston_scaled, col = km3$cluster)
</code></pre>
<p><img 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aFQ50psllpikw4LfM/V/zTdRHz28eT3L3/afXhz8ejpDPD0p4RYQ8EMeMcEs66EUmjA00cB2SqzBHjs7yrwGcDO4wbrZPCQkptOBSst/hSAbyZPFj+FT786e/98Cqp89adfdgPAu6w9vWwPj7xcMBI/I43IMD7GvAz4FnNtXACoDzwrCHpk7ls68K0SezQGvLY0vSx5An4C/M+7i5fTv3//8as3y129cbmZetlh/zpCAMArRIpO6mu7er4wi5M7jjxDNvn4gh9O+h2pBstRRWazTlH1cSZ3s8DDkR+YnIH/9Q8vnr+/+v/86TdnfXchQqgWAV/CkcHVWwl+YY5sFn+kzLLdpOY0gOgThChY3Fvv4vQRLT73bif6rfdO+CnfAL4GXt2Wq48BYlEMpv7ZxzletqUuzFoFAM3VN2PnNPOJzLG7FF4mWN45r8ttUswiSCaAzwKEDtIG3juIiVak1oFXAwZnaSCrDHPyTEUk8jApcSnwsmwZJu1CxIpiWWkOpYQ7V2abIcrRPIXZlcTKx3uNbfmxHKbsvDbDCvHxtWSJHbr6mImJnSOl44DDmC0nIuT35sGDBw8PsVZv+9GyQogp/3LgedmO9oWsgm6YdEsHBTuY5NF6SPR88xwVVW7CV/spYQatuBA725nVY0WFKUkrXH2OymsA33kXr1XeoT2At/sDL7Gzc/HxPeApABx4Tl6rWZWbugoNeFGzHz3ZEt0/6zWKvo8xudsH+P4TZhd4eSLGzFEoTAVNwTRXDxIrZ9nOHIzQaCo7fYecgKTphBUjymVlqxrHEj+0bxj9hIG3i+1OAb6j/mhC8EQ2C/zMwQiYpQO8Hwe+eejCAuD/9tw3aQz43uKxrdeC1GuFq377K89K2fIa8ZnldqpmXNXGBJW5Zgh/oGbZbEi1PI9XknMe7RpxlJ8zNzTGG6wBf34Y4De6T7QBv1LagF8pbcCvlDbgV0ob8CulDfiV0gb8SmkDfqU08gZXXq7LlpJs/mPKl5yal8RMPuVOrkP1yk7v4/VkE4p0tVqLcbN5KdGRMthm1pnFN3G2I6TCyYsotnHhTzx/UFt8q+RYMj3N0RW5PSSHP2WFzx5pl61aMl08Npa+W8FFb5tv5JleKufIk/aLKl52Bj4py0MAYdzvAMCzgIr4gmQOeK3mvBIK74YE8K2AivAedjpoP5xjbJDZ4/c54LlKPAN+qu0wwItLhY3So2gXzPDm/LARo+jIubKLfjHwkZWYvBeBTDXRhlMwxQvMvJvGRfOqYkvcOfBsd684r5Oks3316S182h3F99V76CZK/DbHnb2PT6k2tU7Dp0mdrPxS4Tmr7CZfi/mYZd/PVs1TJyu/VPh+quh+tmqeOln5pcL3U0X3s1XzdN2sd15F97NV87QBf2vMG/C3Wvb9bNU8Lcy6Te4Oz3wngL+2JMuY3551k69V9ifHvAEfP308ebJ7+/vHZx9OHp+FIOo7gN0G/GzyPPOrsw9vzk8vnv+yexeDqO8Adhvws8lLgL/cvT27ePZvT3+MQdR3ALv7D/wNTO5+fXoy3UP97Id/fvHbEER9B7C7/8BfW5JPVkX3s1XztAF/a8yfLPD8Nun7qaL72ap56mR9vfNwm/TMpcJKmD4JFLPllbpLG1bgpsmZZuRtMIsvFVZPxOjeNJklZse5LLhU2OYLnbMsWHOmcmclLYjTnjdNlig7TY06dbLy26Tn7pa1VHnlI+ggNUO7W7YrW2iWXX63LOyrCBXb+btli8QQLRvuCKXIGyJY3NQTzycIO4/wblmqCGdTm0lJEve975a1B7xbdvQ26Q34ewI8p5mLf6/n6lXywD1yqfD+rp6FSS+4VNgmV98QuyB/Z1z9RveZNuBXShvwK6UN+JXSBvxKaQN+pbQBv1LagF8pbcCvlEbWeoy2dLcwGdenlDDpmbI1oqlx3ZWubjaZHVwu6Yy2IomCiQys6GaYtMqtCUauS6Q15wDsun5XmZ1Ja9Bq2fNoLs86e8Vor3hkldeHKFcgLH55Fz4k2JW7BhhzUmituXsYu9FkE63qXEbUvtckfMqvOMtVBbTsBGtK48ypR+hlz9KQxc+GSbeTITFn7TIPAu/Z9rAO8Ia+XFINpVsztXglscOshEkrotVUacaMuZ182GvEFXyoJD2HwMQzs8xmRv2ibO6FG8y6t24VrUHb9GMpsd3lZlrFG6A4cO4umsmHvUZc0RGMWJ3iAfictcfcMF+1bKKEXHKT+frA9yy+5XUIpxjjcxNEz6WDd+pRgpkBT74e7hpxFCP17E8CeDZ/6xmWEfpVcL9R4KOwEkYjCLsz+Vmt8HDXiDMhyrykJneKv0ngTQ94Xb+tom/C4o3nNoWSGi1VA15FoEX7Ay924BjlqnWqopJ4cOCFdqzKDE9WyNwqGuSWgolUBo5M1Fw9Il/Llu1qPAu6eOfJsXbgsI6XwKfJeNUmFE+v465FUGaltr6UbeBxv2QxiHAV/DDw/P54BCffAGlIaSUr00eBmcsNbWi2inWqintCXmTp0l7A5+kUd/UDwHvP+69SW1/Kpori3Uwin/HaKssc8MaodoutKnedSODZPZANo522IXLB7OI1rbAAMHARETZxlvL15DCEGprMrpn0AHxIDHrIDWXMghOBj1cSP969PXv3hpddm+/S3kh+2dPcnruG2OEaxTbw+dbXsvDCwLG2dve4siiBj+ooEFLg2Z47j+6i7rkzx3b1rgf8ZGmeXddEwbFhU2puxnRWIZw+Ke6WpT9NGeOVxBfPPj56xssOUlU1+emCOgR+Aqi/y1YXO+rXcodd86UaDR3FStaoj3SLeFqAZd7EmzJfMrjLluJeDj+k8weyyzaeo2gMt7sOjQOfvTznDy62DXzYdZ3PNzTBR5ou8OAk/XRowsV33+w+Prn8+jkv2yfDzTTtemXAuxbwBRF6wSHBLt4NCmpAV59rLIkIvHPxiMMEEQfegclT4El7MvC+AXy4vBYvZZ2lUVff5u+7+gi7K66ejIuZmdcmgX85RdS+On11imVnky6u3jJXL7dXs7tlTdxXryz0x2NQ4bhTcPUJ9axz4ep9BMS65Oo58CYNROWYSlZ26TBOuVTY