1.8_most_important_feature_wasting.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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.fillna(df[['fever','Mother_BMI','diar','Father_Edu','currently_working_mot']].mean())"
   ]
  },
  {
   "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>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",
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       "      <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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as sm"
   ]
  },
  {
   "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>   0.010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>3.84e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:04:23</td>     <th>  Log-Likelihood:    </th> <td> -2510.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5054.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6949</td>      <th>  BIC:               </th> <td>   5163.</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>    0.2326</td> <td>    0.041</td> <td>    5.678</td> <td> 0.000</td> <td>    0.152</td> <td>    0.313</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>   -0.0020</td> <td>    0.001</td> <td>   -1.485</td> <td> 0.138</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -0.0009</td> <td>    0.000</td> <td>   -2.630</td> <td> 0.009</td> <td>   -0.002</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0087</td> <td>    0.019</td> <td>   -0.447</td> <td> 0.655</td> <td>   -0.047</td> <td>    0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0023</td> <td>    0.009</td> <td>    0.260</td> <td> 0.795</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0477</td> <td>    0.018</td> <td>    2.581</td> <td> 0.010</td> <td>    0.011</td> <td>    0.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 2.738e-05</td> <td>    0.001</td> <td>    0.030</td> <td> 0.976</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0045</td> <td>    0.005</td> <td>   -0.831</td> <td> 0.406</td> <td>   -0.015</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0138</td> <td>    0.010</td> <td>   -1.452</td> <td> 0.147</td> <td>   -0.033</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0372</td> <td>    0.010</td> <td>   -3.759</td> <td> 0.000</td> <td>   -0.057</td> <td>   -0.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0015</td> <td>    0.009</td> <td>    0.173</td> <td> 0.863</td> <td>   -0.016</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0207</td> <td>    0.010</td> <td>    2.135</td> <td> 0.033</td> <td>    0.002</td> <td>    0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0139</td> <td>    0.008</td> <td>   -1.667</td> <td> 0.096</td> <td>   -0.030</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>    0.0049</td> <td>    0.010</td> <td>    0.508</td> <td> 0.611</td> <td>   -0.014</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td>    0.0015</td> <td>    0.011</td> <td>    0.132</td> <td> 0.895</td> <td>   -0.021</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th>   <td>   -0.0007</td> <td>    0.002</td> <td>   -0.488</td> <td> 0.626</td> <td>   -0.004</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2446.638</td> <th>  Durbin-Watson:     </th> <td>   1.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6143.979</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.025</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.184</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:                       0.010\n",
       "Model:                            OLS   Adj. R-squared:                  0.008\n",
       "Method:                 Least Squares   F-statistic:                     4.711\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           3.84e-09\n",
       "Time:                        20:04:23   Log-Likelihood:                -2510.8\n",
       "No. Observations:                6965   AIC:                             5054.\n",
       "Df Residuals:                    6949   BIC:                             5163.\n",
       "Df Model:                          15                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.2326      0.041      5.678      0.000       0.152       0.313\n",
       "x1            -0.0020      0.001     -1.485      0.138      -0.005       0.001\n",
       "x2            -0.0009      0.000     -2.630      0.009      -0.002      -0.000\n",
       "x3            -0.0087      0.019     -0.447      0.655      -0.047       0.029\n",
       "x4             0.0023      0.009      0.260      0.795      -0.015       0.019\n",
       "x5             0.0477      0.018      2.581      0.010       0.011       0.084\n",
       "x6          2.738e-05      0.001      0.030      0.976      -0.002       0.002\n",
       "x7            -0.0045      0.005     -0.831      0.406      -0.015       0.006\n",
       "x8            -0.0138      0.010     -1.452      0.147      -0.033       0.005\n",
       "x9            -0.0372      0.010     -3.759      0.000      -0.057      -0.018\n",
       "x10            0.0015      0.009      0.173      0.863      -0.016       0.019\n",
       "x11            0.0207      0.010      2.135      0.033       0.002       0.040\n",
       "x12           -0.0139      0.008     -1.667      0.096      -0.030       0.002\n",
       "x13            0.0049      0.010      0.508      0.611      -0.014       0.024\n",
       "x14            0.0015      0.011      0.132      0.895      -0.021       0.024\n",
       "x15           -0.0007      0.002     -0.488      0.626      -0.004       0.002\n",
       "==============================================================================\n",
       "Omnibus:                     2446.638   Durbin-Watson:                   1.957\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6143.979\n",
