{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 8 - Mean Square Error and validation\n",
    "\n",
    "We will continue looking at the insurance data set from Lab 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the CSV file into a dataframe and display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>smoker</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>female</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>southwest</td>\n",
       "      <td>16884.92400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>male</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1725.55230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>male</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>4449.46200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>male</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>21984.47061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>male</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>3866.85520</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     sex     bmi  children smoker     region      charges\n",
       "0   19  female  27.900         0    yes  southwest  16884.92400\n",
       "1   18    male  33.770         1     no  southeast   1725.55230\n",
       "2   28    male  33.000         3     no  southeast   4449.46200\n",
       "3   33    male  22.705         0     no  northwest  21984.47061\n",
       "4   32    male  28.880         0     no  northwest   3866.85520"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insurance = pd.read_csv(\"../data/insurance.csv\")\n",
    "insurance.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More about dummy variables\n",
    "\n",
    "Change the `sex`, `smoker`, and `region` columns to dummy variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>age</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>charges</th>\n",
       "      <th>sex_male</th>\n",
       "      <th>smoker_yes</th>\n",
       "      <th>region_northwest</th>\n",
       "      <th>region_southeast</th>\n",
       "      <th>region_southwest</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>16884.92400</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>1725.55230</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>4449.46200</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>21984.47061</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>3866.85520</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31</td>\n",
       "      <td>25.740</td>\n",
       "      <td>0</td>\n",
       "      <td>3756.62160</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>46</td>\n",
       "      <td>33.440</td>\n",
       "      <td>1</td>\n",
       "      <td>8240.58960</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>37</td>\n",
       "      <td>27.740</td>\n",
       "      <td>3</td>\n",
       "      <td>7281.50560</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>37</td>\n",
       "      <td>29.830</td>\n",
       "      <td>2</td>\n",
       "      <td>6406.41070</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>60</td>\n",
       "      <td>25.840</td>\n",
       "      <td>0</td>\n",
       "      <td>28923.13692</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     bmi  children      charges  sex_male  smoker_yes  region_northwest  \\\n",
       "0   19  27.900         0  16884.92400         0           1                 0   \n",
       "1   18  33.770         1   1725.55230         1           0                 0   \n",
       "2   28  33.000         3   4449.46200         1           0                 0   \n",
       "3   33  22.705         0  21984.47061         1           0                 1   \n",
       "4   32  28.880         0   3866.85520         1           0                 1   \n",
       "5   31  25.740         0   3756.62160         0           0                 0   \n",
       "6   46  33.440         1   8240.58960         0           0                 0   \n",
       "7   37  27.740         3   7281.50560         0           0                 1   \n",
       "8   37  29.830         2   6406.41070         1           0                 0   \n",
       "9   60  25.840         0  28923.13692         0           0                 1   \n",
       "\n",
       "   region_southeast  region_southwest  \n",
       "0                 0                 1  \n",
       "1                 1                 0  \n",
       "2                 1                 0  \n",
       "3                 0                 0  \n",
       "4                 0                 0  \n",
       "5                 1                 0  \n",
       "6                 1                 0  \n",
       "7                 0                 0  \n",
       "8                 0                 0  \n",
       "9                 0                 0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insurance_new = pd.get_dummies(insurance, columns = [\"sex\",\"smoker\", \"region\"], drop_first = True)\n",
