1.6_most_important_feature_stunting.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.metrics import accuracy_score,confusion_matrix,classification_report\n",
    "from sklearn.impute import SimpleImputer\n",
    "from sklearn.model_selection import train_test_split,cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('finalChildMalnutrition.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.fillna(df[['fever','Mother_BMI','diar','Father_Edu','currently_working_mot']].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>Division</th>\n",
       "      <th>Age at 1st Birth</th>\n",
       "      <th>Child Age</th>\n",
       "      <th>stunting</th>\n",
       "      <th>underweight</th>\n",
       "      <th>wasting</th>\n",
       "      <th>diar</th>\n",
       "      <th>fever</th>\n",
       "      <th>ari</th>\n",
       "      <th>Mother_BMI</th>\n",
       "      <th>Birth_Order</th>\n",
       "      <th>Mother_edu</th>\n",
       "      <th>wealth_index_cat</th>\n",
       "      <th>Father_Edu</th>\n",
       "      <th>residence</th>\n",
       "      <th>sex</th>\n",
       "      <th>currently_working_mot</th>\n",
       "      <th>Breastfeeding</th>\n",
       "      <th>household_no</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>20.96</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "      <td>47</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>19.71</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>23</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>20.66</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>21</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>18.41</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>15</td>\n",
       "      <td>51</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>19.47</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Division  Age at 1st Birth  Child Age  stunting  underweight  wasting  \\\n",
       "0         1                16         13         0            1        1   \n",
       "1         1                18         47         0            1        1   \n",
       "2         1                16         23         0            0        0   \n",
       "3         1                21         11         0            0        0   \n",
       "4         1                15         51         1            1        0   \n",
       "\n",
       "   diar  fever  ari  Mother_BMI  Birth_Order  Mother_edu  wealth_index_cat  \\\n",
       "0   0.0    1.0    1       20.96            2           0                 0   \n",
       "1   0.0    1.0    0       19.71            2           0                 0   \n",
       "2   0.0    0.0    0       20.66            3           0                 0   \n",
       "3   0.0    0.0    0       18.41            1           0                 0   \n",
       "4   0.0    1.0    0       19.47            3           0                 1   \n",
       "\n",
       "   Father_Edu  residence  sex  currently_working_mot  Breastfeeding  \\\n",
       "0         0.0          1    1                    0.0              1   \n",
       "1         0.0          1    1                    0.0              0   \n",
       "2         0.0          1    1                    1.0              1   \n",
       "3         0.0          1    1                    0.0              1   \n",
       "4         0.0          1    1                    1.0              0   \n",
       "\n",
       "   household_no  \n",
       "0             6  \n",
       "1             5  \n",
       "2             5  \n",
       "3             2  \n",
       "4             4  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X  = df.iloc[:, [1,2,6,7,8,9,10,11,12,13,14,15,16,17,18]].values\n",
    "\n",
    "y_stun = df.iloc[:, 3].values\n",
    "y_underweight = df.iloc[:, 4].values\n",
    "y_wast = df.iloc[:, 5].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ---------\n",
    "# stunting |\n",
    "# ---------"
   ]
  },
  {
   "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>y</td>        <th>  R-squared:         </th> <td>   0.075</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.073</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   37.74</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 26 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>1.94e-106</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:53:49</td>     <th>  Log-Likelihood:    </th> <td> -4502.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9037.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6949</td>      <th>  BIC:               </th> <td>   9147.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    15</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>const</th> <td>    0.4125</td> <td>    0.055</td> <td>    7.566</td> <td> 0.000</td> <td>    0.306</td> <td>    0.519</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>   -0.0069</td> <td>    0.002</td> <td>   -3.934</td> <td> 0.000</td> <td>   -0.010</td> <td>   -0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0051</td> <td>    0.000</td> <td>   11.670</td> <td> 0.000</td> <td>    0.004</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0129</td> <td>    0.026</td> <td>    0.497</td> <td> 0.619</td> <td>   -0.038</td> <td>    0.064</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0263</td> <td>    0.012</td> <td>    2.279</td> <td> 0.023</td> <td>    0.004</td> <td>    0.