       "Skew:                           2.025   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.184   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_wast, 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>   0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4.898</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>1.27e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:05:39</td>     <th>  Log-Likelihood:    </th> <td> -2514.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5056.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6951</td>      <th>  BIC:               </th> <td>   5152.</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>    0.1174</td> <td>    0.020</td> <td>    5.845</td> <td> 0.000</td> <td>    0.078</td> <td>    0.157</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.1174</td> <td>    0.020</td> <td>    5.845</td> <td> 0.000</td> <td>    0.078</td> <td>    0.157</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -0.0020</td> <td>    0.001</td> <td>   -1.527</td> <td> 0.127</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0009</td> <td>    0.000</td> <td>   -2.738</td> <td> 0.006</td> <td>   -0.002</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   -0.0091</td> <td>    0.019</td> <td>   -0.469</td> <td> 0.639</td> <td>   -0.047</td> <td>    0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0024</td> <td>    0.009</td> <td>    0.282</td> <td> 0.778</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 4.278e-05</td> <td>    0.001</td> <td>    0.046</td> <td> 0.963</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0050</td> <td>    0.005</td> <td>   -0.931</td> <td> 0.352</td> <td>   -0.016</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0148</td> <td>    0.010</td> <td>   -1.555</td> <td> 0.120</td> <td>   -0.033</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0381</td> <td>    0.010</td> <td>   -3.885</td> <td> 0.000</td> <td>   -0.057</td> <td>   -0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0016</td> <td>    0.009</td> <td>    0.180</td> <td> 0.857</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0207</td> <td>    0.010</td> <td>    2.140</td> <td> 0.032</td> <td>    0.002</td> <td>    0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0144</td> <td>    0.008</td> <td>   -1.729</td> <td> 0.084</td> <td>   -0.031</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>    0.0054</td> <td>    0.010</td> <td>    0.553</td> <td> 0.580</td> <td>   -0.014</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td>    0.0012</td> <td>    0.011</td> <td>    0.102</td> <td> 0.919</td> <td>   -0.021</td> <td>    0.024</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2450.228</td> <th>  Durbin-Watson:     </th> <td>   1.958</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6159.755</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.028</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.186</td>  <th>  Cond. No.          </th> <td>1.38e+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 6.81e-28. 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:                       0.009\n",
       "Model:                            OLS   Adj. R-squared:                  0.007\n",
       "Method:                 Least Squares   F-statistic:                     4.898\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           1.27e-08\n",
       "Time:                        20:05:39   Log-Likelihood:                -2514.2\n",
       "No. Observations:                6965   AIC:                             5056.\n",
       "Df Residuals:                    6951   BIC:                             5152.\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.1174      0.020      5.845      0.000       0.078       0.157\n",
       "x1             0.1174      0.020      5.845      0.000       0.078       0.157\n",
       "x2            -0.0020      0.001     -1.527      0.127      -0.005       0.001\n",
       "x3            -0.0009      0.000     -2.738      0.006      -0.002      -0.000\n",
       "x4            -0.0091      0.019     -0.469      0.639      -0.047       0.029\n",
       "x5             0.0024      0.009      0.282      0.778      -0.015       0.019\n",
       "x6          4.278e-05      0.001      0.046      0.963      -0.002       0.002\n",
       "x7            -0.0050      0.005     -0.931      0.352      -0.016       0.006\n",
       "x8            -0.0148      0.010     -1.555      0.120      -0.033       0.004\n",
       "x9            -0.0381      0.010     -3.885      0.000      -0.057      -0.019\n",
       "x10            0.0016      0.009      0.180      0.857      -0.015       0.019\n",
       "x11            0.0207      0.010      2.140      0.032       0.002       0.040\n",
       "x12           -0.0144      0.008     -1.729      0.084      -0.031       0.002\n",
       "x13            0.0054      0.010      0.553      0.580      -0.014       0.024\n",
       "x14            0.0012      0.011      0.102      0.919      -0.021       0.024\n",
       "==============================================================================\n",
       "Omnibus:                     2450.228   Durbin-Watson:                   1.958\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6159.755\n",
       "Skew:                           2.028   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.186   Cond. No.                     1.38e+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 6.81e-28. 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 'mother bmi'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,7,8,9,10,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>   0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.782</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>2.19e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:07:10</td>     <th>  Log-Likelihood:    </th> <td> -2514.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5053.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6953</td>      <th>  BIC:               </th> <td>   5135.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    11</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>    0.0791</td> <td>    0.012</td> <td>    6.388</td> <td> 0.000</td> <td>    0.055</td> <td>    0.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0791</td> <td>    0.012</td> <td>    6.388</td> <td> 0.000</td> <td>    0.055</td> <td>    0.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0791</td> <td>    0.012</td> <td>    6.388</td> <td> 0.000</td> <td>    0.055</td> <td>    0.