Calculating the Accuracy of the Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating the Accuracy of the Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the same dataset, expand the model by including all other features into the regression. \n",
    "\n",
    "Moreover, calculate the accuracy of the model and create a confusion matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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",
    "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": "markdown",
   "metadata": {},
   "source": [
    "Load the ‘Bank_data.csv’ dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>interest_rate</th>\n",
       "      <th>credit</th>\n",
       "      <th>march</th>\n",
       "      <th>may</th>\n",
       "      <th>previous</th>\n",
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       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.334</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>117.0</td>\n",
       "      <td>no</td>\n",
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       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.767</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>274.0</td>\n",
       "      <td>yes</td>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4.858</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>167.0</td>\n",
       "      <td>no</td>\n",
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       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4.120</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>686.0</td>\n",
       "      <td>yes</td>\n",
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       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4.856</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>157.0</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
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       "      <td>1.334</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>204.0</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>514</td>\n",
       "      <td>514</td>\n",
       "      <td>0.861</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>806.0</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>515</td>\n",
       "      <td>515</td>\n",
       "      <td>0.879</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>290.0</td>\n",
       "      <td>no</td>\n",
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       "    <tr>\n",
       "      <td>516</td>\n",
       "      <td>516</td>\n",
       "      <td>0.877</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>473.0</td>\n",
       "      <td>yes</td>\n",
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       "    <tr>\n",
       "      <td>517</td>\n",
       "      <td>517</td>\n",
       "      <td>4.965</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>142.0</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>518 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Unnamed: 0  interest_rate  credit  march  may  previous  duration    y\n",
       "0             0          1.334     0.0    1.0  0.0       0.0     117.0   no\n",
       "1             1          0.767     0.0    0.0  2.0       1.0     274.0  yes\n",
       "2             2          4.858     0.0    1.0  0.0       0.0     167.0   no\n",
       "3             3          4.120     0.0    0.0  0.0       0.0     686.0  yes\n",
       "4             4          4.856     0.0    1.0  0.0       0.0     157.0   no\n",
       "..          ...            ...     ...    ...  ...       ...       ...  ...\n",
       "513         513          1.334     0.0    1.0  0.0       0.0     204.0   no\n",
       "514         514          0.861     0.0    0.0  2.0       1.0     806.0  yes\n",
       "515         515          0.879     0.0    0.0  0.0       0.0     290.0   no\n",
       "516         516          0.877     0.0    0.0  5.0       1.0     473.0  yes\n",
       "517         517          4.965     0.0    0.0  0.0       0.0     142.0   no\n",
       "\n",
       "[518 rows x 8 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data = pd.read_csv('Bank-data.csv')\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th>previous</th>\n",
       "      <th>duration</th>\n",
       "      <th>y</th>\n",
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       "      <td>0</td>\n",
       "      <td>1.334</td>\n",
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       "      <td>1</td>\n",
       "      <td>0.767</td>\n",
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       "      <td>4.856</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>515</td>\n",
       "      <td>0.879</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>290.0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <td>516</td>\n",
       "      <td>0.877</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>473.0</td>\n",
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       "      <td>517</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>142.0</td>\n",
       "      <td>0</td>\n",
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      ],
      "text/plain": [
       "     interest_rate  credit  march  may  previous  duration  y\n",
       "0            1.334     0.0    1.0  0.0       0.0     117.0  0\n",
       "1            0.767     0.0    0.0  2.0       1.0     274.0  1\n",
       "2            4.858     0.0    1.0  0.0       0.0     167.0  0\n",
       "3            4.120     0.0    0.0  0.0       0.0     686.0  1\n",
       "4            4.856     0.0    1.0  0.0       0.0     157.0  0\n",
       "..             ...     ...    ...  ...       ...       ... ..\n",
       "513          1.334     0.0    1.0  0.0       0.0     204.0  0\n",
       "514          0.861     0.0    0.0  2.0       1.0     806.0  1\n",
       "515          0.879     0.0    0.0  0.0       0.0     290.0  0\n",
       "516          0.877     0.0    0.0  5.0       1.0     473.0  1\n",