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0814</td> <td>    0.025</td> <td>    3.306</td> <td> 0.001</td> <td>    0.033</td> <td>    0.130</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>   -0.0008</td> <td>    0.001</td> <td>   -0.668</td> <td> 0.504</td> <td>   -0.003</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0090</td> <td>    0.007</td> <td>    1.252</td> <td> 0.211</td> <td>   -0.005</td> <td>    0.023</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.1061</td> <td>    0.013</td> <td>   -8.358</td> <td> 0.000</td> <td>   -0.131</td> <td>   -0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0975</td> <td>    0.013</td> <td>   -7.395</td> <td> 0.000</td> <td>   -0.123</td> <td>   -0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   -0.0452</td> <td>    0.012</td> <td>   -3.913</td> <td> 0.000</td> <td>   -0.068</td> <td>   -0.023</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0014</td> <td>    0.013</td> <td>    0.111</td> <td> 0.911</td> <td>   -0.024</td> <td>    0.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0210</td> <td>    0.011</td> <td>   -1.893</td> <td> 0.058</td> <td>   -0.043</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>    0.0079</td> <td>    0.013</td> <td>    0.613</td> <td> 0.540</td> <td>   -0.017</td> <td>    0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td>    0.0645</td> <td>    0.015</td> <td>    4.235</td> <td> 0.000</td> <td>    0.035</td> <td>    0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th>   <td>    0.0029</td> <td>    0.002</td> <td>    1.416</td> <td> 0.157</td> <td>   -0.001</td> <td>    0.007</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>60237.224</td> <th>  Durbin-Watson:     </th> <td>   1.868</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td> 881.234</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.507</td>   <th>  Prob(JB):          </th> <td>4.39e-192</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.584</td>   <th>  Cond. No.          </th> <td>    432.</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:                      y   R-squared:                       0.075\n",
       "Model:                            OLS   Adj. R-squared:                  0.073\n",
       "Method:                 Least Squares   F-statistic:                     37.74\n",
       "Date:                Tue, 26 Feb 2019   Prob (F-statistic):          1.94e-106\n",
       "Time:                        22:53:49   Log-Likelihood:                -4502.7\n",
       "No. Observations:                6965   AIC:                             9037.\n",
       "Df Residuals:                    6949   BIC:                             9147.\n",
       "Df Model:                          15                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.4125      0.055      7.566      0.000       0.306       0.519\n",
       "x1            -0.0069      0.002     -3.934      0.000      -0.010      -0.003\n",
       "x2             0.0051      0.000     11.670      0.000       0.004       0.006\n",
       "x3             0.0129      0.026      0.497      0.619      -0.038       0.064\n",
       "x4             0.0263      0.012      2.279      0.023       0.004       0.049\n",
       "x5             0.0814      0.025      3.306      0.001       0.033       0.130\n",
       "x6            -0.0008      0.001     -0.668      0.504      -0.003       0.002\n",
       "x7             0.0090      0.007      1.252      0.211      -0.005       0.023\n",
       "x8            -0.1061      0.013     -8.358      0.000      -0.131      -0.081\n",
       "x9            -0.0975      0.013     -7.395      0.000      -0.123      -0.072\n",
       "x10           -0.0452      0.012     -3.913      0.000      -0.068      -0.023\n",
       "x11            0.0014      0.013      0.111      0.911      -0.024       0.027\n",
       "x12           -0.0210      0.011     -1.893      0.058      -0.043       0.001\n",
       "x13            0.0079      0.013      0.613      0.540      -0.017       0.033\n",
       "x14            0.0645      0.015      4.235      0.000       0.035       0.094\n",
       "x15            0.0029      0.002      1.416      0.157      -0.001       0.007\n",
       "==============================================================================\n",
       "Omnibus:                    60237.224   Durbin-Watson:                   1.868\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              881.234\n",
       "Skew:                           0.507   Prob(JB):                    4.39e-192\n",
       "Kurtosis:                       1.584   Cond. No.                         432.\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": [
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "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>y</td>        <th>  R-squared:         </th> <td>   0.073</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.071</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   42.09</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 26 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>2.49e-104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:54:49</td>     <th>  Log-Likelihood:    </th> <td> -4511.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9051.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6951</td>      <th>  BIC:               </th> <td>   9147.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</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>const</th> <td>    0.2098</td> <td>    0.027</td> <td>    7.836</td> <td> 0.000</td> <td>    0.157</td> <td>    0.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.2098</td> <td>    0.027</td> <td>    7.836</td> <td> 0.000</td> <td>    0.157</td> <td>    0.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -0.0073</td> <td>    0.002</td> <td>   -4.111</td> <td> 0.000</td> <td>   -0.011</td> <td>   -0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0051</td> <td>    0.000</td> <td>   11.680</td> <td> 0.000</td> <td>    0.004</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0132</td> <td>    0.026</td> <td>    0.510</td> <td> 0.610</td> <td>   -0.038</td> <td>    0.064</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0267</td> <td>    0.012</td> <td>    2.310</td> <td> 0.021</td> <td>    0.004</td> <td>    0.