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0020</td> <td>    0.001</td> <td>   -1.532</td> <td> 0.126</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   -0.0009</td> <td>    0.000</td> <td>   -3.755</td> <td> 0.000</td> <td>   -0.001</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>   -0.0087</td> <td>    0.019</td> <td>   -0.449</td> <td> 0.654</td> <td>   -0.047</td> <td>    0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 4.044e-05</td> <td>    0.001</td> <td>    0.044</td> <td> 0.965</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0051</td> <td>    0.005</td> <td>   -0.943</td> <td> 0.346</td> <td>   -0.016</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0149</td> <td>    0.010</td> <td>   -1.561</td> <td> 0.119</td> <td>   -0.034</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0382</td> <td>    0.010</td> <td>   -3.895</td> <td> 0.000</td> <td>   -0.057</td> <td>   -0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0015</td> <td>    0.009</td> <td>    0.177</td> <td> 0.860</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0207</td> <td>    0.010</td> <td>    2.146</td> <td> 0.032</td> <td>    0.002</td> <td>    0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0144</td> <td>    0.008</td> <td>   -1.728</td> <td> 0.084</td> <td>   -0.031</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>    0.0054</td> <td>    0.010</td> <td>    0.557</td> <td> 0.578</td> <td>   -0.014</td> <td>    0.024</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2450.299</td> <th>  Durbin-Watson:     </th> <td>   1.958</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6160.091</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.028</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.186</td>  <th>  Cond. No.          </th> <td>3.39e+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 1.12e-28. 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:                       0.009\n",
       "Model:                            OLS   Adj. R-squared:                  0.007\n",
       "Method:                 Least Squares   F-statistic:                     5.782\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           2.19e-09\n",
       "Time:                        20:07:10   Log-Likelihood:                -2514.3\n",
       "No. Observations:                6965   AIC:                             5053.\n",
       "Df Residuals:                    6953   BIC:                             5135.\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0791      0.012      6.388      0.000       0.055       0.103\n",
       "x1             0.0791      0.012      6.388      0.000       0.055       0.103\n",
       "x2             0.0791      0.012      6.388      0.000       0.055       0.103\n",
       "x3            -0.0020      0.001     -1.532      0.126      -0.005       0.001\n",
       "x4            -0.0009      0.000     -3.755      0.000      -0.001      -0.000\n",
       "x5            -0.0087      0.019     -0.449      0.654      -0.047       0.029\n",
       "x6          4.044e-05      0.001      0.044      0.965      -0.002       0.002\n",
       "x7            -0.0051      0.005     -0.943      0.346      -0.016       0.005\n",
       "x8            -0.0149      0.010     -1.561      0.119      -0.034       0.004\n",
       "x9            -0.0382      0.010     -3.895      0.000      -0.057      -0.019\n",
       "x10            0.0015      0.009      0.177      0.860      -0.015       0.019\n",
       "x11            0.0207      0.010      2.146      0.032       0.002       0.040\n",
       "x12           -0.0144      0.008     -1.728      0.084      -0.031       0.002\n",
       "x13            0.0054      0.010      0.557      0.578      -0.014       0.024\n",
       "==============================================================================\n",
       "Omnibus:                     2450.299   Durbin-Watson:                   1.958\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6160.091\n",
       "Skew:                           2.028   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.186   Cond. No.                     3.39e+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 1.12e-28. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'birth_order'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,8,9,10,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>3.78e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:08:12</td>     <th>  Log-Likelihood:    </th> <td> -2514.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5049.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6955</td>      <th>  BIC:               </th> <td>   5118.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     9</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>    0.0594</td> <td>    0.009</td> <td>    6.409</td> <td> 0.000</td> <td>    0.041</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0594</td> <td>    0.009</td> <td>    6.409</td> <td> 0.000</td> <td>    0.041</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0594</td> <td>    0.009</td> <td>    6.409</td> <td> 0.000</td> <td>    0.041</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0594</td> <td>    0.009</td> <td>    6.409</td> <td> 0.000</td> <td>    0.041</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   -0.0020</td> <td>    0.001</td> <td>   -1.539</td> <td> 0.124</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>   -0.0009</td> <td>    0.000</td> <td>   -3.724</td> <td> 0.000</td> <td>   -0.001</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 3.916e-05</td> <td>    0.001</td> <td>    0.042</td> <td> 0.966</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0049</td> <td>    0.005</td> <td>   -0.918</td> <td> 0.359</td> <td>   -0.015</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0149</td> <td>    0.010</td> <td>   -1.568</td> <td> 0.117</td> <td>   -0.034</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0383</td> <td>    0.010</td> <td>   -3.912</td> <td> 0.000</td> <td>   -0.058</td> <td>   -0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0015</td> <td>    0.009</td> <td>    0.177</td> <td> 0.859</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0209</td> <td>    0.010</td> <td>    2.160</td> <td> 0.031</td> <td>    0.002</td> <td>    0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>   -0.0144</td> <td>    0.008</td> <td>   -1.724</td> <td> 0.085</td> <td>   -0.031</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2450.523</td> <th>  Durbin-Watson:     </th> <td>   1.958</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6161.059</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.028</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.186</td>  <th>  Cond. No.          </th> <td>2.10e+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 2.94e-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:                       0.009\n",
