week-2-regression-example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AMAV Webinar 2\n",
    "\n",
    "### Example linear regression in Python: A simple case study\n",
    "\n",
    "\n",
    "##### Supervised learning with continuous data \n",
    "\n",
    "<br> Why use linear regression?<br>\n",
    "\n",
    "\n",
    "1) Widely used\n",
    "\n",
    "2) Runs fast\n",
    "\n",
    "3) Easy to use (not a lot of model fitting, testing and tuning)\n",
    "\n",
    "4) Highly interpretable\n",
    "\n",
    "5) Basis for many other methods\n",
    "\n",
    "6) Available in many libraries\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "\n",
    "I will be using Statsmodels for teaching purposes since it has some nice characteristics for linear modeling and allows us to unpack all the details of the model object (plus it uses R style model objects). \n",
    "\n",
    "However, I recommend that you spend most of your energy on scikit-learn since it provides significantly more useful functionality for machine learning in general and is much faster and easier to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# this allows plots to appear directly in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Advertising Data \n",
    "\n",
    "Let's take a look at some data, ask some questions about that data, and then use linear regression to answer those questions!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  radio  newspaper  sales\n",
       "1  230.1   37.8       69.2   22.1\n",
       "2   44.5   39.3       45.1   10.4\n",
       "3   17.2   45.9       69.3    9.3\n",
       "4  151.5   41.3       58.5   18.5\n",
       "5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read data into a DataFrame\n",
    "# Advertsing data from http://www-bcf.usc.edu/ The UCL research computing page, one of their many free datasets\n",
    "\n",
    "addata = pd.read_csv('http://faculty.marshall.usc.edu/gareth-james/ISL/Advertising.csv', index_col=0)\n",
    "addata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "addata.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What do we know about the dataset?\n",
    "\n",
    "__What are the predictor variables?__\n",
    "\n",
    "TV: advertising dollars spent on TV for a single product in a given market (in thousands of dollars)\n",
    "\n",
    "Radio: advertising dollars spent on Radio\n",
    "\n",
    "Newspaper: advertising dollars spent on Newspaper\n",
    "\n",
    "__What is the response variable?__\n",
    "\n",
    "sales: sales of a single product in a given market (in thousands of items)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the shape of the DataFrame\n",
    "addata.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x113775e48>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "addata['sales'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x113d04400>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "addata['TV'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1141d30b8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "addata['radio'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12072d470>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the relationship between the features and the response using scatterplots\n",
    "# Using malpotlib scatter plot\n",
    "# Using matplotlib subplot to create three plots\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, sharey=True)\n",
    "addata.plot(kind='scatter', x='TV', y='sales', ax=axs[0], figsize=(16, 8))\n",
    "addata.plot(kind='scatter', x='radio', y='sales', ax=axs[1])\n",