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0810</td> <td>    0.025</td> <td>    3.289</td> <td> 0.001</td> <td>    0.033</td> <td>    0.129</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0012</td> <td>    0.001</td> <td>   -0.970</td> <td> 0.332</td> <td>   -0.004</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0107</td> <td>    0.007</td> <td>    1.488</td> <td> 0.137</td> <td>   -0.003</td> <td>    0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.1112</td> <td>    0.013</td> <td>   -8.799</td> <td> 0.000</td> <td>   -0.136</td> <td>   -0.086</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   -0.1002</td> <td>    0.013</td> <td>   -7.697</td> <td> 0.000</td> <td>   -0.126</td> <td>   -0.075</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0072</td> <td>    0.013</td> <td>    0.558</td> <td> 0.577</td> <td>   -0.018</td> <td>    0.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0207</td> <td>    0.011</td> <td>   -1.867</td> <td> 0.062</td> <td>   -0.043</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>    0.0063</td> <td>    0.013</td> <td>    0.491</td> <td> 0.623</td> <td>   -0.019</td> <td>    0.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td>    0.0659</td> <td>    0.015</td> <td>    4.330</td> <td> 0.000</td> <td>    0.036</td> <td>    0.096</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>57667.080</td> <th>  Durbin-Watson:     </th> <td>   1.863</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td> 888.723</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.509</td>   <th>  Prob(JB):          </th> <td>1.04e-193</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.576</td>   <th>  Cond. No.          </th> <td>5.05e+17</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 5.07e-29. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.073\n",
       "Model:                            OLS   Adj. R-squared:                  0.071\n",
       "Method:                 Least Squares   F-statistic:                     42.09\n",
       "Date:                Tue, 26 Feb 2019   Prob (F-statistic):          2.49e-104\n",
       "Time:                        22:54:49   Log-Likelihood:                -4511.5\n",
       "No. Observations:                6965   AIC:                             9051.\n",
       "Df Residuals:                    6951   BIC:                             9147.\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.2098      0.027      7.836      0.000       0.157       0.262\n",
       "x1             0.2098      0.027      7.836      0.000       0.157       0.262\n",
       "x2            -0.0073      0.002     -4.111      0.000      -0.011      -0.004\n",
       "x3             0.0051      0.000     11.680      0.000       0.004       0.006\n",
       "x4             0.0132      0.026      0.510      0.610      -0.038       0.064\n",
       "x5             0.0267      0.012      2.310      0.021       0.004       0.049\n",
       "x6             0.0810      0.025      3.289      0.001       0.033       0.129\n",
       "x7            -0.0012      0.001     -0.970      0.332      -0.004       0.001\n",
       "x8             0.0107      0.007      1.488      0.137      -0.003       0.025\n",
       "x9            -0.1112      0.013     -8.799      0.000      -0.136      -0.086\n",
       "x10           -0.1002      0.013     -7.697      0.000      -0.126      -0.075\n",
       "x11            0.0072      0.013      0.558      0.577      -0.018       0.032\n",
       "x12           -0.0207      0.011     -1.867      0.062      -0.043       0.001\n",
       "x13            0.0063      0.013      0.491      0.623      -0.019       0.032\n",
       "x14            0.0659      0.015      4.330      0.000       0.036       0.096\n",
       "==============================================================================\n",
       "Omnibus:                    57667.080   Durbin-Watson:                   1.863\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              888.723\n",
       "Skew:                           0.509   Prob(JB):                    1.04e-193\n",
       "Kurtosis:                       1.576   Cond. No.                     5.05e+17\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 5.07e-29. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'residence'\n",
    "# ------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,6,7,8,9,10,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.059</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.058</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   43.99</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 22 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>1.89e-85</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:22:42</td>     <th>  Log-Likelihood:    </th> <td> -4561.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9146.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6954</td>      <th>  BIC:               </th> <td>   9221.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    10</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>const</th> <td>    0.1151</td> <td>    0.012</td> <td>    9.244</td> <td> 0.000</td> <td>    0.091</td> <td>    0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.1151</td> <td>    0.012</td> <td>    9.244</td> <td> 0.000</td> <td>    0.091</td> <td>    0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1151</td> <td>    0.012</td> <td>    9.244</td> <td> 0.000</td> <td>    0.091</td> <td>    0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.1151</td> <td>    0.012</td> <td>    9.244</td> <td> 0.000</td> <td>    0.091</td> <td>    0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   -0.0088</td> <td>    0.002</td> <td>   -4.968</td> <td> 0.000</td> <td>   -0.012</td> <td>   -0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0040</td> <td>    0.000</td> <td>   12.172</td> <td> 0.000</td> <td>    0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0146</td> <td>    0.026</td> <td>    0.557</td> <td> 