       "Model:                            OLS   Adj. R-squared:                  0.008\n",
       "Method:                 Least Squares   F-statistic:                     7.011\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           3.78e-10\n",
       "Time:                        20:08:12   Log-Likelihood:                -2514.5\n",
       "No. Observations:                6965   AIC:                             5049.\n",
       "Df Residuals:                    6955   BIC:                             5118.\n",
       "Df Model:                           9                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0594      0.009      6.409      0.000       0.041       0.078\n",
       "x1             0.0594      0.009      6.409      0.000       0.041       0.078\n",
       "x2             0.0594      0.009      6.409      0.000       0.041       0.078\n",
       "x3             0.0594      0.009      6.409      0.000       0.041       0.078\n",
       "x4            -0.0020      0.001     -1.539      0.124      -0.005       0.001\n",
       "x5            -0.0009      0.000     -3.724      0.000      -0.001      -0.000\n",
       "x6          3.916e-05      0.001      0.042      0.966      -0.002       0.002\n",
       "x7            -0.0049      0.005     -0.918      0.359      -0.015       0.006\n",
       "x8            -0.0149      0.010     -1.568      0.117      -0.034       0.004\n",
       "x9            -0.0383      0.010     -3.912      0.000      -0.058      -0.019\n",
       "x10            0.0015      0.009      0.177      0.859      -0.015       0.019\n",
       "x11            0.0209      0.010      2.160      0.031       0.002       0.040\n",
       "x12           -0.0144      0.008     -1.724      0.085      -0.031       0.002\n",
       "==============================================================================\n",
       "Omnibus:                     2450.523   Durbin-Watson:                   1.958\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6161.059\n",
       "Skew:                           2.028   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.186   Cond. No.                     2.10e+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 2.94e-30. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'mother_edu'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,9,10,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>   0.007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   6.578</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>9.10e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:09:21</td>     <th>  Log-Likelihood:    </th> <td> -2523.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5062.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6957</td>      <th>  BIC:               </th> <td>   5117.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     7</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>    0.0408</td> <td>    0.007</td> <td>    5.630</td> <td> 0.000</td> <td>    0.027</td> <td>    0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0408</td> <td>    0.007</td> <td>    5.630</td> <td> 0.000</td> <td>    0.027</td> <td>    0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0408</td> <td>    0.007</td> <td>    5.630</td> <td> 0.000</td> <td>    0.027</td> <td>    0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0408</td> <td>    0.007</td> <td>    5.630</td> <td> 0.000</td> <td>    0.027</td> <td>    0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0408</td> <td>    0.007</td> <td>    5.630</td> <td> 0.000</td> <td>    0.027</td> <td>    0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>   -0.0020</td> <td>    0.001</td> <td>   -1.472</td> <td> 0.141</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 2.617e-06</td> <td>    0.001</td> <td>    0.003</td> <td> 0.998</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0058</td> <td>    0.005</td> <td>   -1.093</td> <td> 0.275</td> <td>   -0.016</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0135</td> <td>    0.010</td> <td>   -1.414</td> <td> 0.157</td> <td>   -0.032</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0388</td> <td>    0.010</td> <td>   -3.953</td> <td> 0.000</td> <td>   -0.058</td> <td>   -0.020</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>    0.0020</td> <td>    0.009</td> <td>    0.227</td> <td> 0.820</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>    0.0212</td> <td>    0.010</td> <td>    2.190</td> <td> 0.029</td> <td>    0.002</td> <td>    0.040</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2459.534</td> <th>  Durbin-Watson:     </th> <td>   1.960</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6201.550</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.035</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.193</td>  <th>  Cond. No.          </th> <td>2.76e+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 7.59e-31. 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:                       0.007\n",
       "Model:                            OLS   Adj. R-squared:                  0.006\n",
       "Method:                 Least Squares   F-statistic:                     6.578\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           9.10e-08\n",
       "Time:                        20:09:21   Log-Likelihood:                -2523.0\n",
       "No. Observations:                6965   AIC:                             5062.\n",
       "Df Residuals:                    6957   BIC:                             5117.\n",