       "517          4.965     0.0    0.0  0.0       0.0     142.0  0\n",
       "\n",
       "[518 rows x 7 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We make sure to create a copy of the data before we start altering it. Note that we don't change the original data we loaded.\n",
    "data = raw_data.copy()\n",
    "# Removes the index column thata comes with the data\n",
    "data = data.drop(['Unnamed: 0'], axis = 1)\n",
    "# We use the map function to change any 'yes' values to 1 and 'no'values to 0. \n",
    "data['y'] = data['y'].map({'yes':1, 'no':0})\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>interest_rate</th>\n",
       "      <th>credit</th>\n",
       "      <th>march</th>\n",
       "      <th>may</th>\n",
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       "      <th>y</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>2.835776</td>\n",
       "      <td>0.034749</td>\n",
       "      <td>0.266409</td>\n",
       "      <td>0.388031</td>\n",
       "      <td>0.127413</td>\n",
       "      <td>382.177606</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>1.876903</td>\n",
       "      <td>0.183321</td>\n",
       "      <td>0.442508</td>\n",
       "      <td>0.814527</td>\n",
       "      <td>0.333758</td>\n",
       "      <td>344.295990</td>\n",
       "      <td>0.500483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>0.635000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>1.042750</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>155.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>1.466000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>266.500000</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>4.956500</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>482.750000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>4.970000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2653.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       interest_rate      credit       march         may    previous  \\\n",
       "count     518.000000  518.000000  518.000000  518.000000  518.000000   \n",
       "mean        2.835776    0.034749    0.266409    0.388031    0.127413   \n",
       "std         1.876903    0.183321    0.442508    0.814527    0.333758   \n",
       "min         0.635000    0.000000    0.000000    0.000000    0.000000   \n",
       "25%         1.042750    0.000000    0.000000    0.000000    0.000000   \n",
       "50%         1.466000    0.000000    0.000000    0.000000    0.000000   \n",
       "75%         4.956500    0.000000    1.000000    0.000000    0.000000   \n",
       "max         4.970000    1.000000    1.000000    5.000000    1.000000   \n",
       "\n",
       "          duration           y  \n",
       "count   518.000000  518.000000  \n",
       "mean    382.177606    0.500000  \n",
       "std     344.295990    0.500483  \n",
       "min       9.000000    0.000000  \n",
       "25%     155.000000    0.000000  \n",
       "50%     266.500000    0.500000  \n",
       "75%     482.750000    1.000000  \n",
       "max    2653.000000    1.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declare the dependent and independent variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use 'duration' as the independet variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['y']\n",
    "x1 = data['duration']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the regression and graph the scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.546118\n",
      "         Iterations 7\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nimis\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>  <td>   518</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   516</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 22 Jul 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.2121</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>18:02:54</td>     <th>  Log-Likelihood:    </th> <td> -282.89</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -359.05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>5.387e-35</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>   -1.7001</td> <td>    0.192</td> <td>   -8.863</td> <td> 0.000</td> <td>   -2.076</td> <td>   -1.324</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>duration</th> <td>    0.0051</td> <td>    0.001</td> <td>    9.159</td> <td> 0.000</td> <td>    0.004</td> <td>    0.006</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  518\n",
       "Model:                          Logit   Df Residuals:                      516\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Wed, 22 Jul 2020   Pseudo R-squ.:                  0.2121\n",
       "Time:                        18:02:54   Log-Likelihood:                -282.89\n",
       "converged:                       True   LL-Null:                       -359.05\n",
       "Covariance Type:            nonrobust   LLR p-value:                 5.387e-35\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -1.7001      0.192     -8.863      0.000      -2.076      -1.324\n",
       "duration       0.0051      0.001      9.159      0.000       0.004       0.006\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a scatter plot of x1 (Duration, no constant) and y (Subscribed)\n",
    "plt.scatter(x1,y,color = 'C0')\n",
    "# Don't forget to label your axes!\n",
    "plt.xlabel('Duration', fontsize = 20)\n",
    "plt.ylabel('Subscription', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expand the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can be omitting many causal factors in our simple logistic model, so we instead switch to a multivariate logistic regression model. Add the ‘interest_rate’, ‘march’, ‘credit’ and ‘previous’ estimators to our model and run the regression again. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declare the independent variable(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To avoid writing them out every time, we save the names of the estimators of our model in a list. \n",