5Pb6usH6GJM7bQxB7GIkkXYHW9ncHjE2jFkWLYBvV510F+3C8mu84kG4MTAiv9JC4AuTBnwMhvCtgIp053ABHv3YVIDPt9qmM3wBO3apsIFIhHQOdB3CGPB59kc272t60mkAePVwZBwN8/278p5BW+7b9nVEpczdu2UXAF/jPbgOEnbBqLM/pW/x0n1wlIn2SKFSYlQ2+YPqEuRCWg40CTh1LxUOcRs09gjmrNrdspbhfiTgl940mWOHvGcWb8N10K488wGzrK15JyP7MQMPgSuaYPGmVrz22/gCTFUdMjuQBVtVbh9Xb5oUwTQ8mRIVgNSc3GR8fuDAcyLF3dht0gtCqCy70fewwKMGVOCjBPEA9MosbpfVbiRWa1aV3qyZqUS0SgJfVea1a8S7wN/ubdKiGfBYfAvAuyQBMDOJNWa9ZuCT44S41dY3XAMtTZSdDEVxF1LdR5nczQNf7sVtA49LWZ2yh4FnKtZdvcvDMTLPAt+o+aDANzRGFTYLPJZ4g7dJU4lDD8RmwIy/D7zvOUX80dAqckXq5EPxxxqzcPWtmlWlN51gCvdutcp6KEYFkzGDzFY8Gh3sNmmjUC2pUL42GZY6rMY+XraWTCrWgpV5QoM53VwzJJi8zEaKXW7jmW0Vrrrm6XpXJTwdEdtuk95I0Ab8SmkDfqW0Ab9S2oBfKW3Ar5Q24FdKG/ArpQHgjbqYUZLTDohFSx38HlWvLO84di+wCVf00nwktSeYSLGw9Yrcg6wyR7H1dZKUahshq1Ni3OVBC+gINr2CL8yqvtvMYdvBAJoDWfsbMeKNzZ09dyVVuVRYXRbVFr1dTeCrri3BDK7ATrtXLd3TGOQu6ZxZrNYb2ap66bDxngEfkmxeUMVWcZEl8J1WoTDK8m6fRpZs5zZiyKVmsaqds/KgXykzbLbMqLtofqzqGeBteY+Q10CdhWMxq2x5D4my3E5KNrxV5EUKbMQorOlvHkwgZCZdMCwWt98S5E8G31BpmtCpAzyPs1XLbb3HSqdA68DnV/KL385R4GXVs8BbTrCLmWC7CHjlJU3jDVrhTX+zZC63k5YzC3xHyj51gOdxturbXmHxFkQRKkpZRZi/2HoFW7UpYkWEAVfPcWf3x1e9qTtwmEoVi7ddiy9FzFh82BmGwDumcmROac6SE5iXUgd4Gmcb50QGmsUlAZ+ZmwrNSJJN5QjguSCwSzx2onhoidyxNwS8YQdnG7I/s/ZMrBlUagTwYYNUTSTMZV9WqprtkBYyQ9nxG6ocmNPObNo0TRM6dYDncbbR2pBBzuqROPBlezUDXomk4dvmTD29mok+5+oB9lxMbUGcdwPCVLAZ4B1slePAO6ycbZtLmTOHFZE0YjrPmWMYUCreamfVtGggq5Mb6zEKStt0l1Mr8GmrK1YOg2RpmKfcMaSoaAG3zfUaRlWfysBIGnLydzZQ0SoWAVeKdjlDTSStYlbgtH31NY7QGrIf0eej3VOeMosHZkekVwbiDo1kNXzE8SyYaxnwMYSK7SATXkoCT0+QgkDUpcCbck4+AB++Uolx69UM8GEbX2kpA55ZvBJJYwxx2uyiAnqIV3ILEniTgPcCnD4NWzxxO4a5egV4xdVn4CFgbYnFw9leoKJ+w6q5l7P/jbB4MsED4GPYzZzFl1gbBN5QlZTAFyipwFoMuKTaKmyxeTAVelGBIwsci2hh1iRVFTPPXxvA5ydnPg2iwNOgyWHgjXT1P508/fbxvz8+4w2jis8m0gFeuPqAbRf4iH5OhAkYwT2VpLn6Gixb9VBvqKj9gwJfYudMWiW6AYs3Pgd5IvDkuWIJ8NexeAX489Pz0/fPL17yhuWaSdAkB36yGtJvKbPpAe/SnTTTv/FOGsXiHfV1jk0Tk/tyOXROsXg6zmvAB54bAj5F9noJfDKYhPtBgQclKK7+7dnbs19PJfBR+XG8rGUU5oxInZ6jq0/Iq4K57Ol14F18xna56UaWVBqjAF8DpTXgs72HmMU0Yzoy8MXVew588ni2EUIFzZgBXizZujmLbwKf5mDF1WvAOxioqMUb50C6BvBOcfWOzBGS8FazeKO5+vJDIz6+pBZF3IDFa/wOz47gcQsF9twkVJEEnh6rYpnb8xrwrYYlxVuXOycCn9QXbTMJTgRDNLwCfHT1piRCzckgS8X8FqrsOk1BkjQgxcrSQ5uAGafIR5zc5bpx/lKUoJSF4BDgZ49CAXVH3ZEL0Lzi6lsNi1XnfoSLQEGYVLbOzHEH4ItcDeCr48odjumuKtSk04oNpjp4mhevZVkw2HEsvtRtOKA5uVN8+hAHI6X/SGZ48Im/0NYPWHytmbSDfusy8yUGBN6n4HZDyoZiaiC0L9qryUWVQR2OCRaaXEVWLJ7q8GiuvnTQawCfcxr2Y5+5fILWjwFPU4aAF2kceJ7YZE7dnX/PcyWD3NmFpET+ECW7giptkzpZL3/55ecncMVo19XfGeCZfm8ReO8rmsXjk9ScP33kFu85GAcC/vzhH3/8zX/sSFbRw24ceE90dyiL18BtMh8aeOo+mWBkKMj6grKj8+WDx1LqZf3w6D+fYFYJz80CD8uF+wPvAfhbtXjPbJy2yki9iLK1EhdRN+vlD58TmXWqJXWTr8V8zLJvj/moZc9SP2svsn6jO0194HuR9RvdaeoD34us3+hO08CosNF9og34ldIG/EppA36ltAG/UtqAXykNAI+xwGKtyMkrbuk6lKs0/e74Roz+MlVkoxtwWBRUTUjbHZYvkLm6bVFtFdlmypPF7ijO7LDZdN8ECFa34IDGeiopHEnv7sgBFUUAY3ATWNqF1Ci+7j9KwJuRXbalefrWK8Q9xen3m4g9smzDESxRp63t1RTXKkplLk22tZJejwQZFDOSwGe9uBpMrzW3o4B5KnLA+ySazDercP2mHLmjmhHg2WZLmmzyi0Pn8u45Gnh3XeBjpIgq2BzwmWwfeH17tXLBObzWSj4w/Mln12tN1Wkvi4e3ZayVjeK5qzdjwMvNlgg84D7d9DD3yooBn/ERLDHRNnbZkr2AbeBN2pXnGiFU3pSRjiqwMFfU9e3VeYfw0V1949V/1FzrgG/Ddtm6sYCKEHEHwIOr99ECXHQk7CauZRafTjTXWuXa++rJVVElseXqUzZp8WFbVokvKszVjdcIJgX4GEgTIw+Oc2x5FMBD9aiiAG7rCAEHO2XpDSV+yfZqHOPxlXouImUIOhgCPm6BrmeKS+AbFk/8WEkERxXgsbR/SIv3ZY0f1HYAACAASURBVBspBb602JkadIeuvjQ4CX+ke+cS8LgbQwDfOjvC4RbpsO21Czz9ySUNZmYsmwJfAiCHgXfkHqrFwPctPp2PTyOoVODjjky2k5tG+rmsdWROyfEQHwz9mqVR4Nv8GXhP62+6+jHgq6v33NA9B97uAXyK9K2xj7XmFC3Ri51rAx91YW2NqGDAgxU5Bnye1qhXO4SJTeqUpgQwHcnVK/vTKHalfv0WKptjS5N/m7l3jj5CxblLnOjIqXcCngx5dmByl5/8XY6fYq2yPeDzLVT6vXM1hjoUE4BCwUC2eEca1Vjqy4rYU4/J4RZpkD+aqzfhXtAmv2Hx8ZjMY+ckMysYBo1ow1F5sur0wZFAd8+A/3Dy+OzDyR++uzx5smPMKVDF5sA/FCyBhkfgwBhvU5C8EkJFAjFdHK1MD3hclrJpfDNd4LOvYgY3T4d39Unz0cctBV66ergwMwHv4CgRCbxrAv/L7l24mPbVn/7nGWN2xWqU/uqLm6rFIfDZjXslaLKcsJZK4cCjOo3lrt7m+2ihLflTPKmxntVyRFevPCd2gIcuKF09Z2YFC4vPwYsN4NNSRkEPgf+3pz9+983uCvg//vU7xpwRcVR2WnN/ctcFnlDuX80xyKWLkVmbDSgdmeOhOQT5I7r6Nj919eXUK3Z4VxN46eqhGUUJTVc/3R/tqghcRT/884vfvv/sd799/+TFc8Y8PUNbajn8FqrqyJOoOMb3XD0FXnX1lVzUoGHAWwMmAcyO+PpItPqLLz979OAZ16peeZ9wmiH4XTwkAEl19fJsSi8vQhYWnw6NUqpOwLvic7w6uXt39t/PFWYyI9SBt2Dw4KHrw1o9/QhqBpO3GOTIgU9eDdvsXA94Et4tHudeT5OZ88PcNKkco9Zw9eoBhy4tjikro7JsCXy4oFSr2pTq1UMtZmb1YeJuxfyk1swsnjKnGh2sW7UtPuRuuvqUCZijypSao6u38gySQj9cjWkfvrkB4JkITP259cE29gXedYD39IBH4erbchvPlWf7rt573qoO8GRyV2ppCqYAz3v7HPDE1V++e/ToaTsuYsjVd8+yXXS3LC7nj7l6azuu3sPD0xDwTHLd1c+dZaviaegxulMTHTxySeDpo0zl02pOwFuc1HMlXgZ/r9KQxXeBV2D3yqXCdMYHzLI6UXaj6mrx+wEv5VZapTNDlaI+w4v2jYy0rkabxem/XhH8OLP6hcCDPAJ4q9vGsrIbyfGDoyCNjPHyNmm1VSqzgjvWzEvurCWnBmDNNdE7XrZAHh4q+OHjLQXM0yw4Za3eR7OWY/z1gG8lXxt4TyYHfOVOefM0BHyZ3eQ8hwTeU7EtlsgPH28pYJ5mwInzdZvFYclJRfhkNAK8WOGRrr5gNOjqYZAXNctNBhrwqtjUHTuhEiGYg0k/u+9Dc/WedA+2aoWHjys0BLxRaGFy+NK+fnf2UuHe/Sz0N2XrmVayZMYKKnP3Ip6+XLTmJZcK4ybRpWVDLgIXP3yc0QDwG901OtD98RvdNTrQ/fEb3TXa7o/fSNAG/EppA36ltAG/UtqAXymNLOvLu3d7yxExsCOnajf34gpNv+z+MgqrVBGscy+wRlhz887hhSrBIpoai/kWa0wrfADNhdlCqd1lVfGuCVbM1S2g8B6rX3YvmdRcq+GvM1j9GnOz5s5bgkUqabyMFVVP+ZZrTMl3rLdzXX6DOeMSMl157jHPlN1PLvqlq+bsHRkvYgB4WTl59ZT+br6kKflSjn6kR2etXi2bvyg4DPAXX37x9e8+p1kXWnx6TQJvDW7A4m1+K6gx723xmuDIzEvXbSHm6G7EwB5ktJ0V/AUQbXGrMTp1sr7enZ/S3Xozb9BMMcz8Sp4ma9136O1cJ5m+qCq6YkZbX9vpzL2aO8Dbovse8NUw53bgWAC+80KYvvnTNjHOUifrq1PvL0/IpcJzwJftP3mvGQO+03/nge90G6Zfy17L1leuRO0DwHdey0KNkpm6ovL2tOnqLbYzh4bojgpdfZbgMMBf/mXn350SwRbukrHkG1dRh3mu7HZy+kD2GeO2ObpDo9wMKCvptaphdxRShZmCU7J1gIeiClN7ly12PHso4DnNW3wFvgjEmtFiXtKpmsnxA2y1VLfN2RS8aCVzv+YmtIs2YhABZDIlLIn21mbZFfkjAb/M1ZfulzuvaEaL+aDAt129zTdDHgp4HEckM9VJynQU4A/q6jktAYeT4urVaO9lZTeS0dVbblggUD6e4tAWr00fvNhla7ubAXXgIZYGmGUQyCcDvJgGOYh77wKvbK/uPopDvR3BUsQuL+Xi5dv6AEOYnVK1BnzjQbKjkqUWH+NIHL94nTUMFwHm6XDAOydDaRB4lw/CkcyybFB20sAc8HpARVFgzODyvYeU+ePJ71/+tLt49FQRTMRT0FY59DOcmYKTphcjwFeNpSsRGfAiaM0vpsON8VoIlQyahLj3QeBZmBUf4y2N3pPA11B2BfhXZ++fvz179adfdlIwqdHaqhqoqT7HU1XkPt8HHiJpirxeBb4euCE63zyNWLz2DoBIgidixCkec4pRTyXWGZh5bQJ4/hJCjPGpd6rAu8BOTiBF5j/vJlf/9x+/esMEU0LniBgJGqLzZrTs1O/a0bIR10lGFi1bbr5VXD2e6HA84NW3PxQ7eqpEhB5cfTxLpnUUitb94Yt4/cSBzwfC6sBPKeQYQWbxv/7hxZXFnz9N25HpGJ+MWlVDPhmJ4A5v0OgULYmgAp+GH+AuTc7IM42VcwcJ7scZ4/EsSim8w+NEMDk3vnkUyhLgUQLu6tMhkOLUq2iQ5Yb2pEvZALVVM8CXpwQd+DT05icJDnz5GE3awLGNtgpckWfAO4fIHx74pC2JPMWuLJ0pybnfu3KWLWdmBfMDDvPJlracEYbAVydejsHJJeWaDcmzFPjE0DzurAweNVGZXZAzTdHNpdzqkab09ESXQsQF8I6f6rCUhiw+2moZoY1XgPc4HuYPseNnSdnN54vOssUjTflt0hnVdAASHGJss9rpIeNdBTDgO0ehpH6R11UZ8HlCSTHkwJuIuzzSlLCI06M9Oct2Oi7loMB/bx48ePCwPtwStacDLuF8PgeTHF58ndy5fY4tDyMeBZ6qiAyFsXx+lm2pmCiyqwCCXTpEUBesdmYd+NLk0nL19GqjtUoBHlRCgY9PlbS3z1LP4lmoJQAfTX/gvPp6oq8vQ9cA8Bm8oiKykEm0FrWEBznjSLCPxePZBAg8GjKCkw/ESshzN0cRV7oziCuBr2ccxxO7HSTP0tAYz3H3CLzxEj7yoTyUpMLQ1YvJAwM+YlAqlxZf4G9OAqtvMAPAizOXCHOac7WAJ6fgZ3tvAG/KifuGMhtBgrkAj25ulvpZIepOEUOTRE/up+6R7PQbKo4gmKJ/zoxZoGbJrQomnfm1WjVP/azb3bL3lvrAb3fL3lsacA4b3SfagF8pbcCvlDbgV0ob8CulDfiV0gb8Smlkrec6S0nXW4c6Ytm3x3zUsufRHMjKKzFsn5FSlrokXl4v9pjxHWTMgi1sq0gyc3apX13smaV8kWo8fWFpZCKUfTDgSfFLaV/gvU9/keRe8ZCo7bnTqsNieEubKtKYRS7G3BB7FHi+504kHgX4XlNadN0+sr+KBpiPWfb9bNU8bcDfGvMG/K2Wfb9atbn6O8C8Wfytln0/WzVPG/C3xrwBf6tljzBfvDxkzdsYf6tlL2H+6eSPJ4/PpojaQ9a8Wfytlr2E+fw03kb9/vkha74zwKtxGgaSRRZoRjtVKxtCD7Tjj4SKSpwbhpHlw3mu/rgc1wLMqWwSIcf0+/bs357++HKKqFVb1TzgRVVOB7sQSVxZchxC60QMnwI1ahj+sYBfdAaOnswD2hizLJtGTKRTHueOQmmEiltOk7oIs5VsAvjpNuopolZvVaPN+ZNN51Xwq8247mOQH4odu6kS6WdCdF0VOyF/jDF+wRWj4QwIar61/+aAoiYzr40CnxHrXTFKzV0CT+KYgtUT5siWu+0MOGqrLMTacOZ0DJ04aE0Dnl8xmkNp1LJLc5RGH/Ia8ZlLhYUI4HuKflw63wGZlbLFGTgpIrlUh8BzLSCzA+QdYXbpIKxiOd6rPVdtdO5Q0CcJODVM2hYEEbv4pisLzy8VplFfMj6+sCmNPuQ14jyWiLeSnogB9pObQTuwCw2mzKxgYbTBQRe3B7FzvsbG1foFcw1wNKS6FIJU73q23QOK8Md0FAmYKg2apEcYTeP39DdiF6CvUrETMWo/TaGGVGNGAk8t/nDXiE/Vd/hdbBec98PPcCrATwcE8MA7JHJ+GOG2WTMC+Bw+L3VQaq6406BJk02tuqoR4MtpKD5PD5ijKsi7gDyN3wbgw7HzDiZ3gHyILiaCuXyyC62EjPGHvEZ8FnhB2AwaVMyjZQXwAjsbI04lRwI+RTQ7VjPeGVywL8wmRs6TDmPHXH3mk8CjQkzsuVA2cfUc+KQraxLqHHgf05pj/ESHuUZcumPvW64+y8GAT2cE+OgQx1y9DQ0l8rIxPsTcF+Sp3RG5quPMqSmIFbW32OLRVaSm1Hy5uyfkwxEGatmaq0+y2vhz2v1Smd2Mq5+hg07u8sludYQXwFcPDaeCyLKlqw82oFWdn5qyP2HY0XNF61hTmAOHR90NA0+Fpa2i7j6eU9guO3YRDnxstBPTYePIeRxZ8mM9znX3AgVXH84sseFwhvA3e+JtBhQrZfOJeTjRpLtJqeKOm5SoNZd5VGUugscQ8/YOJ6XmdMJh42ZfUwpOeVjgvmgxPGemxZmGuie58/lxVmpMHmjCaAD4je4Wte+On2gDfqW0AX+PabtGfKW0XSO+UtquEd9I0Ab8SmkDfqU0tGTbW8u4q3Glt8d8N6NlvRI0qZTFl1Vz1vhTlxlayevHsmXrBbPIxZgbYntcIOeC9Rd0WbK5gaBJTR6drmHxPEx6MfCmINlhNlyDtxUmrXSK/YD3QrBDAZ9bOITmwmyaDAx4rawu8F3mTwZ4pUn7As9bdQeAV6oya42Pp8wytcd8V119/8d+8rWYj1n2/WzVPI24+utI8smq6H62ap42i7815jsD/EwkDZbEIxOMxm949v2SjZZNCqZflkPE1i6LNN0oklFwZrd1kb0UhgullN2OUJmlEVevXXlCZxvk57wXiTQDtifJec5clI6sBFWUN6tqzCCSj1cukJY5kYF0OXXeKStpiI1k22cjpXssiB5M/DnvFfNsScHkncV61bM0ZPFKZqMl101oVUVxD165piv/WVp23DHHm14/TCkQggS9Jm9JK/dRwQ0gxuW9nTmaAmsWG0EZ8O/eNMQuRpsuq7xqpJWPGxOF3XhBfmoqZauYi3v12C5bGZZ2HODnQ6jCv1nFQYW0L4SgxdhFU0SJZIbqQP0+X1onkwPwrmw1Zrsp2Qb1vL+6VkP3qSa7B1ePAVLQ6PDh8vsvfj55fPb27B2/n3T6lEMaQyExnIAkQySNbYdQRb0x4C3ZVx93ZB7H1fPYNd7KaBg2bbWNnxD4dCuyT5E0AI64cFDEzpWt2Tw56JdurQ7b9qtglkfS0CGB7VDmwLOtr6zR8UOMov746JlQCdnUn4J0udGSSBpn+yFUzN85A7ts461IfjF1gOdRdzPAW7p/Pds8Ap8u4yqoDQHvLI0Y7gEf1GAEcw94CDtlrh7umcRGZ+CnKOrLr3ksradhRSm+rhNCNQu8Z8CzffUHA/71zkPU3YJoWaq+8A8D3hJXz5l5yczVV2aRTKZBVQLF1av3PXLgpcWXOFfZ6Pjh/eff/vOL3746fXXKWmWiNZCYT74Bf8zVe+YuRAjVYVw9j7qTPd83gc861IDX4kqVMGma0RaT16oOFl8vNCyVY9VMkYWZKw+Bl8Xxmjsqwdj7FOyrRV6kW8QB+BxCZanIADwM8lLKPnWAp1F3C8Z4EkukHNEAileZWcEwsmaT0btNBt4B8sjcBz6GRVSMWascO5RhKfAV8PRpapY2q0+3UYKrr/4/yitcfSEQfSnNOAcadecU3EF4xeTBcWXkSjnAzAqW2CW8ZLchrr4NPL/cl9RcThQpbAA8vR9eq7mtkhodX6L7GyFUBOPC7KpomsU7Hhp+UOApDQDvhSQ2T7AcOdljCPhol03gK/JcB8XYabRuBd6Wg3EqH7r6uTG+qRJbO53NzzQ68CE3ejQ2wEe1oasXuB8e+OTqe/zEZnRXnyY32eDngiYF8FPUpHoQUAGePljg41ysvESzwwJO7VVZd1BzcL/7AV+OyEn4e44dttinTKXNLtuKz74OHxWJ1IcEXl4jvmhWX+Xms3ooID/Lt8qWRssfVLn6ae9XRto4Bwi4W5zVx+