       "Df Model:                           7                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0408      0.007      5.630      0.000       0.027       0.055\n",
       "x1             0.0408      0.007      5.630      0.000       0.027       0.055\n",
       "x2             0.0408      0.007      5.630      0.000       0.027       0.055\n",
       "x3             0.0408      0.007      5.630      0.000       0.027       0.055\n",
       "x4             0.0408      0.007      5.630      0.000       0.027       0.055\n",
       "x5            -0.0020      0.001     -1.472      0.141      -0.005       0.001\n",
       "x6          2.617e-06      0.001      0.003      0.998      -0.002       0.002\n",
       "x7            -0.0058      0.005     -1.093      0.275      -0.016       0.005\n",
       "x8            -0.0135      0.010     -1.414      0.157      -0.032       0.005\n",
       "x9            -0.0388      0.010     -3.953      0.000      -0.058      -0.020\n",
       "x10            0.0020      0.009      0.227      0.820      -0.015       0.019\n",
       "x11            0.0212      0.010      2.190      0.029       0.002       0.040\n",
       "==============================================================================\n",
       "Omnibus:                     2459.534   Durbin-Watson:                   1.960\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6201.550\n",
       "Skew:                           2.035   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.193   Cond. No.                     2.76e+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 7.59e-31. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'walth_index'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,10,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>   0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7.748</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>2.81e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:10:28</td>     <th>  Log-Likelihood:    </th> <td> -2526.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5065.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6959</td>      <th>  BIC:               </th> <td>   5106.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</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>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0317</td> <td>    0.004</td> <td>    8.007</td> <td> 0.000</td> <td>    0.024</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>   -0.0002</td> <td>    0.001</td> <td>   -0.253</td> <td> 0.800</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0039</td> <td>    0.005</td> <td>   -0.746</td> <td> 0.456</td> <td>   -0.014</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0135</td> <td>    0.009</td> <td>   -1.420</td> <td> 0.156</td> <td>   -0.032</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0469</td> <td>    0.009</td> <td>   -5.033</td> <td> 0.000</td> <td>   -0.065</td> <td>   -0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   -0.0003</td> <td>    0.009</td> <td>   -0.029</td> <td> 0.977</td> <td>   -0.017</td> <td>    0.017</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2464.011</td> <th>  Durbin-Watson:     </th> <td>   1.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6222.315</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.038</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.198</td>  <th>  Cond. No.          </th> <td>3.37e+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 3.08e-31. 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:                       0.006\n",
       "Model:                            OLS   Adj. R-squared:                  0.005\n",
       "Method:                 Least Squares   F-statistic:                     7.748\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           2.81e-07\n",
       "Time:                        20:10:28   Log-Likelihood:                -2526.7\n",
       "No. Observations:                6965   AIC:                             5065.\n",
       "Df Residuals:                    6959   BIC:                             5106.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x1             0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x2             0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x3             0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x4             0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x5             0.0317      0.004      8.007      0.000       0.024       0.039\n",
       "x6            -0.0002      0.001     -0.253      0.800      -0.002       0.002\n",
       "x7            -0.0039      0.005     -0.746      0.456      -0.014       0.006\n",
       "x8            -0.0135      0.009     -1.420      0.156      -0.032       0.005\n",
       "x9            -0.0469      0.009     -5.033      0.000      -0.065      -0.029\n",
       "x10           -0.0003      0.009     -0.029      0.977      -0.017       0.017\n",
       "==============================================================================\n",
       "Omnibus:                     2464.011   Durbin-Watson:                   1.957\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6222.315\n",
       "Skew:                           2.038   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.198   Cond. No.                     3.37e+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 3.08e-31. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'father_edu'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,11,12,13,14,15]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>   0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.449</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th> <td>0.000223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:11:24</td>     <th>  Log-Likelihood:    </th> <td> -2535.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5080.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6960</td>      <th>  BIC:               </th> <td>   5114.