    "estimators=['interest_rate','march','credit','previous','duration']\n",
    "\n",
    "X1 = data[estimators]\n",
    "y = data['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.336664\n",
      "         Iterations 7\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>              <td>Logit</td>      <td>Pseudo R-squared:</td>    <td>0.514</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>         <td>y</td>              <td>AIC:</td>         <td>360.7836</td> \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2020-07-22 18:02</td>       <td>BIC:</td>         <td>386.2834</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>518</td>        <td>Log-Likelihood:</td>    <td>-174.39</td> \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>5</td>            <td>LL-Null:</td>        <td>-359.05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>512</td>         <td>LLR p-value:</td>    <td>1.2114e-77</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>Converged:</td>           <td>1.0000</td>           <td>Scale:</td>         <td>1.0000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>No. Iterations:</td>        <td>7.0000</td>              <td></td>               <td></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>-0.0211</td>  <td>0.3113</td>  <td>-0.0677</td> <td>0.9460</td> <td>-0.6313</td> <td>0.5891</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>interest_rate</th> <td>-0.8001</td>  <td>0.0895</td>  <td>-8.9434</td> <td>0.0000</td> <td>-0.9755</td> <td>-0.6248</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>march</th>         <td>-1.8322</td>  <td>0.3297</td>  <td>-5.5563</td> <td>0.0000</td> <td>-2.4785</td> <td>-1.1859</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit</th>        <td>2.3585</td>   <td>1.0875</td>  <td>2.1688</td>  <td>0.0301</td> <td>0.2271</td>  <td>4.4900</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>previous</th>      <td>1.5363</td>   <td>0.5010</td>  <td>3.0666</td>  <td>0.0022</td> <td>0.5544</td>  <td>2.5182</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>duration</th>      <td>0.0070</td>   <td>0.0007</td>  <td>9.3810</td>  <td>0.0000</td> <td>0.0055</td>  <td>0.0084</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                         Results: Logit\n",
       "=================================================================\n",
       "Model:              Logit            Pseudo R-squared: 0.514     \n",
       "Dependent Variable: y                AIC:              360.7836  \n",
       "Date:               2020-07-22 18:02 BIC:              386.2834  \n",
       "No. Observations:   518              Log-Likelihood:   -174.39   \n",
       "Df Model:           5                LL-Null:          -359.05   \n",
       "Df Residuals:       512              LLR p-value:      1.2114e-77\n",
       "Converged:          1.0000           Scale:            1.0000    \n",
       "No. Iterations:     7.0000                                       \n",
       "-----------------------------------------------------------------\n",
       "                   Coef.  Std.Err.    z    P>|z|   [0.025  0.975]\n",
       "-----------------------------------------------------------------\n",
       "const             -0.0211   0.3113 -0.0677 0.9460 -0.6313  0.5891\n",
       "interest_rate     -0.8001   0.0895 -8.9434 0.0000 -0.9755 -0.6248\n",
       "march             -1.8322   0.3297 -5.5563 0.0000 -2.4785 -1.1859\n",
       "credit             2.3585   1.0875  2.1688 0.0301  0.2271  4.4900\n",
       "previous           1.5363   0.5010  3.0666 0.0022  0.5544  2.5182\n",
       "duration           0.0070   0.0007  9.3810 0.0000  0.0055  0.0084\n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = sm.add_constant(X1)\n",
    "reg_logit = sm.Logit(y,X)\n",
    "results_logit = reg_logit.fit()\n",
    "results_logit.summary2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confusion Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the confusion matrix of the model and estimate its accuracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def confusion_matrix(data,actual_values,model):\n",
    "        \n",
    "        # Confusion matrix \n",
    "        \n",
    "        # Parameters\n",
    "        # ----------\n",
    "        # data: data frame or array\n",
    "            # data is a data frame formatted in the same way as your input data (without the actual values)\n",
    "            # e.g. const, var1, var2, etc. Order is very important!\n",
    "        # actual_values: data frame or array\n",
    "            # These are the actual values from the test_data\n",
    "            # In the case of a logistic regression, it should be a single column with 0s and 1s\n",
    "            \n",
    "        # model: a LogitResults object\n",
    "            # this is the variable where you have the fitted model \n",
    "            # e.g. results_log in this course\n",
    "        # ----------\n",
    "        \n",
    "        #Predict the values using the Logit model\n",
    "        pred_values = model.predict(data)\n",
    "        # Specify the bins \n",
    "        bins=np.array([0,0.5,1])\n",
    "        # Create a histogram, where if values are between 0 and 0.5 tell will be considered 0\n",
    "        # if they are between 0.5 and 1, they will be considered 1\n",
    "        cm = np.histogram2d(actual_values, pred_values, bins=bins)[0]\n",
    "        # Calculate the accuracy\n",
    "        accuracy = (cm[0,0]+cm[1,1])/cm.sum()\n",
    "        # Return the confusion matrix and \n",
    "        return cm, accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[218.,  41.],\n",
       "        [ 30., 229.]]), 0.862934362934363)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   ]
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