Q8/ZbP8dzgB4CHRzrhrWWTnWWDY/ZRXmEW9n4oi2dRd5ZHbuK72mhuNSGYHQAPfHgwglK2eCIrYeKNLQtEDWLLQlVNUiUBPsf1p0rDAQVYs5CN1dxSSYqWNTF4OAvvW9y4ZJuAT5TDjClzmQQobm6WBrJudJ+oD3wv6m6jO0194LdrxO8t9YHfrhG/t7SN8SulDfiV0gb8SmkDfqW0Ab9SGlnrMd2VO7bulnLnVKtyLy+7l5yrjAcF68zAz3fZSsErsyo41CxyNFTSTQ4Lc9NJt7XsdLRfWrlTmOOrB73seTSXZ51dq6dlpVeyFfjwU3n7ZPKfZWWHVejIrCx1m/g/vu2H7RDhJSe87iIvaQpXfEEjNmJI0WjNYXvK1R+2L5p9UltlygurtAvVGnHAYX05F/SFb+f4xpYhM16e1VLT8ErQJJEgnxtO+6+vLxcNB145J9fgirl3dK0eyy6GXDAE24h9IhlWXPgmRhtLdS5vi2JveAzf+INBk/EFQdg9Fxvcu1SY/SidAT3LNsvachd1z52p5WkV6jTk6tmJoobFxwPwMqAi7hxIO8R7vSYLhkZrPH1J4zvAK2HSEewO8Ca8O1QCKuIh+Q3BTO7LU3nJw+kb573y48GAN1JjhzzSlAvBgJ8UXm8IECFUZRdEkbB/Xj00I72cczCCy3dkRQ+810z+wkIWwhxLzS+5mFZiP2GxWQT4tA3AFQ9nrgM8uHqj4A6m4kqWIhjNcrAjTUEKabTpvPq8jZS5ehvf28axPHC5PvDc1eMJyFA2gT0mwvHJdd9WtRAGPJxcjlqJW1lhzx1hzm+CyRa+a7l6BN4YkJgDn5NNNjiaPEtjrr7fjGQyabMlm9xZYvITuRlX78X7eH5TAkzuYJu0skMa9tVTDeYOQXbvoK8xTmzFQD8W542kKYpyNGaebHpXk3jW2T3pFqXNx5rc9XfZFpupV7Ew4Mu2u5DdY9CD2HpFd6AXo20Cn7ceFvA04CkRsV3eWKf3muynlJpj0SzHvsDzXbawESOJDMz599pnjwP87L76Any9GoADHxsQkXfAvGDrlRezrPrB8Y1IiqsX4QmBmZpNw100N1sm4ONoIFUyBjzeaeRrHGDaeCWvsBLb6o9zUYG1HBzgL4ojyHPg0zZSuctWli2Bt64DvNzdLQSD/dV0Ys615yVzY189YdLCRKZPOZT23Zu3Z0oybTGZXZKyC/TKZktSPWv0LB0OeOfItSTtgAq6k7oLPDUioVzgNpBJ6AD7Q3T68JzJOwy3eAvDjteBVy3+28f/+/0Xf52uJP6vq393H08e7zoOAcsh3dWXsDNktoL8Yjq8xXeBx9CoHvAykmaa3qlVm8xAiaiIIR/MnjALTyGBb+6rnwH+9OLZ+WkMpj0/fXv26uzi2SjwDhzdDPDHmtwtBL7j6mWYa6tsES1r+RyDA0+HaVARB94x4B3h5TdNJuU3x3i6o1u0ypx9fDIBPgXTXv37X9/sPj7pTQE04K0lV8siM1zxd9RZ/ZyrdzbvTRddsAK/0OLl41xzbm2KAASEhiuyYozncb5MMFe6g1Yz6eyKSsw/npy+//x1uJJ4+vfXpyeno8DnmaiMlvUQTRGXmm9rclfn9Vwd6buLLRBh0rJsdYzvhUnHa5mKlTTHIOVxjiYrrRLC1e7slWkVtXiuLs+w8zRMWpvcubruJKJlDY0cCkTRfP/g4Wln9W4M+N7jnAGT5xpLX1L0lHIwggBePMeD++cjhmO3Borg+ixOH3hp8Qru6uROVQnXlkgOsGOMPpbtCPLInHp6M4Tq9e7y5OxGgPfxeTdZTuwAqCKyajcLvJjclfgxKCIX4/IVsV3gvbV5pafUw0yetaoPfL1KUn03ehPAk6ahoK9O/cevHh0I+B5/POij5I1gIfCQ189YPHf1Ps6lCvLC1aPpqpM7Z9MBTDSEyubuWsVnwDcbXQY1dUVxyQLOjKtPuJeZEbr6jHztNWSMnyLcLw9ym/QM8AbdM3suioptMivAM1dffmqGSaflO5tOH0HBos+w3glXn/NTpSPwbbmlnflB4LHNHHiXH+JbzK6sOWuSHOj6sSHgbYR+KfBGpPFZvV8MvLMC+LSy1AE+VqFavG/LbWx5HaW3SqHeczwdMw4A/IGuH5sHnqg7qcvQ722XOV+2jbk68fE+PfUk+2Uqij8qrt6U4y5U4I0mGq1Zdoz9gffWKocfdZnzKrRn41ugA10/pkZJE0mQUu6SOhdj3S27n8zq1e8Fto1tiVLk0ZpFlpZKZpMBu3wN8ywzzbYczYGsG90n2oBfKW3Ar5Q24FdKG/ArpQ34ldIG/EppA36ltAG/UuoAzy8q4LFzYinJ8X0B/F1T3vZkUvyPWVp2WJyyNHYONvKUX1L500oWvtoLh1nWgAqInYuhWVR2WvOU2IxGzoeOThUYuXxGFeFsajN5idBd2KMN0oK/yUUFdZGvjSanTtbXO88uKmCxqvFlMkkWsOsbiQJMEKSuHGIsgYdYMgm8ya+up3B1dV99VSXXryFnX8JLxRRoQ9frAfj0RrTkYMDD1pBUv7ZHi7a71uOovIqduRxCdWDg6UUF2UhD4Ql5g/z1bFBC+D4+HRmbUELguSDSdGjsHAe+gm/yOaLIbGkGMKwcNKn2V58KpO+GAHgageMF8KiL+P586Tsca6DBBgNFWYMPCjy9qIBUlWxd8BsDe3AsbnnMuKfweOMwaFLKLDSISlAsPlF4gwedKuvFWsVn5vKKucPbZB/PooXDBwhzOE47Na2WRsSOG4lsPbpi+cs7eRAHV3dVhk9tPs5LGlMlbwFPiG1yNmSHbZLVmB7wNH7QWzrQGJN2KxEZUD1MsLA3yLkcpKsBn996yz13SVhUQ63Z4vt9BN7UTcXlZIblwJfwZCKyCjz5SStRp2HgcWDvGq2HZviyUS40hkfLCmbq/QNivioBkw1ALwUjVdNm0K+tsLw0h+JqQLn8AuBz4gjwNTK9lKsATzdqHBF4zjAGPLV4t5w5KYH6adxsaeLsnAo4AzyiwbBFd8H3QnDgqcnPA+/GgHe5t8ceQ5mNEb3y8MBTl9PgvwHg8/OcN3yXbTCKeCiIDjw5ZkgCz436UwHeFWnzTFhYPEp3HIt3qdsBy3Vc/SDwYdiLzxRG7rINyJMH9JZ+wxDDnuON99cA/niuPp52FVvGN6QnG4BIs2MBn/rd/sDnOKBscUPA+