0.578</td> <td>   -0.037</td> <td>    0.066</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0275</td> <td>    0.012</td> <td>    2.364</td> <td> 0.018</td> <td>    0.005</td> <td>    0.050</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0897</td> <td>    0.025</td> <td>    3.619</td> <td> 0.000</td> <td>    0.041</td> <td>    0.138</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0013</td> <td>    0.001</td> <td>   -1.075</td> <td> 0.282</td> <td>   -0.004</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0248</td> <td>    0.007</td> <td>    3.579</td> <td> 0.000</td> <td>    0.011</td> <td>    0.038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>   -0.1419</td> <td>    0.012</td> <td>  -11.483</td> <td> 0.000</td> <td>   -0.166</td> <td>   -0.118</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>    0.0025</td> <td>    0.013</td> <td>    0.192</td> <td> 0.848</td> <td>   -0.023</td> <td>    0.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>   -0.0184</td> <td>    0.011</td> <td>   -1.646</td> <td> 0.100</td> <td>   -0.040</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>47588.950</td> <th>  Durbin-Watson:     </th> <td>   1.844</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td> 945.524</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.525</td>   <th>  Prob(JB):          </th> <td>4.81e-206</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.532</td>   <th>  Cond. No.          </th> <td>1.34e+18</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 7.24e-30. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.059\n",
       "Model:                            OLS   Adj. R-squared:                  0.058\n",
       "Method:                 Least Squares   F-statistic:                     43.99\n",
       "Date:                Fri, 22 Feb 2019   Prob (F-statistic):           1.89e-85\n",
       "Time:                        19:22:42   Log-Likelihood:                -4561.8\n",
       "No. Observations:                6965   AIC:                             9146.\n",
       "Df Residuals:                    6954   BIC:                             9221.\n",
       "Df Model:                          10                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.1151      0.012      9.244      0.000       0.091       0.139\n",
       "x1             0.1151      0.012      9.244      0.000       0.091       0.139\n",
       "x2             0.1151      0.012      9.244      0.000       0.091       0.139\n",
       "x3             0.1151      0.012      9.244      0.000       0.091       0.139\n",
       "x4            -0.0088      0.002     -4.968      0.000      -0.012      -0.005\n",
       "x5             0.0040      0.000     12.172      0.000       0.003       0.005\n",
       "x6             0.0146      0.026      0.557      0.578      -0.037       0.066\n",
       "x7             0.0275      0.012      2.364      0.018       0.005       0.050\n",
       "x8             0.0897      0.025      3.619      0.000       0.041       0.138\n",
       "x9            -0.0013      0.001     -1.075      0.282      -0.004       0.001\n",
       "x10            0.0248      0.007      3.579      0.000       0.011       0.038\n",
       "x11           -0.1419      0.012    -11.483      0.000      -0.166      -0.118\n",
       "x12            0.0025      0.013      0.192      0.848      -0.023       0.028\n",
       "x13           -0.0184      0.011     -1.646      0.100      -0.040       0.004\n",
       "==============================================================================\n",
       "Omnibus:                    47588.950   Durbin-Watson:                   1.844\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              945.524\n",
       "Skew:                           0.525   Prob(JB):                    4.81e-206\n",
       "Kurtosis:                       1.532   Cond. No.                     1.34e+18\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 7.24e-30. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'breastfeeding'\n",
    "# ------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,6,7,8,9,10,12,14,15]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.060</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   56.25</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 22 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>3.26e-89</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:22:42</td>     <th>  Log-Likelihood:    </th> <td> -4557.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9132.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6956</td>      <th>  BIC:               </th> <td>   9194.</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>const</th> <td>    0.0695</td> <td>    0.007</td> <td>   10.648</td> <td> 0.000</td> <td>    0.057</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0695</td> <td>    0.007</td> <td>   10.648</td> <td> 0.000</td> <td>    0.057</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0695</td> <td>    0.007</td> <td>   10.648</td> <td> 0.000</td> <td>    0.057</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0695</td> <td>    0.007</td> <td>   10.648</td> <td> 0.000</td> <td>    0.057</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0695</td> <td>    0.007</td> <td>   10.648</td> <td> 0.000</td> <td>    0.057</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0039</td> <td>    0.000</td> <td>   11.896</td> <td> 0.000</td> <td>    0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0134</td> <td>    0.026</td> <td>    0.515</td> <td> 0.607</td> <td>   -0.038</td> <td>    0.065</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0270</td> <td>    0.012</td> <td>    2.325</td> <td> 0.020</td> <td>    0.004</td> <td>    0.050</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0850</td> <td>    0.025</td> <td>    3.433</td> <td> 0.001</td> <td>    0.036</td> <td>    