logit_accuracy_bank_data.ipynb

{
 "cells": [
  {
   "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": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <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",
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       "      <td>no</td>\n",
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       "      <td>274.0</td>\n",
       "      <td>yes</td>\n",
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       "      <td>4.858</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>167.0</td>\n",
       "      <td>no</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
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       "      <td>686.0</td>\n",
       "      <td>yes</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <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",
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       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
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       "      <td>yes</td>\n",
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       "    <tr>\n",
       "      <th>515</th>\n",
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       "      <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",
       "      <th>516</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
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       "      <td>473.0</td>\n",
       "      <td>yes</td>\n",
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       "      <th>517</th>\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>no</td>\n",
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       "  </tbody>\n",
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       "<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(r'D:\\Stu\\Data Science\\Exercises Regression\\Bank_data.csv')\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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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": [
    {
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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",
       "      <th>previous</th>\n",
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       "      <th>y</th>\n",
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       "      <th>count</th>\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",
       "      <th>mean</th>\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",
       "      <th>std</th>\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",
       "      <th>min</th>\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",
       "      <th>25%</th>\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",
       "      <th>50%</th>\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",
       "      <th>75%</th>\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",
       "      <th>max</th>\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": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['y']\n",
    "x1 = data['duration']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Logistic Regression"
   ]
  },
  {
   "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"
     ]
    },
    {
     "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>Thu, 23 Jul 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.2121</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>18:48:58</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:                Thu, 23 Jul 2020   Pseudo R-squ.:                  0.2121\n",
       "Time:                        18:48:58   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": {},
     "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": [
    "### 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>2020-07-23 18:49</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:               2020-07-23 18:49 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": "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.]]),\n",
       " 0.862934362934363)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(X,y,results_logit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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