Binary_Predictors_Regression+Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "#Apply a fix to the statsmodels library\n",
    "from scipy import stats\n",
    "stats.chisqprob = lambda chisq, df: stats.chi2.sf(chisq, df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>SAT</th>\n",
       "      <th>Admitted</th>\n",
       "      <th>Gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1363</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1792</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1954</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1653</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1593</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>1722</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>164</th>\n",
       "      <td>1750</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>1555</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>1524</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>1461</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>168 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SAT  Admitted  Gender\n",
       "0    1363         0       0\n",
       "1    1792         1       1\n",
       "2    1954         1       1\n",
       "3    1653         0       0\n",
       "4    1593         0       0\n",
       "..    ...       ...     ...\n",
       "163  1722         1       1\n",
       "164  1750         1       0\n",
       "165  1555         0       0\n",
       "166  1524         0       0\n",
       "167  1461         0       0\n",
       "\n",
       "[168 rows x 3 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data = pd.read_csv('Binary_predictors.csv')\n",
    "data = raw_data.copy()\n",
    "data['Admitted'] = data['Admitted'].map({'Yes': 1, 'No': 0})\n",
    "data['Gender'] = data['Gender'].map({'Female': 1, 'Male': 0})\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Declare the dependent and the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['Admitted']\n",
    "x1 = data[['SAT','Gender']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.120117\n",
      "         Iterations 10\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Admitted</td>     <th>  No. Observations:  </th>  <td>   168</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   165</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Fri, 28 Oct 2022</td> <th>  Pseudo R-squ.:     </th>  <td>0.8249</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>13:28:33</td>     <th>  Log-Likelihood:    </th> <td> -20.180</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -115.26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>5.118e-42</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>  -68.3489</td> <td>   16.454</td> <td>   -4.154</td> <td> 0.000</td> <td> -100.598</td> <td>  -36.100</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th>    <td>    0.0406</td> <td>    0.010</td> <td>    4.129</td> <td> 0.000</td> <td>    0.021</td> <td>    0.060</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Gender</th> <td>    1.9449</td> <td>    0.846</td> <td>    2.299</td> <td> 0.022</td> <td>    0.287</td> <td>    3.603</td>\n",
       "</tr>\n",
       "</table><br/><br/>Possibly complete quasi-separation: A fraction 0.27 of observations can be<br/>perfectly predicted. This might indicate that there is complete<br/>quasi-separation. In this case some parameters will not be identified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:               Admitted   No. Observations:                  168\n",
       "Model:                          Logit   Df Residuals:                      165\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Fri, 28 Oct 2022   Pseudo R-squ.:                  0.8249\n",
       "Time:                        13:28:33   Log-Likelihood:                -20.180\n",
       "converged:                       True   LL-Null:                       -115.26\n",
       "Covariance Type:            nonrobust   LLR p-value:                 5.118e-42\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -68.3489     16.454     -4.154      0.000    -100.598     -36.100\n",
       "SAT            0.0406      0.010      4.129      0.000       0.021       0.060\n",
       "Gender         1.9449      0.846      2.299      0.022       0.287       3.603\n",
       "==============================================================================\n",
       "\n",
       "Possibly complete quasi-separation: A fraction 0.27 of observations can be\n",
       "perfectly predicted. This might indicate that there is complete\n",
       "quasi-separation. In this case some parameters will not be identified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "reg_log = sm.Logit(y,x)\n",
    "results_log = reg_log.fit()\n",
    "# Get the regression summary\n",
    "results_log.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.958750970637272"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(1.94)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 1.00, 1.00, 0.23, 0.02, 0.99, 1.00, 1.00, 1.00, 0.01, 1.00,\n",
       "       1.00, 0.76, 0.00, 0.60, 1.00, 0.11, 0.12, 0.51, 1.00, 1.00, 1.00,\n",
       "       0.00, 0.01, 0.97, 1.00, 0.48, 0.99, 1.00, 0.99, 0.00, 0.83, 0.25,\n",
       "       1.00, 1.00, 1.00, 0.31, 1.00, 0.23, 0.00, 0.02, 0.45, 1.00, 0.00,\n",
       "       0.99, 0.00, 0.99, 0.00, 0.00, 0.01, 0.00, 1.00, 0.92, 0.02, 1.00,\n",