0.134</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0014</td> <td>    0.001</td> <td>   -1.113</td> <td> 0.266</td> <td>   -0.004</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   -0.1528</td> <td>    0.012</td> <td>  -13.253</td> <td> 0.000</td> <td>   -0.175</td> <td>   -0.130</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>   -0.0585</td> <td>    0.012</td> <td>   -5.058</td> <td> 0.000</td> <td>   -0.081</td> <td>   -0.036</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>    0.0377</td> <td>    0.012</td> <td>    3.055</td> <td> 0.002</td> <td>    0.014</td> <td>    0.062</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>48063.384</td> <th>  Durbin-Watson:     </th> <td>   1.865</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td> 938.430</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.521</td>   <th>  Prob(JB):          </th> <td>1.67e-204</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.535</td>   <th>  Cond. No.          </th> <td>1.51e+18</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 4.77e-30. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.061\n",
       "Model:                            OLS   Adj. R-squared:                  0.060\n",
       "Method:                 Least Squares   F-statistic:                     56.25\n",
       "Date:                Fri, 22 Feb 2019   Prob (F-statistic):           3.26e-89\n",
       "Time:                        19:22:42   Log-Likelihood:                -4557.1\n",
       "No. Observations:                6965   AIC:                             9132.\n",
       "Df Residuals:                    6956   BIC:                             9194.\n",
       "Df Model:                           8                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0695      0.007     10.648      0.000       0.057       0.082\n",
       "x1             0.0695      0.007     10.648      0.000       0.057       0.082\n",
       "x2             0.0695      0.007     10.648      0.000       0.057       0.082\n",
       "x3             0.0695      0.007     10.648      0.000       0.057       0.082\n",
       "x4             0.0695      0.007     10.648      0.000       0.057       0.082\n",
       "x5             0.0039      0.000     11.896      0.000       0.003       0.005\n",
       "x6             0.0134      0.026      0.515      0.607      -0.038       0.065\n",
       "x7             0.0270      0.012      2.325      0.020       0.004       0.050\n",
       "x8             0.0850      0.025      3.433      0.001       0.036       0.134\n",
       "x9            -0.0014      0.001     -1.113      0.266      -0.004       0.001\n",
       "x10           -0.1528      0.012    -13.253      0.000      -0.175      -0.130\n",
       "x11           -0.0585      0.012     -5.058      0.000      -0.081      -0.036\n",
       "x12            0.0377      0.012      3.055      0.002       0.014       0.062\n",
       "==============================================================================\n",
       "Omnibus:                    48063.384   Durbin-Watson:                   1.865\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              938.430\n",
       "Skew:                           0.521   Prob(JB):                    1.67e-204\n",
       "Kurtosis:                       1.535   Cond. No.                     1.51e+18\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 4.77e-30. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'ari'\n",
    "# ------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,6,7,8,9,10,12,14,15]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "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>y</td>        <th>  R-squared:         </th> <td>   0.038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   46.14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 22 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>1.01e-55</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:22:43</td>     <th>  Log-Likelihood:    </th> <td> -4639.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9293.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6958</td>      <th>  BIC:               </th> <td>   9341.</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>const</th> <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0650</td> <td>    0.007</td> <td>    9.882</td> <td> 0.000</td> <td>    0.052</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>   -0.0126</td> <td>    0.002</td> <td>   -7.152</td> <td> 0.000</td> <td>   -0.016</td> <td>   -0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0040</td> <td>    0.000</td> <td>   12.105</td> <td> 0.000</td> <td>    0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0184</td> <td>    0.026</td> <td>    0.698</td> <td> 0.486</td> <td>   -0.033</td> <td>    0.070</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>    0.0279</td> <td>    0.012</td> <td>    2.377</td> <td> 0.017</td> <td>    0.005</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.1001</td> <td>    0.025</td> <td>    3.999</td> <td> 0.000</td> <td>    0.051</td> <td>    0.149</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0340</td> <td>    0.007</td> <td>    4.869</td> <td> 0.000</td> <td>    0.020</td> <td>    0.048</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>38404.344</td> <th>  Durbin-Watson:     </th> <td>   1.824</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1031.425</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.537</td>   <th>  Prob(JB):          </th> <td>1.07e-224</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.450</td>   <th>  Cond. No.          </th> <td>3.01e+19</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.11e-32. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.038\n",
       "Model:                            OLS   Adj. R-squared:                  0.037\n",
       "Method:                 Least Squares   F-statistic:                     46.14\n",