</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>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0295</td> <td>    0.004</td> <td>    7.469</td> <td> 0.000</td> <td>    0.022</td> <td>    0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0553</td> <td>    0.018</td> <td>    2.992</td> <td> 0.003</td> <td>    0.019</td> <td>    0.092</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0008</td> <td>    0.001</td> <td>   -0.851</td> <td> 0.395</td> <td>   -0.003</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>   -0.0026</td> <td>    0.005</td> <td>   -0.502</td> <td> 0.616</td> <td>   -0.013</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0288</td> <td>    0.009</td> <td>   -3.242</td> <td> 0.001</td> <td>   -0.046</td> <td>   -0.011</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2475.293</td> <th>  Durbin-Watson:     </th> <td>   1.951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6275.113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.046</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.211</td>  <th>  Cond. No.          </th> <td>1.24e+20</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 2.27e-34. 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:                       0.003\n",
       "Model:                            OLS   Adj. R-squared:                  0.003\n",
       "Method:                 Least Squares   F-statistic:                     5.449\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):           0.000223\n",
       "Time:                        20:11:24   Log-Likelihood:                -2535.1\n",
       "No. Observations:                6965   AIC:                             5080.\n",
       "Df Residuals:                    6960   BIC:                             5114.\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x1             0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x2             0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x3             0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x4             0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x5             0.0295      0.004      7.469      0.000       0.022       0.037\n",
       "x6             0.0553      0.018      2.992      0.003       0.019       0.092\n",
       "x7            -0.0008      0.001     -0.851      0.395      -0.003       0.001\n",
       "x8            -0.0026      0.005     -0.502      0.616      -0.013       0.008\n",
       "x9            -0.0288      0.009     -3.242      0.001      -0.046      -0.011\n",
       "==============================================================================\n",
       "Omnibus:                     2475.293   Durbin-Watson:                   1.951\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6275.113\n",
       "Skew:                           2.046   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.211   Cond. No.                     1.24e+20\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 2.27e-34. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'householding'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,11,12,13,14]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3.426</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th>  <td>0.0164</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:12:30</td>     <th>  Log-Likelihood:    </th> <td> -2540.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5090.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6961</td>      <th>  BIC:               </th> <td>   5117.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0221</td> <td>    0.002</td> <td>   12.004</td> <td> 0.000</td> <td>    0.018</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0023</td> <td>    0.009</td> <td>    0.263</td> <td> 0.793</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>    0.0582</td> <td>    0.018</td> <td>    3.151</td> <td> 0.002</td> <td>    0.022</td> <td>    0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0027</td> <td>    0.005</td> <td>    0.530</td> <td> 0.596</td> <td>   -0.007</td> <td>    0.012</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2482.426</td> <th>  Durbin-Watson:     </th> <td>   1.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6308.282</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.051</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.218</td>  <th>  Cond. No.          </th> <td>1.27e+32</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 4.4e-60. 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:                       0.001\n",
       "Model:                            OLS   Adj. R-squared:                  0.001\n",
       "Method:                 Least Squares   F-statistic:                     3.426\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):             0.0164\n",
       "Time:                        20:12:30   Log-Likelihood:                -2540.9\n",
       "No. Observations:                6965   AIC:                             5090.\n",
       "Df Residuals:                    6961   BIC:                             5117.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x1             0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x2             0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x3             0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x4             0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x5             0.0221      0.002     12.004      0.000       0.018       0.026\n",
       "x6             0.0023      0.009      0.263      0.793      -0.015       0.019\n",
       "x7             0.0582      0.018      3.151      0.002       0.022       0.094\n",
       "x8             0.0027      0.005      0.530      0.596      -0.007       0.012\n",
       "==============================================================================\n",
       "Omnibus:                     2482.426   Durbin-Watson:                   1.950\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6308.282\n",