    "insurance_new.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First remember the scatter plot showing the relation being age, smoker and insurance charges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1a16b03cf8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GL35yOvkd9PStnPzUd76TJZl0JJl05KaYE30pMYQQnTLPnmYxcP24nvzigw2R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\n+ZEptPy0I9edS7cauGJYPp9srGLpzno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EWAgMBmqA7siV0ARFUep60UwAzhVC3BPYNgB1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\nr4/89DjO65cVXvOj0cPQG2HDJ8ExlQZ6BCIGDeNriiJdiI1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nPgcDp/32ArWmJBh8PfS+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WzfV8Tol+btD1o3vLaQ927qS/cmQS7MKBidE1e37/56NE3kxSt78NKcjSRGhXH34NYkB5muCkBK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\nw9B/QHQDWPeZsiJQ1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5BqrjrlxSrxbZmrKaT7tsDbV8FlrysTrLwG1flyDYKr7NPW707t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\nL936BgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0e617dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.relplot(x = \"age\", y = \"charges\", hue = \"smoker\", data = insurance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at a linear model with `age` and `smoker_yes` as the independent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>charges</td>     <th>  R-squared:         </th> <td>   0.721</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.721</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1728.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 24 Sep 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:59:30</td>     <th>  Log-Likelihood:    </th> <td> -13623.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1338</td>      <th>  AIC:               </th> <td>2.725e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1335</td>      <th>  BIC:               </th> <td>2.727e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>-2391.6264</td> <td>  528.302</td> <td>   -4.527</td> <td> 0.000</td> <td>-3428.019</td> <td>-1355.234</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age</th>        <td>  274.8712</td> <td>   12.455</td> <td>   22.069</td> <td> 0.000</td> <td>  250.437</td> <td>  299.305</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>smoker_yes</th> <td> 2.386e+04</td> <td>  433.488</td> <td>   55.031</td> <td> 0.000</td> <td>  2.3e+04</td> <td> 2.47e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>265.239</td> <th>  Durbin-Watson:     </th> <td>   2.080</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 636.675</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.074</td>  <th>  Prob(JB):          </th> <td>5.59e-139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.609</td>  <th>  Cond. No.          </th> <td>    130.</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:                charges   R-squared:                       0.721\n",
       "Model:                            OLS   Adj. R-squared:                  0.721\n",
       "Method:                 Least Squares   F-statistic:                     1728.\n",
       "Date:                Tue, 24 Sep 2019   Prob (F-statistic):               0.00\n",
       "Time:                        11:59:30   Log-Likelihood:                -13623.\n",
       "No. Observations:                1338   AIC:                         2.725e+04\n",
       "Df Residuals:                    1335   BIC:                         2.727e+04\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept  -2391.6264    528.302     -4.527      0.000   -3428.019   -1355.234\n",
       "age          274.8712     12.455     22.069      0.000     250.437     299.305\n",
       "smoker_yes  2.386e+04    433.488     55.031      0.000     2.3e+04    2.47e+04\n",
       "==============================================================================\n",
       "Omnibus:                      265.239   Durbin-Watson:                   2.080\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              636.675\n",
       "Skew:                           1.074   Prob(JB):                    5.59e-139\n",
       "Kurtosis:                       5.609   Cond. No.                         130.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = smf.ols(\"charges ~ age + smoker_yes\", data = insurance_new).fit()\n",
    "lm.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What's the linear model if $X_1$ is age and $X_2$ is smoker_yes?\n",
    "\n",
    "$$y = -2391.6264 + 274.8712x_1 + 23860x_2$$\n",
    "\n",
    "Consider all the non-smokers. For these people, what is $x_2$?  So what is the linear model for only non-smokers?\n",
    "\n",