3KSRfqLA19sXmOmrYATMZLZtGueAx726c8CD2VPgdNvy0JJ/MS8SZra5FKZq/e0xaKpXRoC3hiB0BjwJafiuHqymZLLePExpWY/2nD1pBmeA9+tGbyzWjPJIoDnp9og8L9/vHt79uHk8dnHkydXn17v5OBIH6aYYNH5zfoQnRZmTfMmqaSbBd5Tg6YKjf94otieNsaA5z5OAR66JgKPciLw56cXz96eTUHUr84+vHn77akXGouN0oE3skTRkiaNZKU+R/LfAPBUDah+47Me5lw9rT9/6dbMM2jAl58k8KIqcPUfn8Qg6ldnl7vzb595rrECb8vV+8bD9SwNAw92tz/wQ8xVwVV5DPhKLWZoBXuO79bMu7oEnjgiDjxbrGAW/48np29DEPUUQP32bLqVmAFfxI1lYWGsvKMDb7h4OblTfPxQJ3fzFs816OliBrckgr4UTDZiBPgjWjyvFn4MSNeD/YxnzLwhzRJ12sfV7w08eZybBV6oyIV5jC4D2LwQTGsEAi9eDZJPRimB5atZJPBUTjO6ckc9ffzMG9J6DJ2lhVlRrfu6+usCT6Rg6jcGJTwk8Ae1+MElW8OJN+QYwF/+8svPT7S3c6WRvo8dbwZ19axyhdnw7pUfJyM7Az5D1AfeGJZrgas/4hjPq4UfS5tpV5euviH3LHWynj/844+/+Y+dUlVuAB905ppBCmI/9pnTJ2LvvGxq9DpzzqhavOJuFLmZ9FqqBF5wDrl6tHYJPOuVB3L1Hx795xMmd5Hd3CbwbKAAFZFxVykGS6iFztQMaTcHvPEIvRfAs5dmBwLeX/7wOVaD9j7u6mth7MdB4LWyF1h8nSrdPeCFYEaR/FDA45EKRqWFyddiPmbZt8d81LJnqZ91u1v23lIf+O1u2XtLA85ho/tEG/ArpQ34ldIG/EppA36ltAG/Uhp55L+95Ygjln17zJ/yAg5mzWXTdcd9l2yH1nvJWzDSPqqitI5sesxYP/3SrZknA3P9USlaW7IV71n0xWxNbCaYhjT9evHlF1//7nPfon2A3/t9PCkIu89C4Mt7eMPKpn2yxczagcK0aza8AA2ckmkWeNQdr3wc+PZa/evd+SmNcm+WNEuqQwFJOsfZhw8kkobZ0izwECY+pWBABUmQzHJfPAM+XpqhHzkvmoXgxD315Q49CXwq1+Vd3Qx44cxGgccQKlLAtIHv8uQglwordsWMViAPzSC3iBsn3i73ZEtHthPlYLSs6emNBZuwQLDwOaOnMBt2sSkCn6896AZUxCjmsmUQSkoO1NVNVlIGXSUJ92YkzeVfdv7dqVZIu3idCvCNoXQe+KSFKPBMfDxGyyaragJPSAjGdaNYvN8T+HQR4ADwsPWqbI82dFulkIFWzmi4ugAADJhJREFUDmJ0gZ+h/Vx9Y4wfcPXRc1NmxgmRS8zVm158vCk/5mTwhlp8PBgtMrtumLSrVBMF8DmnBN7UPZS84y4Cnl9uf1Tg80zG4Axr0eSOWHw40qfDrABPwW1bvAReawUAL4LnqGBdV+8Z8j3gk+DCaIuT38PiFdkWIjri6uEMnPIPSZ6xeHD1CLw8A4cD79PpVFk7EJMW/Q2M3g3gWa7E2LF4I9J0i28AnyZ3xWE5CXwwJGc8S14GfOtAh1kasnhHFSt3+PO4Uo/AFwUlidHVc04E3iXNFUcN8fFJdSif3kSWK7WKOWzWnR3cDzIGvEvcGXkBfJ5yJAM2dACTxF09RHwfC3jHTCpHd9RkdoGKV4HPPR+Al10GzsBxZfZcgAcVmTA7AvkY8Kl8pwGfgCO3mwngG6deVbmawLNTyzSLz16bHenkc+R0vJA6/C2Ad06fcc3SMPB1ODb4RIY2w08R4sAb7uqFrzC8U1HgEbuYvx4EiA0LDtd7lw4cE66+Fm4V4Be7euWcO1M7eRt4OkWRwF88enr5/Rc/h+uod8rkbhpf2fEefhHtYfEAZwN4q5x6Ve91TcB3LZ4BP10hCMBj3HkeDZrAx+PSSP0lNf7k8nWFTCvpXMUm8OHkvpjDeq55h12ja/Gli1Cx3569+tMvu3wdtefAp1Krnz2uq8fqabJz+d7lfAFYSY5arYp3Y8Bn3HXgid3qwDu4oxVPxEi/OJsuoEPmDHzD1ccTG5vAZ2dQj/RUgPd1XiqB//uPX705P43XUXsJfHRzytxklsaBz9M6zp+bGCEXBxwqwC939cqRpjgNMuXBKs92KPBB83FEdHlAKKkZeHrFJ/iahcArrr7iTs5UVYAnhxxx4M+ffnP2/vNvw3XU6OppZy+haX4xjY/xkSnzYSvrkaBJh+jqk4ZCE/3M5G4OeKqiNNnLqIaDZZF5OtSy+Hrp6g0caSq6M9xcj64+JmbcOfDkzt9i/fAoEwTPhxxJ4AVBd65O0OWTYs1i8EeBz0wq8JYTsXgOvOPMXLAB4HH6nM51BWYbDpfOynca8E4T20dcbQP41CBbhjjUPFzwnnCC45DTaZsF+RHgXX3IDSeqXrUQeL43Dx48eHiQlzTVRhuuXgDPDzEmrl4wc8EawOfRkD7Hp3l9MnmnHmIcupstbqEyF90Ve7dwiHHy1Kpg9D7fktgAPjod5+H06nr6nvfDwJd5T20gzdu+QrxZvE4wPkl+FXjt2HJ7LeCzO2Mrd9Nftgt81k58lOfA4x3ySqtUweaAZ1bALZ7pd9jVJzdCevaRXL1SKFURO/pbA96WY8sFMy9YaNAkTMXanPFp9EkjuZUXFeTa67N8STVo8AJ41hAGvMWO0Qfe9I8tt0NLtpGFmBv09kAHuk1a7U0wR5W4M1dvyZGmwCxkVoC3+BymAB9ugs33NTDmCj5fuTPgkSMHYe5bfOpO88AnTyexY20eA94TySU+h7pN2mgEUoduF0fTJEthLrLFIVph7pRdu7SWTH+z5boGUjbVDVcR9fKtmsW9wYVZYaU1E2OseRY2ekYlpMlEBkTsQLdJb3SfaAN+pbQBv1LagF8pbcCvlDbgV0ob8CulDfiV0gb8Smnpkn5eFmsvJaX1qbKChovHsMAldjx6vjQWFqRIcnqdHxbmZte4xBorrtkic15Ww9U3IpiyNMdbZev2X43ZwMLd4pU7ZcVw+VrnPKLLs8olQeBPzcNGcxXlrE4yy9qU9yygGfgQlsEJ7nThVLyhg15TftdapSVK4OmmEI05FWAMNpo1OUpPFSAU3lnob/6oUyfr+wcPT+lLXWi95OcKCl/4qnb65jjwsuxwqzPndrQG/XVGFkNZMY97QK0qWM4gNltK4EmyBF5l9tDrlYw0P/3iuVZuBPjXu8uTs72Bj3vvdIvPuyh6wMMLu6xfb8lGBhX4+pKSMVP7m7YwCIbQLbzYbLkIeKtHLtq83dgSFNvYOQG80MqNAP/q1H/86lG9RnwZ8DlX/HAN4HX1ayGtNR99O02Y6W4AH++0NgrLNYC3KvBBZTXPHsA3I5OOCfzl652//GbE4l19N51aCiqqu08WuHrN4mlAsga8I95VcfVRhmn3kwPgcfeNECw2Sm10SdUnCLlsr5ctdA8jWZIWc9wI8JyWWiV1q8I22syyNjG5w1h3DfgqQgN4G3dL1VJyIEUPeC64YvE68LZb9jzwwuRvB3jtaQFn9co+28ycbCNlVZh5bXRyVwqjweqKq7f52anRI6fnLrZP3vGdV57twJHAyll9TTc8uIhmmZnVh4k8akwE57eZmz/qtDBr80ERHiyV3ZY5NX2d/Gx9JgNmVjAoO3NPnE50m7r3N229wrIp7tOfuss31Uwe5W2c5PUsXnuOL+moIwZ8TJPYVfmz8KnsUBpGFSufCB3H4oME7QfLacOnwJ2rKMyuiuKBmddG3Vzp/Ul3BrjJ9mqjlF2rrisiZE8jN3kJfGdfPWlWSQRXXylvKxfYGR8P7YgoE+DjD44eptAA/uKl8mOfhoCHcDfOr2yvFqOhKyEfswEVECadcScBsTxoMmiPxCjx+Vkcb+PmaiWgAsSGffVR6CbwOYSqJpKaiUrS1m8JfIz4lAEViSWHFTvWnc1P3z7+98dnlydPdh9Pfv/dX3Yf3twi8Ax6BnweXmPPP2QIlaeRZGkjLzC7HMiSMyHwDgJp2L76DvC5V7hGCBUZDHLNfHt1cGBaCFWVNcXDoqmY89P3zy9evvrT/zx7dfb++fnptOJynDH+2hbvIITqmkGT+FyXf0rzNhhKY9UmI+TwGIkaNKkCn2JvOrFzqVlWC5rkwIdpEC0p+Cc9aLL01ByuyyYIb89+Pb0C/o9//e7Pu4uXF3/4P/64Fs+gb85kLIuWra0/PPAAu/NGAh+2tbtidgrwIPhii3fE4mWYdA3BrRbvcJqIBK0iwro4KzES+PdPXjz/9Q8vnvvvMYp6lsaB92V2hfwuI1+Wyrxu8Wlufj1XT5ODnzdVTQZdvYmV087Bx3hnHB2P2ZTVUTwk8LYN/DRVsbXp0a1ASR3gfTb40DrW5pud1Re1k0cRmpyAT8hDcm199stm0OJt70SMgmrRDqgoGR2N2iypGZF4MkJ8iKeC9SZ3FHjF1RsyABbgDZQUTUkHnnh70dlv8jm+qDUBXx+sArkUUKwXX+Lj8+XA+GwogRez+mQ0RFdVuDrGm1wsU1F4w2NNPTCvpCZEYOFVjPHdM3DiQFISoWaTQgqr7UrgmxZvLD3i7caA569la+CTqdDTZgjwKPDTX64C77DXUJQTwdkR+biwAjyciJHVZshhF5qK4pjAT8Qo44SmleiaoEmUObvjnEVafEoKns6x5/iqTldbQMr2BlG/IeD5a1ni6ZOxM6NVymJzgerqPU5V+syp2xg61kBcaTGYqhwdeI+ZfPrBsz6LAxibzgLwqTM7kog1wxw0PXHQzGXSlFsAZTOvcDMrd/S1LJEzCVDQJ8md4mmaAnyfuaxxwQnEEnhqFKqKyHjKhGnWbLiOGPBeJLbASWkM+KxCYdPG4++cWQjd+lGnTlb6Wpb1u+TpvV+MnQL88l5Tp5J0cKdlC9zbKhoE3vPkvYH3CvBMB3rZRO83ArzfLhW+s62ap35WFlmfTNx4/H+oLvbXfrxDrFnm/Ec477l6yf/jlReO/eTev+IFZbfpfAPeX1P/dxN4XZAN+LG6N+CVv/bj3YC/Nh20sI3uDm3Ar5Q24FdKG/ArpQ34ldIG/EppA36lNAD85Q8P3+TPPzx8uUdlfyYHaV+++GyoCMI7xBozU9kHK92TFaqn5Y3WX0o6+YdryCFoAPjz55ff7MrHf92NVnX5gh6b/7fTy39ZrgbgHWKNmYnsyylWuhcrq56WN1p/pvPTj/+0vxyCBoD/vu7HefXtw/Y9xS263OHR+SPtYLxDKpgyf386c25/u9K9WFn1tLzR+uvXH55dQwxOA8BfSZEF+b/PR8x1op/++obdmXD59dK+I3gXs06cITORfbTScVZZfaaBgqTC/M+Pb8fiz0/LPfTjVvD3X3bYjo9fLR6xOO9y1ivOmJnIPlrpOKusPtOA0oTC3p3FvfMHogHgP3z1Ivuai69OPt+jMtqO7z97NNSBCe8Q65T5v58R2Ufo1dn7fVlJ9VXWUddB81989eKL/eUQtD3OrZQ24FdKG/ArpQ34ldIG/EppA36ltAG/UtqAXyltwK+UNuBXShvwK6UN+JXSBvxKaQN+pbQBv1LagF8pbcCvlDbgV0ob8CulDfiV0gb8SmkDfqW0Ab9S2oBfKW3Ar5T+P9MiZ02NJmgPAAAAAElFTkSuQmCC" alt="plot of chunk unnamed-chunk-31" /></p>
<pre><code class="language-r"># k-means clustering
km8 <- kmeans(boston_scaled, centers = 8)
# plot the Boston dataset with clusters
pairs(boston_scaled, col = km8$cluster)
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-31" />
It’s difficult to point out any single variable based on which the groups have been clustered (which is a good sign, I suppose). It’s likely that km3 makes a better model of the data as groups 4-7 actually make the model worse; km8 might just overfit the data by dividing groups into unnecessary subgroups.</p>
<hr />
<h1>Dimensionality reduction techniques</h1>
<pre><code class="language-r">date()
</code></pre>