    "addata.plot(kind='scatter', x='newspaper', y='sales', ax=axs[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions About the Advertising Data\n",
    "\n",
    "Let's pretend you have been hired as an anlyatics consultancy you work for the company that manufactures and markets this product.\n",
    "<br><br>\n",
    "The company might ask you the following: \n",
    "    <br><br>\n",
    "    __\"On the basis of this data, how should we spend our advertising money in the future?\"__ <br>\n",
    "\n",
    "This general question might lead you to more specific questions:\n",
    "\n",
    "1) Is there a relationship between ads and sales? <br>\n",
    "2) How strong is that relationship?<br>\n",
    "3) Which ad types contribute to sales?<br>\n",
    "4) What is the effect of each ad type of sales?<br>\n",
    "5) Given ad spending in a particular market, can sales be predicted?<br>\n",
    "\n",
    "#### We will explore these questions below!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y = ax + b + ERROR\n",
    "\n",
    "y = b +  a1 * TV + a2 * radio + a3 * news + ERROR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Linear Regression\n",
    "\n",
    "Simple linear regression is an approach for predicting a quantitative response using a single feature (or \"predictor\" or \"input variable\"). It takes the following form:\n",
    "\n",
    "####  __y = ax + b + ERROR__\n",
    "\n",
    "What does each term represent?<br>\n",
    "__y__ is the response\n",
    "__x__ is the feature/predictor variable\n",
    "__b__ is the intercept\n",
    "__a__ is the coefficient for x\n",
    "__ERROR__ is the error term, the unexplained variance left after having fitted the model\n",
    "\n",
    "Together,  and  are called the model coefficients. To create your model, you must \"learn\" the values of these coefficients. \n",
    "And once we've learned these coefficients, we can use the model to predict sales!\n",
    "\n",
    "Estimating (\"Learning\") Model Coefficients\n",
    "Generally speaking, coefficients are estimated using the least squares criterion, which means we are find the line (mathematically) which minimizes the sum of squared residuals (or \"sum of squared errors\"):\n",
    "\n",
    "<img src=\"08_estimating_coefficients.png\">\n",
    "\n",
    "\n",
    "What elements are present in the diagram? <br>\n",
    "The black dots are the observed values of x and y.\n",
    "The blue line is our least squares line.\n",
    "The red lines are the residuals, which are the distances between the observed values and the least squares line.\n",
    "\n",
    "How do the model coefficients relate to the least squares line? <br>\n",
    "1) b is the intercept (the value of  when =0) <br>\n",
    "2) a is the slope (the change in  divided by change in ) <br>\n",
    "\n",
    "Here is a graphical depiction of those calculations:\n",
    "\n",
    "<img src=\"08_slope_intercept.png\">\n",
    "\n",
    "\n",
    "Let's use Statsmodels to estimate the model coefficients for the advertising data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# statsmodels is the standard import if you're using \"formula notation\" (similar to R, which I and other stats people like!)\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# create a fitted model in one line\n",
    "lm = smf.ols(formula='sales ~ TV', data=addata).fit()\n",
    "lm2 = smf.ols(formula='sales ~ radio', data=addata).fit()\n",