    "Let's visualize this line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a0e2ce978>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KG/eH3iwUZxjpm2Ph/vPKmVqWw+Id9cwoz2VESTq/bNfjCEKp7l/taKC6xcXn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\n3Ev3wWuDay9wi16Aqb+e+DtnawpMeAXGPqUMOS2JRPkED5zbkRuHtaK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NUO2hcxKj+Mf4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\n0koVlA0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0e55a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.relplot(x = \"age\", y = \"charges\", hue = \"smoker\", data = insurance)\n",
    "x = np.linspace(18,65,100)\n",
    "y = -2391.6264 + 274.8712*x\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now consider only the smokers.  What is the value of $x_2$?  What is the linear model for the smokers?  \n",
    "\n",
    "Again, let's visualize the line for the smoker linear model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a16aa10f0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UpBs4uTKbEcXprN8TfrNQmmVkYJ6Ze88ZxswheSza2szsYflUlVn5RZceRxBO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\nFovFUq9YQ2SxWCyWesUaIovFYrHUK/8PLd94g0X1fT0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17471908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.relplot(x = \"age\", y = \"charges\", hue = \"smoker\", data = insurance)\n",
    "x = np.linspace(18,65,100)\n",
    "y = (-2391.6264 + 23860) + 274.8712*x\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are these the same two linear models we would get if we filtered our data set into smokers and non-smokers and separately computed the linear model for each?\n",
    "\n",
    "Try it below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean Squared Error\n",
    "\n",
    "The error is the difference between the actual $y_i$ value and what was predicted $\\hat{y_i}$.  The *mean squared error (MSE)* is the mean of the squares of the error terms:\n",
    "\n",
    "$$MSE =\\frac{\\sum_i (y_i - \\hat{y_i})^2}{n}$$\n",
    "\n",
    "While error in linear regression is often measured by the residual sum of squares (RSS), the mean square error is similar, but used to measure error for other methods of prediction.\n",
    "\n",
    "Let's compute the MSE for the above linear model.  How can you get the error terms?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       -9801.306989\n",
       "1        -830.502686\n",
       "2        -855.304845\n",
       "3       15305.347835\n",
       "4       -2537.396389\n",
       "5       -2372.758803\n",
       "6       -2011.858591\n",
       "7        -497.101918\n",
       "8       -1372.196818\n",
       "9       14822.492127\n",
       "10      -1758.832488\n",
       "11     -10696.966882\n",
       "12      -2103.567916\n",
       "13      -1910.442250\n",
       "14      10726.557224\n",
       "15       -993.689172\n",
       "16      -1104.339106\n",
       "17      -1535.239366\n",
       "18      -2398.775050\n",
       "19       7127.652966\n",
       "20       -871.797843\n",
       "21      -1704.773217\n",
       "22      -1419.043986\n",
       "23       6892.578023\n",
       "24      -1574.705768\n",
       "25        175.360193\n",
       "26       -473.423201\n",
       "27       -457.656614\n",
       "28      -1155.218766\n",
       "29       8726.314781\n",
       "            ...     \n",
       "1308     5565.194896\n",
       "1309    -2002.131262\n",
       "1310    -2212.053597\n",
       "1311    -2107.709725\n",
       "1312    -2417.734960\n",
       "1313     9711.345011\n",
       "1314   -10943.938584\n",
       "1315     8716.276404\n",
       "1316    -1099.249172\n",
       "1317    -1392.592286\n",
       "1318    12267.854024\n",
       "1319    -1126.649040\n",
       "1320     -704.357053\n",
       "1321   -10404.358932\n",
       "1322    -1669.041465\n",
       "1323    10888.108036\n",
       "1324    -1889.487753\n",
       "1325    -1232.179329\n",
       "1326    -2102.942147\n",
       "1327    -2248.899420\n",
       "1328    18465.333324\n",
       "1329    -1576.469306\n",
       "1330     -646.865636\n",
       "1331     6865.526414\n",
       "1332     -489.990306\n",
       "1333     -751.384634\n",
       "1334     -350.074186\n",
       "1335     -926.221486\n",
       "1336    -1372.723544\n",
       "1337    -9089.460496\n",
       "Length: 1338, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errors = insurance_new[\"charges\"] - lm.fittedvalues\n",
    "errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       9.606562e+07\n",
       "1       6.897347e+05\n",
       "2       7.315464e+05\n",
       "3       2.342537e+08\n",
       "4       6.438380e+06\n",
       "5       5.629984e+06\n",
       "6       4.047575e+06\n",
       "7       2.471103e+05\n",
       "8       1.882924e+06\n",
       "9       2.197063e+08\n",
       "10      3.093492e+06\n",
       "11      1.144251e+08\n",
       "12      4.424998e+06\n",
       "13      3.649790e+06\n",
       "14      1.150590e+08\n",
       "15      9.874182e+05\n",
       "16      1.219565e+06\n",
       "17      2.356960e+06\n",
       "18      5.754122e+06\n",
       "19      5.080344e+07\n",
       "20      7.600315e+05\n",
       "21      2.906252e+06\n",
       "22      2.013686e+06\n",