       "Skew:                           2.051   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.218   Cond. No.                     1.27e+32\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 4.4e-60. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'mother_working'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,11,12,14]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>   0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>  -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>  0.5938</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th>  <td> 0.552</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:13:25</td>     <th>  Log-Likelihood:    </th> <td> -2545.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5097.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6962</td>      <th>  BIC:               </th> <td>   5117.</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>const</th> <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0270</td> <td>    0.003</td> <td>    7.868</td> <td> 0.000</td> <td>    0.020</td> <td>    0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0023</td> <td>    0.009</td> <td>    0.265</td> <td> 0.791</td> <td>   -0.015</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.0010</td> <td>    0.001</td> <td>   -1.053</td> <td> 0.292</td> <td>   -0.003</td> <td>    0.001</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2487.158</td> <th>  Durbin-Watson:     </th> <td>   1.951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6329.459</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.054</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.221</td>  <th>  Cond. No.          </th> <td>8.79e+34</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 4.49e-64. 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:                       0.000\n",
       "Model:                            OLS   Adj. R-squared:                 -0.000\n",
       "Method:                 Least Squares   F-statistic:                    0.5938\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):              0.552\n",
       "Time:                        20:13:25   Log-Likelihood:                -2545.4\n",
       "No. Observations:                6965   AIC:                             5097.\n",
       "Df Residuals:                    6962   BIC:                             5117.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x1             0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x2             0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x3             0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x4             0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x5             0.0270      0.003      7.868      0.000       0.020       0.034\n",
       "x6             0.0023      0.009      0.265      0.791      -0.015       0.019\n",
       "x7            -0.0010      0.001     -1.053      0.292      -0.003       0.001\n",
       "==============================================================================\n",
       "Omnibus:                     2487.158   Durbin-Watson:                   1.951\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6329.459\n",
       "Skew:                           2.054   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.221   Cond. No.                     8.79e+34\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 4.49e-64. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "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[:, [0,1,2,3,4,5,12,14]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   9.932</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 27 Feb 2019</td> <th>  Prob (F-statistic):</th>  <td>0.00163</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:14:16</td>     <th>  Log-Likelihood:    </th> <td> -2541.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6965</td>      <th>  AIC:               </th> <td>   5086.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6963</td>      <th>  BIC:               </th> <td>   5100.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>    0.0231</td> <td>    0.001</td> <td>   32.270</td> <td> 0.000</td> <td>    0.022</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0582</td> <td>    0.018</td> <td>    3.152</td> <td> 0.002</td> <td>    0.022</td> <td>    0.094</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2482.702</td> <th>  Durbin-Watson:     </th> <td>   1.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6309.604</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.051</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 5.218</td>  <th>  Cond. No.          </th> <td>6.41e+49</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 1.02e-95. 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:                       0.001\n",
       "Model:                            OLS   Adj. R-squared:                  0.001\n",
       "Method:                 Least Squares   F-statistic:                     9.932\n",
       "Date:                Wed, 27 Feb 2019   Prob (F-statistic):            0.00163\n",
       "Time:                        20:14:16   Log-Likelihood:                -2541.0\n",
       "No. Observations:                6965   AIC:                             5086.\n",
       "Df Residuals:                    6963   BIC:                             5100.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x1             0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x2             0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x3             0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x4             0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x5             0.0231      0.001     32.270      0.000       0.022       0.024\n",
       "x6             0.0582      0.018      3.152      0.002       0.022       0.094\n",
       "==============================================================================\n",
       "Omnibus:                     2482.702   Durbin-Watson:                   1.950\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6309.604\n",
       "Skew:                           2.051   Prob(JB):                         0.00\n",
       "Kurtosis:                       5.218   Cond. No.                     6.41e+49\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 1.02e-95. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eliminate 'sex'\n",
    "# ---------------------------\n",
    "\n",
    "X = np.append( arr = np.ones( (6965,1)).astype(int), values = X, axis = 1)\n",
    "x_opt = X[:, [0,1,2,3,4,5,14]]\n",
    "ols = sm.OLS(endog = y_wast, exog = x_opt).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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