    "lm3 = smf.ols(formula='sales ~ newspaper', data=addata).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sales</td>      <th>  R-squared:         </th> <td>   0.332</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.329</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   98.42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 20 Apr 2020</td> <th>  Prob (F-statistic):</th> <td>4.35e-19</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:50:34</td>     <th>  Log-Likelihood:    </th> <td> -573.34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   1151.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   198</td>      <th>  BIC:               </th> <td>   1157.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    9.3116</td> <td>    0.563</td> <td>   16.542</td> <td> 0.000</td> <td>    8.202</td> <td>   10.422</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radio</th>     <td>    0.2025</td> <td>    0.020</td> <td>    9.921</td> <td> 0.000</td> <td>    0.162</td> <td>    0.243</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>19.358</td> <th>  Durbin-Watson:     </th> <td>   1.946</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  21.910</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.764</td> <th>  Prob(JB):          </th> <td>1.75e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.544</td> <th>  Cond. No.          </th> <td>    51.4</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  sales   R-squared:                       0.332\n",
       "Model:                            OLS   Adj. R-squared:                  0.329\n",
       "Method:                 Least Squares   F-statistic:                     98.42\n",
       "Date:                Mon, 20 Apr 2020   Prob (F-statistic):           4.35e-19\n",
       "Time:                        14:50:34   Log-Likelihood:                -573.34\n",
       "No. Observations:                 200   AIC:                             1151.\n",
       "Df Residuals:                     198   BIC:                             1157.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      9.3116      0.563     16.542      0.000       8.202      10.422\n",
       "radio          0.2025      0.020      9.921      0.000       0.162       0.243\n",
       "==============================================================================\n",
       "Omnibus:                       19.358   Durbin-Watson:                   1.946\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.910\n",
       "Skew:                          -0.764   Prob(JB):                     1.75e-05\n",
       "Kurtosis:                       3.544   Cond. No.                         51.4\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the coefficients\n",
    "# y = b +  a1 * TV  + ERROR\n",
    "lm2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpreting Model Coefficients\n",
    "\n",
    "How do we interpret the TV coefficient ()?\n",
    "\n",
    "A \"unit\" increase in TV ad spending is associated with a 0.047537 \"unit\" increase in Sales.\n",
    "\n",
    "Or more clearly: An additional $1,000 spent on TV ads is associated with an increase in sales of 47.537 items.\n",
    "\n",
    "Note that if an increase in TV ad spending was associated with a decrease in sales,  would be negative.\n",
    "\n",
    "__Using the Model for Prediction__\n",
    "\n",
