indep_regression.ipynb

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       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>z</td>        <th>  R-squared:         </th> <td>   0.672</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.671</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1021.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 20 Aug 2016</td> <th>  Prob (F-statistic):</th> <td>3.69e-242</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:42:40</td>     <th>  Log-Likelihood:    </th> <td> -1405.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   2815.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   998</td>      <th>  BIC:               </th> <td>   2825.</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th> <td>    0.0771</td> <td>    0.044</td> <td>    1.739</td> <td> 0.082</td> <td>   -0.010     0.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>y</th> <td>    0.9550</td> <td>    0.031</td> <td>   30.527</td> <td> 0.000</td> <td>    0.894     1.016</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.995</td> <th>  Durbin-Watson:     </th> <td>   2.012</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.608</td> <th>  Jarque-Bera (JB):  </th> <td>   1.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.075</td> <th>  Prob(JB):          </th> <td>   0.596</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.954</td> <th>  Cond. No.          </th> <td>    2.64</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      z   R-squared:                       0.672\n",
       "Model:                            OLS   Adj. R-squared:                  0.671\n",
       "Method:                 Least Squares   F-statistic:                     1021.\n",
       "Date:                Sat, 20 Aug 2016   Prob (F-statistic):          3.69e-242\n",
       "Time:                        11:42:40   Log-Likelihood:                -1405.6\n",
       "No. Observations:                1000   AIC:                             2815.\n",
       "Df Residuals:                     998   BIC:                             2825.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "x              0.0771      0.044      1.739      0.082        -0.010     0.164\n",
       "y              0.9550      0.031     30.527      0.000         0.894     1.016\n",
       "==============================================================================\n",
       "Omnibus:                        0.995   Durbin-Watson:                   2.012\n",
       "Prob(Omnibus):                  0.608   Jarque-Bera (JB):                1.035\n",
       "Skew:                          -0.075   Prob(JB):                        0.596\n",
       "Kurtosis:                       2.954   Cond. No.                         2.64\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(X['z'], X[['x','y']])\n",
    "result = model.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
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