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           "    <tr style=\"text-align: right;\">\n",
           "      <th></th>\n",
           "      <th>judgeID_J</th>\n",
           "      <th>acceptanceRate_R</th>\n",
           "      <th>X</th>\n",
           "      <th>Z</th>\n",
           "      <th>W</th>\n",
           "      <th>result_Y</th>\n",
           "      <th>probabilities_T</th>\n",
           "      <th>decision_T</th>\n",
           "      <th>B_prob_0_machine</th>\n",
           "      <th>B_prob_1_machine</th>\n",
           "      <th>B_prob_0_tree</th>\n",
           "    </tr>\n",
           "  </thead>\n",
           "  <tbody>\n",
           "    <tr>\n",
           "      <th>28213</th>\n",
           "      <td>56.0</td>\n",
           "      <td>0.622487</td>\n",
           "      <td>1.863196</td>\n",
           "      <td>-1.305263</td>\n",
           "      <td>0.646700</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.725045</td>\n",
           "      <td>1.0</td>\n",
           "      <td>0.958488</td>\n",
           "      <td>0.041512</td>\n",
           "      <td>1.0</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>45271</th>\n",
           "      <td>90.0</td>\n",
           "      <td>0.354855</td>\n",
           "      <td>0.928180</td>\n",
           "      <td>1.103123</td>\n",
           "      <td>-1.695381</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.951794</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.830737</td>\n",
           "      <td>0.169263</td>\n",
           "      <td>1.0</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>46254</th>\n",
           "      <td>92.0</td>\n",
           "      <td>0.205438</td>\n",
           "      <td>2.324192</td>\n",
           "      <td>0.142582</td>\n",
           "      <td>-0.455072</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.676108</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.980215</td>\n",
           "      <td>0.019785</td>\n",
           "      <td>1.0</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>27799</th>\n",
           "      <td>55.0</td>\n",
           "      <td>0.229048</td>\n",
           "      <td>-0.428510</td>\n",
           "      <td>0.093301</td>\n",
           "      <td>-0.314322</td>\n",
           "      <td>1.0</td>\n",
           "      <td>0.530956</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.341636</td>\n",
           "      <td>0.658364</td>\n",
           "      <td>1.0</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>32158</th>\n",
           "      <td>64.0</td>\n",
           "      <td>0.257266</td>\n",
           "      <td>1.031424</td>\n",
           "      <td>-0.625772</td>\n",
           "      <td>0.327365</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.638528</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.853440</td>\n",
           "      <td>0.146560</td>\n",
           "      <td>1.0</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>14483</th>\n",
           "      <td>28.0</td>\n",
           "      <td>0.517479</td>\n",
           "      <td>0.036196</td>\n",
           "      <td>1.109770</td>\n",
           "      <td>-1.484993</td>\n",
           "      <td>0.0</td>\n",
           "      <td>0.633938</td>\n",
           "      <td>1.0</td>\n",
           "      <td>0.528371</td>\n",
           "      <td>0.471629</td>\n",
           "      <td>0.0</td>\n",
           "    </tr>\n",
           "  </tbody>\n",
           "</table>\n",
           "</div>"
          ],
          "text/plain": [
           "       judgeID_J  acceptanceRate_R         X         Z         W  result_Y  \\\n",
           "28213       56.0          0.622487  1.863196 -1.305263  0.646700       0.0   \n",
           "45271       90.0          0.354855  0.928180  1.103123 -1.695381       0.0   \n",
           "46254       92.0          0.205438  2.324192  0.142582 -0.455072       0.0   \n",
           "27799       55.0          0.229048 -0.428510  0.093301 -0.314322       1.0   \n",
           "32158       64.0          0.257266  1.031424 -0.625772  0.327365       0.0   \n",
           "14483       28.0          0.517479  0.036196  1.109770 -1.484993       0.0   \n",
           "\n",
           "       probabilities_T  decision_T  B_prob_0_machine  B_prob_1_machine  \\\n",
           "28213         0.725045         1.0          0.958488          0.041512   \n",
           "45271         0.951794         0.0          0.830737          0.169263   \n",
           "46254         0.676108         0.0          0.980215          0.019785   \n",
           "27799         0.530956         0.0          0.341636          0.658364   \n",
           "32158         0.638528         0.0          0.853440          0.146560   \n",
           "14483         0.633938         1.0          0.528371          0.471629   \n",
           "\n",
           "       B_prob_0_tree  \n",
           "28213            1.0  \n",
           "45271            1.0  \n",
           "46254            1.0  \n",
           "27799            1.0  \n",
           "32158            1.0  \n",
           "14483            0.0  "
          ]
         },
         "metadata": {},
         "output_type": "display_data"
        },
        {
         "name": "stdout",
         "output_type": "stream",
         "text": [
          "1.0    61\n",
          "0.0    18\n",
          "Name: decision_T, dtype: int64\n",
          "0.0    41\n",
          "1.0    20\n",
          "Name: result_Y, dtype: int64\n"
    
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        "# instantiate the model (using the default parameters)\n",
    
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        "lr_causal_decision = LogisticRegression(solver='lbfgs')\n",
    
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        "\n",
        "# fit, reshape X to be of shape (n_samples, n_features)\n",
    
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        "lr_causal_decision.fit(train[['acceptanceRate_R', 'X']].values.reshape(-1,2), train.decision_T)\n",
        "\n",
        "lr_causal_result = LogisticRegression(solver='lbfgs')\n",
        "\n",
        "# fit, reshape X to be of shape (n_samples, n_features)\n",
        "lr_causal_result.fit(train_labeled[['acceptanceRate_R', 'X']].values.reshape(-1,2), train_labeled.result_Y)\n",
        "\n",
        "#def causal_probs(r, df, resultY_col, decisionT_col, x_cols):\n",
        "#    tmp = pd.DataFrame({'acceptanceRate_R' : r * df.shape[0], 'X' : x_cols})\n",
        "#    result_probs = lr_causal_result.predict_proba(tmp)[:,0]\n",
        "#    decision_probs = lr_causal_decision.predict_proba(tmp)[:,0]\n",
        "#    \n",
    
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        "\n",
        "my = np.mean(test.X)\n",
        "sigma = np.var(test.X)\n",
        "\n",
        "display(test.head(6))\n",
        "\n",
        "max_r = max(test.acceptanceRate_R)\n",
        "\n",
        "print(test.loc[(test.acceptanceRate_R.round(1) == 0.8) & (test.X.round(1) == 0.1), 'decision_T'].value_counts())\n",
        "\n",
        "print(test.loc[(test.acceptanceRate_R.round(1) == 0.8) & \\\n",
        "               (test.X.round(1) == 0.1) & \\\n",
        "               (test.decision_T == 1), 'result_Y'].value_counts())"
    
       ]
      }
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