       "23      4.750763e+07\n",
       "24      2.479698e+06\n",
       "25      3.075120e+04\n",
       "26      2.241295e+05\n",
       "27      2.094496e+05\n",
       "28      1.334530e+06\n",
       "29      7.614857e+07\n",
       "            ...     \n",
       "1308    3.097139e+07\n",
       "1309    4.008530e+06\n",
       "1310    4.893181e+06\n",
       "1311    4.442440e+06\n",
       "1312    5.845442e+06\n",
       "1313    9.431022e+07\n",
       "1314    1.197698e+08\n",
       "1315    7.597347e+07\n",
       "1316    1.208349e+06\n",
       "1317    1.939313e+06\n",
       "1318    1.505002e+08\n",
       "1319    1.269338e+06\n",
       "1320    4.961189e+05\n",
       "1321    1.082507e+08\n",
       "1322    2.785699e+06\n",
       "1323    1.185509e+08\n",
       "1324    3.570164e+06\n",
       "1325    1.518266e+06\n",
       "1326    4.422366e+06\n",
       "1327    5.057549e+06\n",
       "1328    3.409685e+08\n",
       "1329    2.485255e+06\n",
       "1330    4.184352e+05\n",
       "1331    4.713545e+07\n",
       "1332    2.400905e+05\n",
       "1333    5.645789e+05\n",
       "1334    1.225519e+05\n",
       "1335    8.578862e+05\n",
       "1336    1.884370e+06\n",
       "1337    8.261829e+07\n",
       "Length: 1338, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "squared_errors = errors**2\n",
    "squared_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40826693.69231889"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "squared_errors.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Altogether:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40826693.69231889"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((insurance_new[\"charges\"] - lm.fittedvalues)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare to the mean squared error with all columns as independent variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>charges</td>     <th>  R-squared:         </th> <td>   0.751</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.749</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   500.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 24 Sep 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:30:29</td>     <th>  Log-Likelihood:    </th> <td> -13548.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1338</td>      <th>  AIC:               </th> <td>2.711e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1329</td>      <th>  BIC:               </th> <td>2.716e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     8</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>-1.194e+04</td> <td>  987.819</td> <td>  -12.086</td> <td> 0.000</td> <td>-1.39e+04</td> <td>   -1e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age</th>              <td>  256.8564</td> <td>   11.899</td> <td>   21.587</td> <td> 0.000</td> <td>  233.514</td> <td>  280.199</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bmi</th>              <td>  339.1935</td> <td>   28.599</td> <td>   11.860</td> <td> 0.000</td> <td>  283.088</td> <td>  395.298</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>children</th>         <td>  475.5005</td> <td>  137.804</td> <td>    3.451</td> <td> 0.001</td> <td>  205.163</td> <td>  745.838</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sex_male</th>         <td> -131.3144</td> <td>  332.945</td> <td>   -0.394</td> <td> 0.693</td> <td> -784.470</td> <td>  521.842</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>smoker_yes</th>       <td> 2.385e+04</td> <td>  413.153</td> <td>   57.723</td> <td> 0.000</td> <td>  2.3e+04</td> <td> 2.47e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>region_northwest</th> <td> -352.9639</td> <td>  476.276</td> <td>   -0.741</td> <td> 0.459</td> <td>-1287.298</td> <td>  581.370</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>region_southeast</th> <td>-1035.0220</td> <td>  478.692</td> <td>   -2.162</td> <td> 0.031</td> <td>-1974.097</td> <td>  -95.947</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>region_southwest</th> <td> -960.0510</td> <td>  477.933</td> <td>   -2.009</td> <td> 0.045</td> <td>-1897.636</td> <td>  -22.466</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>300.366</td> <th>  Durbin-Watson:     </th> <td>   2.088</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 718.887</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.211</td>  <th>  Prob(JB):          </th> <td>7.86e-157</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.651</td>  <th>  Cond. No.          </th> <td>    311.</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:                charges   R-squared:                       0.751\n",
       "Model:                            OLS   Adj. R-squared:                  0.749\n",
       "Method:                 Least Squares   F-statistic:                     500.8\n",
       "Date:                Tue, 24 Sep 2019   Prob (F-statistic):               0.00\n",
       "Time:                        12:30:29   Log-Likelihood:                -13548.\n",