    "Let's say that there was a new market where the TV advertising spend was $50,000. What would we predict for the Sales in that market?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lm_full = smf.ols(formula='sales ~ TV + radio + newspaper', data=addata).fit()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sales</td>      <th>  R-squared:         </th> <td>   0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.896</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   570.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 20 Apr 2020</td> <th>  Prob (F-statistic):</th> <td>1.58e-96</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:52:31</td>     <th>  Log-Likelihood:    </th> <td> -386.18</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   780.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   196</td>      <th>  BIC:               </th> <td>   793.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    2.9389</td> <td>    0.312</td> <td>    9.422</td> <td> 0.000</td> <td>    2.324</td> <td>    3.554</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TV</th>        <td>    0.0458</td> <td>    0.001</td> <td>   32.809</td> <td> 0.000</td> <td>    0.043</td> <td>    0.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radio</th>     <td>    0.1885</td> <td>    0.009</td> <td>   21.893</td> <td> 0.000</td> <td>    0.172</td> <td>    0.206</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>newspaper</th> <td>   -0.0010</td> <td>    0.006</td> <td>   -0.177</td> <td> 0.860</td> <td>   -0.013</td> <td>    0.011</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>60.414</td> <th>  Durbin-Watson:     </th> <td>   2.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 151.241</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.327</td> <th>  Prob(JB):          </th> <td>1.44e-33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.332</td> <th>  Cond. No.          </th> <td>    454.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  sales   R-squared:                       0.897\n",
       "Model:                            OLS   Adj. R-squared:                  0.896\n",
       "Method:                 Least Squares   F-statistic:                     570.3\n",
       "Date:                Mon, 20 Apr 2020   Prob (F-statistic):           1.58e-96\n",
       "Time:                        14:52:31   Log-Likelihood:                -386.18\n",
       "No. Observations:                 200   AIC:                             780.4\n",
       "Df Residuals:                     196   BIC:                             793.6\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      2.9389      0.312      9.422      0.000       2.324       3.554\n",
       "TV             0.0458      0.001     32.809      0.000       0.043       0.049\n",
       "radio          0.1885      0.009     21.893      0.000       0.172       0.206\n",
       "newspaper     -0.0010      0.006     -0.177      0.860      -0.013       0.011\n",
       "==============================================================================\n",
       "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
       "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
       "Kurtosis:                       6.332   Cond. No.                         454.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_full.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.409444"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# manually calculate the prediction\n",
    "7.032594 + 0.047537*50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we would predict Sales of __9,409__ items in that market.\n",
    "\n",
    "Of course, we can also use Statsmodels to make the prediction:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The important bit: Plotting the Least Squares Line\n",
    "#### (or plotting our model)\n",
    "\n",
    "Let's make predictions for the smallest and largest observed values of x, and then use the predicted values to plot the least squares line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   TV\n",