       "Date:                Fri, 22 Feb 2019   Prob (F-statistic):           1.01e-55\n",
       "Time:                        19:22:43   Log-Likelihood:                -4639.5\n",
       "No. Observations:                6965   AIC:                             9293.\n",
       "Df Residuals:                    6958   BIC:                             9341.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x1             0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x2             0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x3             0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x4             0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x5             0.0650      0.007      9.882      0.000       0.052       0.078\n",
       "x6            -0.0126      0.002     -7.152      0.000      -0.016      -0.009\n",
       "x7             0.0040      0.000     12.105      0.000       0.003       0.005\n",
       "x8             0.0184      0.026      0.698      0.486      -0.033       0.070\n",
       "x9             0.0279      0.012      2.377      0.017       0.005       0.051\n",
       "x10            0.1001      0.025      3.999      0.000       0.051       0.149\n",
       "x11            0.0340      0.007      4.869      0.000       0.020       0.048\n",
       "==============================================================================\n",
       "Omnibus:                    38404.344   Durbin-Watson:                   1.824\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1031.425\n",
       "Skew:                           0.537   Prob(JB):                    1.07e-224\n",
       "Kurtosis:                       1.450   Cond. No.                     3.01e+19\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 1.11e-32. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'currently working mother'\n",
    "# ----------------------------------                                \n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,6,7,8,9,10,12]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   44.75</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 22 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>3.69e-37</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:22:43</td>     <th>  Log-Likelihood:    </th> <td> -4687.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   9384.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6960</td>      <th>  BIC:               </th> <td>   9418.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</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>const</th> <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0313</td> <td>    0.002</td> <td>   17.761</td> <td> 0.000</td> <td>    0.028</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0042</td> <td>    0.000</td> <td>   12.649</td> <td> 0.000</td> <td>    0.004</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0200</td> <td>    0.027</td> <td>    0.754</td> <td> 0.451</td> <td>   -0.032</td> <td>    0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>    0.0276</td> <td>    0.012</td> <td>    2.338</td> <td> 0.019</td> <td>    0.004</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.1051</td> <td>    0.025</td> <td>    4.171</td> <td> 0.000</td> <td>    0.056</td> <td>    0.154</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>35567.407</td> <th>  Durbin-Watson:     </th> <td>   1.802</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1083.966</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.548</td>   <th>  Prob(JB):          </th> <td>4.17e-236</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 1.408</td>   <th>  Cond. No.          </th> <td>5.62e+31</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 2.58e-57. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.025\n",
       "Model:                            OLS   Adj. R-squared:                  0.025\n",
       "Method:                 Least Squares   F-statistic:                     44.75\n",
       "Date:                Fri, 22 Feb 2019   Prob (F-statistic):           3.69e-37\n",
       "Time:                        19:22:43   Log-Likelihood:                -4687.0\n",
       "No. Observations:                6965   AIC:                             9384.\n",
       "Df Residuals:                    6960   BIC:                             9418.\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x1             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x2             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x3             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x4             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x5             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x6             0.0313      0.002     17.761      0.000       0.028       0.035\n",
       "x7             0.0042      0.000     12.649      0.000       0.004       0.005\n",
       "x8             0.0200      0.027      0.754      0.451      -0.032       0.072\n",
       "x9             0.0276      0.012      2.338      0.019       0.004       0.051\n",
       "x10            0.1051      0.025      4.171      0.000       0.056       0.154\n",
       "==============================================================================\n",
       "Omnibus:                    35567.407   Durbin-Watson:                   1.802\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1083.966\n",
       "Skew:                           0.548   Prob(JB):                    4.17e-236\n",
       "Kurtosis:                       1.408   Cond. No.                     5.62e+31\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 2.58e-57. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'mother eduction'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,6,8,9,10,11]]\n",
    "ols = sm.OLS(endog = y_stun, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}