       "No. Observations:                1338   AIC:                         2.711e+04\n",
       "Df Residuals:                    1329   BIC:                         2.716e+04\n",
       "Df Model:                           8                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================\n",
       "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------\n",
       "Intercept        -1.194e+04    987.819    -12.086      0.000   -1.39e+04      -1e+04\n",
       "age                256.8564     11.899     21.587      0.000     233.514     280.199\n",
       "bmi                339.1935     28.599     11.860      0.000     283.088     395.298\n",
       "children           475.5005    137.804      3.451      0.001     205.163     745.838\n",
       "sex_male          -131.3144    332.945     -0.394      0.693    -784.470     521.842\n",
       "smoker_yes        2.385e+04    413.153     57.723      0.000     2.3e+04    2.47e+04\n",
       "region_northwest  -352.9639    476.276     -0.741      0.459   -1287.298     581.370\n",
       "region_southeast -1035.0220    478.692     -2.162      0.031   -1974.097     -95.947\n",
       "region_southwest  -960.0510    477.933     -2.009      0.045   -1897.636     -22.466\n",
       "==============================================================================\n",
       "Omnibus:                      300.366   Durbin-Watson:                   2.088\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              718.887\n",
       "Skew:                           1.211   Prob(JB):                    7.86e-157\n",
       "Kurtosis:                       5.651   Cond. No.                         311.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = smf.ols(\"charges ~ age + bmi + children + sex_male + smoker_yes + region_northwest + \\\n",
    "                    region_southeast + region_southwest\", data = insurance_new).fit()\n",
    "lm2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36501893.007415496"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((insurance_new[\"charges\"] - lm2.fittedvalues)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the p-values to determine which columns to remove from model.  Remove columns one at a time, as the p-values of the other columns will change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>charges</td>     <th>  R-squared:         </th> <td>   0.751</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.750</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   668.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 24 Sep 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:36:54</td>     <th>  Log-Likelihood:    </th> <td> -13548.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1338</td>      <th>  AIC:               </th> <td>2.711e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1331</td>      <th>  BIC:               </th> <td>2.715e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>-1.217e+04</td> <td>  949.538</td> <td>  -12.812</td> <td> 0.000</td> <td> -1.4e+04</td> <td>-1.03e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age</th>              <td>  257.0064</td> <td>   11.889</td> <td>   21.617</td> <td> 0.000</td> <td>  233.683</td> <td>  280.330</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bmi</th>              <td>  338.6413</td> <td>   28.554</td> <td>   11.860</td> <td> 0.000</td> <td>  282.625</td> <td>  394.657</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>children</th>         <td>  471.5441</td> <td>  137.656</td> <td>    3.426</td> <td> 0.001</td> <td>  201.498</td> <td>  741.590</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>smoker_yes</th>       <td> 2.384e+04</td> <td>  411.659</td> <td>   57.921</td> <td> 0.000</td> <td>  2.3e+04</td> <td> 2.47e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>region_southeast</th> <td> -858.4696</td> <td>  415.206</td> <td>   -2.068</td> <td> 0.039</td> <td>-1672.998</td> <td>  -43.941</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>region_southwest</th> <td> -782.7452</td> <td>  413.756</td> <td>   -1.892</td> <td> 0.059</td> <td>-1594.430</td> <td>   28.940</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>300.125</td> <th>  Durbin-Watson:     </th> <td>   2.092</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 716.587</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.211</td>  <th>  Prob(JB):          </th> <td>2.48e-156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.643</td>  <th>  Cond. No.          </th> <td>    295.</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:                charges   R-squared:                       0.751\n",
       "Model:                            OLS   Adj. R-squared:                  0.750\n",
       "Method:                 Least Squares   F-statistic:                     668.3\n",
       "Date:                Tue, 24 Sep 2019   Prob (F-statistic):               0.00\n",