       "0  50"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you have to create a DataFrame since the Statsmodels formula interface expects it\n",
    "X_new = pd.DataFrame({'TV': [50]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    9.409426\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use the model to make predictions on a new value\n",
    "lm.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>296.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV\n",
       "0    0.7\n",
       "1  296.4"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a DataFrame with the minimum and maximum values of TV\n",
    "X_new = pd.DataFrame({'TV': [addata.TV.min(), addata.TV.max()]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'preds' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-679c3454d649>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;31m# then, plot the least squares line\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_new\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpreds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'red'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'preds' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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EInIXgHUADqvqcuPYFwF8HMCLxsv+SlUf9Ck7SShBKlGvKZatBmjTul4snz/Ts9JL8r67drTr+wM0Zp/7h4/iA3f+MhYD7UbedtfYrEjzOcFYTXHz5b348Mo3+Pr8OEhK/Ugrbg1BQUQKAN4LYIuqjonIZNM8ke8A2ALg7pbjX1XVr3gTk6SJuJSolQHq3z6EXRvXeP5cKxdIudYI+MWFk6vNru/PlEIOqopN63rRv30oFgNthR83U1IVqRvM9y8pG/Y0cRss/lsATwOYBuDnIvIGAG1jBKr6cwAvdyQdSSVx9XIPMpBpDvhNKTTOKapYt+XRQIKuXnHTtro1SNmTAwp5QU4EgODl0UqigpVzppewaW0vinnBtGLedavnTvdWjgpzENzv5kdR4WpFoKpfA/A106FnRGS1z8+8XkSuATAA4LOqesTneUjABFXoEpcvNGgDtL5vAXrnnY7LvvYLAEC5pkBNI48VeHG1narIfhUfv3sA5WodY7VG0HjLzoPw2joiTLYODqN/xxCKPTlUDDdP0oPxbjG7KCu1GuoKjNWcm/jFhdtg8VwA/wPAfFW9VER6AbwNwLc9ft7XAfSj8W3sB3AbgD+1+cwNADYAwOLFiz1+DPGKVXC3kyV4HEv4MAzQ8UoNpZ48KrVTqSqFXA4HnjuKmVOLkYzNjy995tQCWnaPhAhw3cXn4I5HDsYerLQKbPdvH8J7lr0+McrRL1aGu5WkxZvcxgi+A+B/Afi88feTAH4Ij4ZAVV9oPhaRbwLY3ua1dwK4EwBWrFjhFI8gHWD1xf2LeweRz+VQzPsPKsbRSydoA2S1yjhZreHjdw+gmM93nFbqtAobGS3j6IkKKrWJW0E6zeSnFfOTsodOjtVx6fLX4+qVi2P3sacxGO8Wp6A9kJy00SZuDcEZqnqviPwlAKhqVUQmb1LqgIjMU9XnjT/fB2C/13OQ4LH64lbrQLVeR7mazKVsO4I0QJP77ddRq9dRrgHlamOV4PfaOKXYmp+vK9CTA6YWelzN5I9XaijlpeHOMijlG7UFS+fG3+yum/cEthpbTw6TJlZx3wMzbg3BcRGZA8PBKCJvBXC03RtE5AcALgZwhogcAnAzgItFpM84z9MAPuFPbBIkdtkmZpI+WwuzkZd5lXH0xBiuu+dxHCtPdBV5vTZuGpO1Pl/qyeGOD1+IZfNPd/yshbOnQnICmAyB5CQxijbJOfWdYje2JGc7uTUEfwFgG4A3icguAGcCuLLdG1T1QxaHvcYUSARY7TLVDG41CWu2FoQCj6ICuLnKCKo61Mk1YvV8T15w+NWTrlpyp0HRpjkV1Am7sSV1jKLqzv0uIj0A3gxAAPxWVcfCFMzMihUrdGBgIKqPyyxmpbzr4EuTlEjQyjUIBT4yWsaqWx6e4A+fUsj5qh1wy7bB4Y6vjZPcVs8DDd+/l46bSWx5TKJDRPao6grH17UzBCLyH9u9WVV/7EM2z9AQxEOYSiQoBb732VfwkW/tnuCqmVHqwfc+tjLUop0gro2TQWk+n88JjpcnhuTCNnakO3BrCJxcQ5e3eU4BRGIISDyEmfUTVNZIXEHHIK6Nk2uk+fzO3xzGzdsOjDeRA5IfsyHpoq0hUNX/EpUgJDqS4C4ISoGnwRfeDieDMmd6CavPOwv/bevEBLtuybAhycB1G2oRWQtgGYApzWOq+tdhCEXCIymtlYNU4GEEHZNgLJuk3djZYXeNk3Tts4KrYLGIfAPAaQBWA/gWGhlDv1LVj4YrXgPGCIIh6MBqED/YJP7ok2IsW0nitfKL3TVO6rVPK0HFCJr8kaqeLyL7VHWziNyGRjtqkiKCrOYM6gcbVBwiKKN04LlXceN9+1CuJm8fgjgqtcPAroaid97prnsqdZNRTAJuDcFJ4//XRGQ+Gl1F54UjEgmLoPzySdu0JQij1DxHDjJeTd2EgdlgsZuQDD77iquJClcNweO2DfUDIjILjY1oHgfw7wC+H5pUJBRa2xS7bfvbilW755wIDjzXttg8FPxupm5uEWw+x2tjkzunJD0wG9W+ykF9jt2EpG/RLMeJit/7TdrjdkXwGwA1Vb3f6Dx6IYB/DE8sEhZBBFatfsivVRqN2G698oJIZ2d+3F2tM8rrLl5q2STstGIedaN4K0mrAbNb5NGDL0UyOw5yFm4X/F46d4ZjULxbm9XF7epyawg2qeqPROTtANYA+AoaLaVXhiYZCY12vmY3X8jmD/kGw5fepFyNvle/V3eXlVvLqk9/qUfwjY9ciGXzZ4Y+Fi9KYGKf+0YDvGo92A3qreQL2hVoNyFxmqhEWTcSlXJOgqvLrWuouV5eC+CbqroDQDEckUiYtFvee9lFaX3fAnzzmhU4rTBx68aod7zy6u6ycmsV8zlcv/qcCee49coLcNG5Z4VuBLxc81a3SLnaMAJmwrj+Qe78ZsZupzG7403FvGldb8fuTSei2lEsKa4utyuCYRH5WwDvAnCLiJTg3oiQhNBu5uFn1rds/umoh7jjldsZmRd3l92M8uqViyPv0+/1msfV5z4JLaNbv7ub1vZi+YKZobU/iSoZIimuLrfK/CoA/wzgj1X1FQCvA3BDaFKRwHGaefiZ9QUVfLbC64zMbhbpRWbzOaIIwHq95lYKuZAXlHok1Nlx85qVegSnFfIo9YirzwnqGlp9dzc/cADTivlQlGVYKyArkmBkAfd7Fr8GU18hY3OZ5+3fQZKG08zD7xcyrKreMGdkTjJH5bP1es3j7HPfWPdJo/ewSvsXI9hraPXdrdQUl/3PR/GVK4O/N1Eq56RUjbtuMUHSjdOX2/yFzOcEYzXFpnW9rr6QQRc6RbFctpM5SreAHyUQR5/75jUxJwa0uyZBX0O7jZMq1Xpo9+a6i5diy86DkewoloR9GWgIMoIbpbO+bwGOnaxi8wMHUMjn0L99CDNKPZFnMNgZrWnFPPY++8r4jyWMrI6ofbZ+lEDUFcZer0mQ13A8QLy2F5sfOIBKbWJMKuh7Y17JAIoNF52Nq1cuDv16x101TkPQJbhRik5KZ2S0jP4dQ6jUdHyz9Dgqhq2M1lUrFmLdlkdP/f0HC3HvnkOBu2/i8NmalUDzPk4r5nG8Uos0cB1UyqZbQ+5Eq3vpc+9+M77y0JOomFYmQScntK5k7njkIK5eudj1+9Pa9oKGIOG4+XJ58ce2m3nYBcPiKNYxG61pxTzWbXl0wg/07sd+BwCTetV0qjzj9Nk276PWFeWaYkqhEbAMO6/c6fvj9Zo4GfJKrYbrV5/TdqZtpZRv/+mTuHldL/p3DIVybzpZySShFqATaAgSjJsvV5D+2GnF/KStEU+ONWZyUWI2fhcsmoW9Fj1orLjsa79AqSff8Q8xDp+t+T42aT4Oc1Xm9vvj9Zo4GfLbHnoSW3YexK02wV47pbx8wUzs2rgmlHvjdzWYtN5bfmAtQEJxW2jiN9XNKrXveKWGYn5iRkgpLxN2xvI7FrdphFZpo3bBQjMnx+qo1DSwohy36ahBYXUfm4RZpOelb5TXa9J8/fFKDVqf3O6+XLW/T+2Uclj3xm86dJTppmFBQ5BQ3H65/Mxi7HL09w8fnRSMk5x05IPtpHK2qdABTPqBXvO2xeN/F3tyKLUYMC8/xKiatrWjnbELM0bRrm9UUNW004p5lGvW+57Y3acwa1Tasb5vAXZtXIPvfWwldm1c42pVmZRagE6gayihuP1yefXftusF379jaNLrN611l0Lq5bO8VM42FYWVa+LTl5w7wfUAk7Jx+0NMim/XfB+tYgRhKcAo+kYdr9QwpZCb5HYE2t+nuNIqvWbwJKUWoBNoCBKKly+Xlx+Ml17w00p5LF8w0/cYvAbf3NQ6tGbXNMfr9lqZ3wcgUb7dVr96VFlD6/sWYNZpRXzy7/ZMaMMdVGqmnaJ3U6Ecd1qlW5JQC9AJNAQRY04PfO7oSQBq2+HSy5fL7Q/GTtkumXMaytWJsYBaXTta3gZVOeu28tfpWrlpPx13S+O4FF+YfaNa72ulVsf1q5dGkp8fJWkxWla42rM4brplz+LW9MAmhbzgtv8UXR//bYPDE1P7jJx8oBF0LeUFkpNA3CStn9U8Z7u0WKfn/Oy7bPW+Uo8ALTuSdbKHc9qxu1dBkeY8+7QS9J7FpEOs0gObjNUUN9wXnUvCLrWviYpgx/Vvx9K5MxzP1epqcdNf3k3eertaBz+zeKv3FfN5bLjobNzxyMHU+naDZH3fAvTOOx2Dz76CvkWzXN1/L6R5xtzt0BBEhFML4XxOxrMnopg1Nc+98zeH0ZNrTRnNuUoZNSv0k9UaVBVTCz2TlHurb98uWO3GJ+43QyOu9tNpmgUnJXBOooeGICKccuFrdcX+4aP4wJ2/jOSH2PzR52VynYDfIhoAOFauArAPuloZRK03OkmW8u4qo/1kaDi9z8oF1cilFyybf7ovJZ4mxdoNRVHEPzQEEWGVHtikkBd84fJe9G8fiuSHaOemmlbKo1Z3t0ev0wrHzl1jZRAb10LHe8g4jdtvhobb920dHMbnfrQXY8Y96skBt1/V50mJp02xJmWDFBIPoRkCEbkLwDoAh1V1uXHsdQB+CGAJgKcBXKWqR8KSIWm0+ubNWUOHjpxAXqyLooL+IVr96KcV89h8+TKsPs/d9oxOKxy7VUXrzLxcrSGXkwlGyc24/fqbnd43MlrGjfftGzcCAFCtAzfct7dt2+VW45I2xdoNRVHEP2FWFn8HwHtajt0E4Geqeg6Anxl/Z4pmefzSuTNw0blnju+Lu3/46CQXzYmxaig/RKsffU0Vq887CwBcVdm2Vn4W8oKeHFxVgZqrNx/883dMej5OBXToyAnkc5M3XsmLdQWsXeV02hRrXJW8JBmEtiJQ1Z+LyJKWw1cAuNh4/F0AjwDYGJYMaWFktIy/3n5g0nER552g/GDnL3/04EuefNqtrhbAfaDbPDNPUlXmwtlTUbPoi1PTyUrcyf2TpHG5Ie1FUcQ/UccI5hrbXALA7wHMjfjzE0nDLZQDMHFFUMh7dyW0S+c0P2elxJt59l582q2uFvPjVpeJXQZNkhTQnOkl3Hrl+fhsS4zg1isvcBX4Nrt/kjQutzDFM5vEFixWVRUR22o2EdkAYAMALF7sbmOIuLBTcG5TBxfOnoqaTva3e63sbZfOabeRS1Muq1bPnfi0zbJUanW8Y+kc/MuTL6LYk0dN1VPtQNQ0FbhT1pAb90+SxkWIHVEbghdEZJ6qPi8i8wActnuhqt4J4E6gUVkclYBesUsR9LpZzAdWLBrfbAVo1BXceqV7V4JTOqfVRi7m2b6VUqvU/Pm0rWT56W9eBACMVeLb+cwLc6aXcNG5Zzm+Jm3uH0KsiLoN9TYA1xqPrwWwNeLP90y7FsV2bZMPvnDM1V4C5vM0Wzw06ckBq5ae4VrOdv3srchBcOC5V8f/biq1gqmdc61ex66DL7k+pxdZ8iKWwde04adtMSFJIzRDICI/APBLAG8WkUMi8lEAXwLwLhF5CsA7jb8Ti1Mv/QPPHUXOIuWz2cmz9Xi7rSBbX1/M5z0pSjebt5h5bWxyz/lVS8+AOWGmWoevDV7cyDLmc7WRRJqZYFwJkLQSmiFQ1Q+p6jxVLajqQlX9tqqOqOolqnqOqr5TVV8O6/M7xWmHsK2Dw/j43QN4zaIqt2/RrEA2+/aiKJ3SOa9522KjydopWneIOnTkBIr5idtS+tlpqSlLqcf+63Xz5cuoOAlJCKwstqFdRgjQ6GNfrk4MXZR6GrnXS+fO6Hizbz++Zqd0znf+h7n45Pcen2C8zAHhIHPfm7J8f/fv8Dc/exLNBp95Af76vcvx4ZVv8HxOQkg40BDY0E4pWhmJKT053HTpeeN+/U42++4k1bBdOuey+TNRV/ue83YGCWhkFXmVa870Ej51yTm4euXijvv2EELCg/sRtGHb4DBuuG8v8pJDTeu49coLxnvpt/a2B4DppTyq9cmpkWHiNkW1+br9zx1F//ahttlM5nN6KTJLU6dNQrIA9yMIgIaJFEAA6Cn/unnmnAPwmmEQRsvRpka6TVFtfd2mtb1YvmCmrcJuriq8NE5LU6dNQshEok4fTQ1NJViu1vFapTYpsLq+bwE2re1FxaIdgZ8Aqxst2mfXAAALzUlEQVR5zGmsTsHs1nGYX9e/Y8jVrN0qm8lqbG5lIYQkE64IbHBqHzAyWkb/jiFUa5MNQdDNxaxm22+YM81VJXAnXTDdBo/T1mmTEDIRrghscFKCdkVTxZ5guzbazbbHqjWUa85KupNMILcdKdPWaZMQMhGuCGwwxwHyIhirNXzr7VoyFPOCBz/lbq9ft9htAHP1t3ajGbWYUmgYJCsl3WlqqptsJrZaICTd0BC0YX3fAhw7WcXm7UMo9uTQv2MIM6b0jDdrs1J+QW/4bWVwWrOV6nXFg3/+DtvP7jQ11U3jtDR22iSENKAhaEMzDlCp1lFp9G6bkDUThfKbtKNXrQ7RiVtdlnryjpvNR9EFk502CUknNARtsHLLNJu1XXTumQD8Kz8vOfetW1yu2/IoYDIE9McTQjqBweI2WLllrJq1ecWpmZ0V5i0uuaUgISRIWFnsQLO6uLWv0JRCDrs2rvGsgK2qkv2ci1W8hBAnWFnsgnbbOjZZ37cAs04r2DZra32fk4IOKuee/nhCSFBk1hCYi7ROjFUhIpjSk7dsj2DXrG3/8FF84M5fjmcNXbViIe4dmLwdpBnm3BNCkkYmYwStRVrVOjBWU9v2CHOml7BpXS+KPTlMK+UxpZDDpnW96N8xNKHQ6+5f/s6xzYLbIi1CCImKTK4I7Iq0mrS6arYODhsdOwVj1TpuvnwZls+f2fYcVudpwpx7QkiSyOSKwGkrRbOrxrx6OF6poVJT9O8YwrRi3nk7xjYuH25vSAhJCpk0BHOml7BpbS+KecG0Yh49OaCQF0tXzaEjJ6AtHUa1rjheqY27eKaV8lYfg03reqnoCSGJJ5Ouoa2Dw+jf0WgbUakpNl+xHO9Z9npLV820Yn5CFS8AlGuKacX8uItn528O4+ZtByZU904r5rF8/szIxkQIIX7J3IrA7OoZLddQqdbRv30IACxdNc8dtd5XoHl8zvQSVp93FmotWUU1VWYCEUJSQeYMgdvNVk4hjseZCUQISTOZcw15zeNfNv909OSAquktPbnGcTPMBCKEpJXMrQj8zN4/fcm5KOaB0wp5lHoEt1/VZ9uXn5lAhJC0kbkVAeB+9m6uPhbJ4c8ufhOuXrmYip4Q0lVkbkXQZM70EhbOnopDR05YbrLeWn1crtZxxyMHY5CUEELCJZMrAsB6Q/j1fQvGm8YdPVHhhuyEkEyQSUMwMlrGjfftQ7laH1f0N96/D8dOVtG/YwiFXA6VWg0tdWRsDkcI6UoyZwhGRsu47SdPolydmDmUzwk2P3AAlZqOG4eeHFDqyaGY54bshJDuJVOGYOvg8PhKoJWxqgItRWF5EXzzmhWYObXAlFBCSNcSS7BYRJ4WkV+LyKCIRLL1WDP4a2UEAODqlQtRaXmqXFPMnzmFKaGEkK4mzqyh1ara52YbtSCwqihuUuoRrDlvLqYUJj4/pZCb0D+IEEK6kcykj9q1ni7kBV+4fBmW2TSIY3CYENLtxGUIFMBPRGSPiGyweoGIbBCRAREZePHFFzv+wNaK4kJekBegmM+hf/sQdh18if2CCCGZRLQlQBrJh4osUNVhETkLwEMAPqWqP7d7/YoVK3RgIJhQwshoGQeeO4qP3z2AcvXU2KcUcti1cQ0A603sCSEkbYjIHjfu91hWBKo6bPx/GMA/APjDqD57zvQSZk4topifuJmMuViMwWFCSJaI3BCIyDQRmdF8DODdAPZHKYPXDqSEENLNxLEimAvgURHZC+BXAHao6v+OUgDuH0AIIaeIvKBMVf8NwAVRf24r3D+AEEIaZKqyuJU500s0AISQzJOZOgJCCCHW0BAQQkjGoSEghJCMQ0NACCEZJ1OGYGS0jL3PvmK5NSUhhGSVzGQN2W1NSQghWScTK4LWjehPjtVx4/37uDIghBBkxBBY7UXQ7C1ECCFZJxOGgL2FCCHEnkwYAvYWIoQQezITLGZvIUIIsSYzhgBgbyFCCLEiE64hQggh9tAQEEJIxqEhIISQjENDQAghGYeGgBBCMk5XGwI2mSOEEGe6Nn2UTeYIIcQdXbkiYJM5QghxT1caAjaZI4QQ93SlIWCTOUIIcU9XGgI2mSOEEPd0bbCYTeYIIcQdXWsIADaZI4QQN3Sla4gQQoh7aAgIISTj0BAQQkjGoSEghJCMQ0NACCEZR1Q1bhkcEZEXATzj461nAHgpYHHipJvG001jAbprPN00FqC7xuN1LG9Q1TOdXpQKQ+AXERlQ1RVxyxEU3TSebhoL0F3j6aaxAN01nrDGQtcQIYRkHBoCQgjJON1uCO6MW4CA6abxdNNYgO4aTzeNBeiu8YQylq6OERBCCHGm21cEhBBCHOhaQyAi7xGR34rIQRG5KW55vCIiT4vIr0VkUEQGjGOvE5GHROQp4//Zcctph4jcJSKHRWS/6Zil/NLga8a92iciF8Yn+WRsxvJFERk27s+giFxmeu4vjbH8VkT+OB6p7RGRRSKyU0SGROSAiHzaOJ66+9NmLKm8PyIyRUR+JSJ7jfFsNo6/UUR2G3L/UESKxvGS8fdB4/klvj5YVbvuH4A8gP8H4GwARQB7AfTGLZfHMTwN4IyWY18GcJPx+CYAt8QtZxv5LwJwIYD9TvIDuAzAPwEQAG8FsDtu+V2M5YsAPmfx2l7j+1YC8Ebje5iPewwtMs4DcKHxeAaAJw25U3d/2owllffHuMbTjccFALuNa34vgA8ax78B4M+Mx/8VwDeMxx8E8EM/n9utK4I/BHBQVf9NVSsA/h7AFTHLFARXAPiu8fi7AN4boyxtUdWfA3i55bCd/FcAuFsbPAZglojMi0ZSZ2zGYscVAP5eVcuq+u8ADqLxfUwMqvq8qj5uPD4G4AkAC5DC+9NmLHYk+v4Y13jU+LNg/FMAawDcZxxvvTfNe3YfgEtERLx+brcaggUAnjX9fQjtvxxJRAH8RET2iMgG49hcVX3eePx7AHPjEc03dvKn9X5db7hK7jK56VI1FsOV8BY0Zp6pvj8tYwFSen9EJC8igwAOA3gIjVXLK6paNV5ilnl8PMbzRwHM8fqZ3WoIuoG3q+qFAC4FcJ2IXGR+UhtrwdSmfKVdfgBfB/AmAH0AngdwW7zieEdEpgO4H8BnVPVV83Npuz8WY0nt/VHVmqr2AViIxmrlvLA/s1sNwTCARaa/FxrHUoOqDhv/HwbwD2h8IV5oLsmN/w/HJ6Ev7ORP3f1S1ReMH2wdwDdxyr2QirGISAENxXmPqv7YOJzK+2M1lrTfHwBQ1VcA7ATwNjTccc0dJc0yj4/HeH4mgBGvn9WthuBfAZxjRNqLaARRtsUsk2tEZJqIzGg+BvBuAPvRGMO1xsuuBbA1Hgl9Yyf/NgDXGNkpbwVw1OSiSCQtPvL3oXF/gMZYPmhkc7wRwDkAfhW