       "       0.00, 0.37, 0.98, 0.12, 1.00, 0.00, 0.78, 1.00, 1.00, 0.98, 0.00,\n",
       "       0.00, 0.00, 1.00, 0.00, 0.78, 0.12, 0.00, 0.99, 1.00, 1.00, 0.00,\n",
       "       0.30, 1.00, 1.00, 0.00, 1.00, 1.00, 0.85, 1.00, 1.00, 0.00, 1.00,\n",
       "       1.00, 0.89, 0.83, 0.00, 0.98, 0.97, 0.00, 1.00, 1.00, 0.03, 0.99,\n",
       "       0.96, 1.00, 0.00, 1.00, 0.01, 0.01, 1.00, 1.00, 1.00, 0.00, 0.00,\n",
       "       0.02, 0.33, 0.00, 1.00, 0.09, 0.00, 0.97, 0.00, 0.75, 1.00, 1.00,\n",
       "       0.01, 0.01, 0.00, 1.00, 0.00, 0.99, 0.57, 0.54, 0.87, 0.83, 0.00,\n",
       "       1.00, 0.00, 0.00, 0.00, 1.00, 0.04, 0.00, 0.01, 1.00, 0.99, 0.52,\n",
       "       1.00, 1.00, 0.05, 0.00, 0.00, 0.00, 0.68, 1.00, 1.00, 1.00, 1.00,\n",
       "       1.00, 0.00, 1.00, 1.00, 0.04, 1.00, 0.02, 1.00, 0.99, 0.97, 0.94,\n",
       "       0.01, 0.00, 0.00])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(formatter={'float': lambda x: \"{0:0.2f}\".format(x)})\n",
    "#np.set_printoptions(formatter=None)\n",
    "results_log.predict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0,\n",
       "       1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0,\n",
       "       0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1,\n",
       "       1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0,\n",
       "       0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0,\n",
       "       1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], dtype=int64)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(data['Admitted'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[69.00, 5.00],\n",
       "       [4.00, 90.00]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_log.pred_table()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Predicted 0</th>\n",
       "      <th>Predicted 1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Actual 0</th>\n",
       "      <td>69.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual 1</th>\n",
       "      <td>4.0</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Predicted 0  Predicted 1\n",
       "Actual 0         69.0          5.0\n",
       "Actual 1          4.0         90.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm_df = pd.DataFrame(results_log.pred_table())\n",
    "cm_df.columns = ['Predicted 0','Predicted 1']\n",
    "cm_df = cm_df.rename(index={0: 'Actual 0',1:'Actual 1'})\n",
    "cm_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9464285714285714"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm = np.array(cm_df)\n",
    "accuracy_train = (cm[0,0]+cm[1,1])/cm.sum()\n",
    "accuracy_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the model and assessing its accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>Admitted</th>\n",
       "      <th>Gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1323</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1725</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1762</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1777</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1665</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1556</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1731</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1809</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1930</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1708</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1970</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2039</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1681</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1444</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1726</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1876</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1485</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1500</td>\n",
       "      <td>No</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1900</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT Admitted  Gender\n",
       "0   1323       No    Male\n",
       "1   1725      Yes  Female\n",
       "2   1762      Yes  Female\n",
       "3   1777      Yes    Male\n",
       "4   1665       No    Male\n",
       "5   1556      Yes  Female\n",
       "6   1731      Yes  Female\n",
       "7   1809      Yes  Female\n",
       "8   1930      Yes  Female\n",
       "9   1708      Yes    Male\n",
       "10  1970      Yes  Female\n",
       "11  2039      Yes  Female\n",
       "12  1681      Yes  Female\n",
       "13  1444       No    Male\n",
       "14  1726       No    Male\n",
       "15  1876      Yes  Female\n",
       "16  1485       No    Male\n",
       "17  1500       No  Female\n",
       "18  1900      Yes    Male"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = pd.read_csv('Test_dataset.csv')\n",
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>SAT</th>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>1930</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1708</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1970</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2039</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1681</td>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1444</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1726</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1876</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1485</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1500</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1900</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT  Admitted  Gender\n",