       "Time:                        12:36:54   Log-Likelihood:                -13548.\n",
       "No. Observations:                1338   AIC:                         2.711e+04\n",
       "Df Residuals:                    1331   BIC:                         2.715e+04\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================\n",
       "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------\n",
       "Intercept        -1.217e+04    949.538    -12.812      0.000    -1.4e+04   -1.03e+04\n",
       "age                257.0064     11.889     21.617      0.000     233.683     280.330\n",
       "bmi                338.6413     28.554     11.860      0.000     282.625     394.657\n",
       "children           471.5441    137.656      3.426      0.001     201.498     741.590\n",
       "smoker_yes        2.384e+04    411.659     57.921      0.000     2.3e+04    2.47e+04\n",
       "region_southeast  -858.4696    415.206     -2.068      0.039   -1672.998     -43.941\n",
       "region_southwest  -782.7452    413.756     -1.892      0.059   -1594.430      28.940\n",
       "==============================================================================\n",
       "Omnibus:                      300.125   Durbin-Watson:                   2.092\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              716.587\n",
       "Skew:                           1.211   Prob(JB):                    2.48e-156\n",
       "Kurtosis:                       5.643   Cond. No.                         295.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm3 = smf.ols(\"charges ~ age + bmi + children +  smoker_yes  + \\\n",
    "                    region_southeast + region_southwest\", data = insurance_new).fit()\n",
    "lm3.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36521183.493927866"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((insurance_new[\"charges\"] - lm3.fittedvalues)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and test sets\n",
    "\n",
    "Humans learn some things by training (ex. doing homework or practicing a sport or musical instrument), and can check if they know them by testing (ex. test in a university class, a game for a sport, or a performance for a musical instrument).  When you take a test in a math class, say, the questions are different from the ones you practiced on for homework, to ensure you understand the concepts and didn't simply memorize the answers.  We want to test the computer's ability to make a prediction in a similar way.\n",
    "\n",
    "Therefore, we want to divide our data into *training data* and *test data*.  We will \"learn\" the linear model on the training data, and then make prediction on the new, previously-unseen test data.\n",
    "\n",
    "We can use the sci-kit learn package to split up our data.  Notice we are specifying which columns to use as the input data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(insurance_new[[\"age\",\"smoker_yes\"]], insurance[\"charges\"], test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display X_train, X_test, y_train, and y_test below.  Are they what you expect?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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>age</th>\n",
       "      <th>smoker_yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1003</th>\n",
       "      <td>48</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>292</th>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>269</th>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>228</th>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>938</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      age  smoker_yes\n",
       "1003   48           0\n",
       "292    25           1\n",
       "269    49           0\n",
       "228    41           0\n",
       "938    18           0"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1003    21232.18226\n",
       "292     42112.23560\n",
       "269      9282.48060\n",
       "228      7358.17565\n",
       "938      2304.00220\n",
       "Name: charges, dtype: float64"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also make a linear model with Sci-kit learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lm = linear_model.LinearRegression()\n",
    "model = lm.fit(X_train, y_train)\n",
    "predictions = lm.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39286899.79340403"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((predictions - y_test)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get R-squared:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7034526096487327"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens if you use a different test size?  Are the scores of the predictions more or less variable?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens if you use more columns to make the predictions?  Are the scores of the predictions more or less variable?"
   ]
  },
  {
   "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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