1fO0wfMjfBvCEqt5ueip198duLGm9PyJypojMMh5PBfAuNOIeOwFcabys9d4079mVAB42VnPeiDtKHtY/NDIdnkTDv/b5uOXxKPvZaGQ27AVwoCk/Gr6/nwF4CsBPAbwublnbjOEHaCzJx9DwaX7UTn40MiXuMO7VrwGsiFt+F2P5O0PWfcaPcZ7p9Z83xvJbAJfGLb/FeN6OhttnH4BB499labw/bcaSyvsD4HwA/9eQez+ALxjHz0bDYB0E8CMAJeP4FOPvg8bzZ/v5XFYWE0JIxulW1xAhhBCX0BAQQkjGoSEghJCMQ0NACCEZh4aAEEIyDg0BIS4QkTmmTpa/N3W21NYOliLyGRH5elyyEuIVGgJCXKCqI6rap43S/28A+Krx+BNoFCya+SAatQeEpAIaAkI64z4Aa0394ZcAmA/gFzHKRIgnaAgI6QBVfRmNis5LjUMfBHCvslKTpAgaAkI65wc45R6iW4ikDhoCQjpnKxobglwI4DRV3RO3QIR4gYaAkA7Rxo5SOwHcBa4GSAqhISAkGH4A4ALQEJAUwu6jhBCScbgiIISQjENDQAghGYeGgBBCMg4NASGEZBwaAkIIyTg0BIQQknFoCAghJOPQEBBCSMb5/8Rehxt1ONu2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# first, plot the observed data\n",
    "addata.plot(kind='scatter', x='TV', y='sales')\n",
    "\n",
    "# then, plot the least squares line\n",
    "plt.plot(X_new, preds, c='red', linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>6.129719</td>\n",
       "      <td>7.935468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TV</th>\n",
       "      <td>0.042231</td>\n",
       "      <td>0.052843</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0         1\n",
       "Intercept  6.129719  7.935468\n",
       "TV         0.042231  0.052843"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the confidence intervals for the model coefficients\n",
    "lm.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    9.409426\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make predictions for those x values and store them\n",
    "preds = lm.predict(X_new)\n",
    "preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    1.406300e-35\n",
       "TV           1.467390e-42\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the p-values for the model coefficients\n",
    "lm.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.611875050850071"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the R-squared value for the model\n",
    "\n",
    "lm.rsquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression in scikit-learn\n",
    "\n",
    "#### That was a lot of work!\n",
    "\n",
    "Let's redo some of the Statsmodels code above in scikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create X and y\n",
    "feature_cols = ['TV', 'radio', 'newspaper']\n",
    "X = addata[feature_cols]\n",
    "y = addata.sales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# follow the usual sklearn pattern: import, instantiate, fit\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Classes and instances\n",
    "lm = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Cellar/python3/3.6.4_2/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/linalg/basic.py:1226: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  warnings.warn(mesg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9388893694594067\n",
      "[ 0.04576465  0.18853002 -0.00103749]\n"
     ]
    }
   ],
   "source": [
    "# print intercept and coefficients\n",
    "print (lm.intercept_)\n",
    "print (lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TV 0.045764645455397615\n",
      "radio 0.1885300169182046\n",
      "newspaper -0.001037493042476266\n"
     ]
    }
   ],
   "source": [
    "# pair the feature names with the coefficients\n",
    "for name, coef in zip(feature_cols, lm.coef_):\n",
    "    print(name, coef)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8972106381789521"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the R-squared\n",
    "lm.score(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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