<pre><code>## [1] "Tue Dec 13 02:32:54 2022"
</code></pre>
<pre><code class="language-r">library(GGally)
library(dplyr)
#library(MASS)
library(tidyr)
library(corrplot)
library(ggplot2)
library(FactoMineR)
human <- read.table("https://raw.githubusercontent.com/KimmoVehkalahti/Helsinki-Open-Data-Science/master/datasets/human2.txt", sep =",", header = TRUE)
</code></pre>
<h2>1.</h2>
<pre><code class="language-r"># Note: the variables and data set are described in create_human.R
summary(human)
</code></pre>
<pre><code>## Edu2.FM Labo.FM Edu.Exp Life.Exp GNI
## Min. :0.1717 Min. :0.1857 Min. : 5.40 Min. :49.00 Min. : 581
## 1st Qu.:0.7264 1st Qu.:0.5984 1st Qu.:11.25 1st Qu.:66.30 1st Qu.: 4198
## Median :0.9375 Median :0.7535 Median :13.50 Median :74.20 Median : 12040
## Mean :0.8529 Mean :0.7074 Mean :13.18 Mean :71.65 Mean : 17628
## 3rd Qu.:0.9968 3rd Qu.:0.8535 3rd Qu.:15.20 3rd Qu.:77.25 3rd Qu.: 24512
## Max. :1.4967 Max. :1.0380 Max. :20.20 Max. :83.50 Max. :123124
## Mat.Mor Ado.Birth Parli.F
## Min. : 1.0 Min. : 0.60 Min. : 0.00
## 1st Qu.: 11.5 1st Qu.: 12.65 1st Qu.:12.40
## Median : 49.0 Median : 33.60 Median :19.30
## Mean : 149.1 Mean : 47.16 Mean :20.91
## 3rd Qu.: 190.0 3rd Qu.: 71.95 3rd Qu.:27.95
## Max. :1100.0 Max. :204.80 Max. :57.50
</code></pre>
<pre><code class="language-r">corhum <- cor(human)
corrplot(corhum, type="upper", col=COL2(diverging="PuOr"))
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-33" /></p>
<pre><code class="language-r">#human_scaled <- scale(human)
</code></pre>
<p>Life expectancy and maternal mortality make the strongest negative correlation, which is not surprising because an early maternal death brings life expectancy down. Adolescent birth rate and maternal mortality are, likewise, strongly correlated. Expected years of schooling strongly correlates with life expectancy. While strong, the correlation between share of population with at least secondary education and expected years of education is not among the highest. Perhaps education caps at some stage.</p>
<pre><code class="language-r">ggpairs(human)
</code></pre>
<pre><code>## plot: [1,1] [>--------------------------------------------------------------------] 2% est: 0s
## plot: [1,2] [=>-------------------------------------------------------------------] 3% est: 1s
## plot: [1,3] [==>------------------------------------------------------------------] 5% est: 2s
## plot: [1,4] [===>-----------------------------------------------------------------] 6% est: 2s
## plot: [1,5] [====>----------------------------------------------------------------] 8% est: 2s
## plot: [1,6] [=====>---------------------------------------------------------------] 9% est: 2s
## plot: [1,7] [=======>-------------------------------------------------------------] 11% est: 2s
## plot: [1,8] [========>------------------------------------------------------------] 12% est: 2s
## plot: [2,1] [=========>-----------------------------------------------------------] 14% est: 2s
## plot: [2,2] [==========>----------------------------------------------------------] 16% est: 2s
## plot: [2,3] [===========>---------------------------------------------------------] 17% est: 2s