       "0   1323         0       0\n",
       "1   1725         1       1\n",
       "2   1762         1       1\n",
       "3   1777         1       0\n",
       "4   1665         0       0\n",
       "5   1556         1       1\n",
       "6   1731         1       1\n",
       "7   1809         1       1\n",
       "8   1930         1       1\n",
       "9   1708         1       0\n",
       "10  1970         1       1\n",
       "11  2039         1       1\n",
       "12  1681         1       1\n",
       "13  1444         0       0\n",
       "14  1726         0       0\n",
       "15  1876         1       1\n",
       "16  1485         0       0\n",
       "17  1500         0       1\n",
       "18  1900         1       0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test['Admitted'] = test['Admitted'].map({'Yes': 1, 'No': 0})\n",
    "test['Gender'] = test['Gender'].map({'Female': 1, 'Male': 0})\n",
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>Gender</th>\n",
       "    </tr>\n",
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       "      <td>1.0</td>\n",
       "      <td>1954</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
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       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1722</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>164</th>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1555</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1524</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1461</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>168 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     const   SAT  Gender\n",
       "0      1.0  1363       0\n",
       "1      1.0  1792       1\n",
       "2      1.0  1954       1\n",
       "3      1.0  1653       0\n",
       "4      1.0  1593       0\n",
       "..     ...   ...     ...\n",
       "163    1.0  1722       1\n",
       "164    1.0  1750       0\n",
       "165    1.0  1555       0\n",
       "166    1.0  1524       0\n",
       "167    1.0  1461       0\n",
       "\n",
       "[168 rows x 3 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Gender</th>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1970</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2039</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1681</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1444</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1726</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1876</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1485</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1900</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    const   SAT  Gender\n",
       "0     1.0  1323       0\n",
       "1     1.0  1725       1\n",
       "2     1.0  1762       1\n",
       "3     1.0  1777       0\n",
       "4     1.0  1665       0\n",
       "5     1.0  1556       1\n",
       "6     1.0  1731       1\n",
       "7     1.0  1809       1\n",
       "8     1.0  1930       1\n",
       "9     1.0  1708       0\n",
       "10    1.0  1970       1\n",
       "11    1.0  2039       1\n",
       "12    1.0  1681       1\n",
       "13    1.0  1444       0\n",
       "14    1.0  1726       0\n",
       "15    1.0  1876       1\n",
       "16    1.0  1485       0\n",
       "17    1.0  1500       1\n",
       "18    1.0  1900       0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_actual = test['Admitted']\n",
    "test_data = test.drop(['Admitted'],axis=1)\n",
    "test_data = sm.add_constant(test_data)\n",
    "#test_data = test_data[x.columns.values]\n",
    "test_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def confusion_matrix(data,actual_values,model):\n",
    "    \n",
    "        pred_values = model.predict(data)\n",
    "        bins=np.array([0,0.5,1])\n",
    "        cm = np.histogram2d(actual_values, pred_values, bins=bins)[0]\n",
    "        accuracy = (cm[0,0]+cm[1,1])/cm.sum()\n",
    "        return cm, accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[5.00, 1.00],\n",
       "        [1.00, 12.00]]),\n",
       " 0.8947368421052632)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm = confusion_matrix(test_data,test_actual,results_log)\n",
    "cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\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>Predicted 0</th>\n",
       "      <th>Predicted 1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Actual 0</th>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual 1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Predicted 0  Predicted 1\n",
       "Actual 0          5.0          1.0\n",
       "Actual 1          1.0         12.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm_df = pd.DataFrame(cm[0])\n",
    "cm_df.columns = ['Predicted 0','Predicted 1']\n",
    "cm_df = cm_df.rename(index={0: 'Actual 0',1:'Actual 1'})\n",
    "cm_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Missclassification rate: 0.10526315789473684\n"
     ]
    }
   ],
   "source": [
    "print ('Missclassification rate: '+str((1+1)/19))"
   ]
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