Building a Logistic Regression .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building a Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a logistic regression based on the bank data provided. \n",
    "\n",
    "The data is based on the marketing campaign efforts of a Portuguese banking institution. The classification goal is to predict if the client will subscribe a term deposit (variable y).\n",
    "\n",
    "Note that the first column of the dataset is the index.\n",
    "\n",
    "Source: [Moro et al., 2014] S. Moro, P. Cortez and P. Rita. A Data-Driven Approach to Predict the Success of Bank Telemarketing. Decision Support Systems, Elsevier, 62:22-31, June 2014"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "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",
    "# this part not be needed after the latests updates of the 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": "markdown",
   "metadata": {},
   "source": [
    "Load the ‘Example_bank_data.csv’ dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "      <td>142</td>\n",
       "      <td>no</td>\n",
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       "<p>518 rows × 3 columns</p>\n",
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      ],
      "text/plain": [
       "     Unnamed: 0  duration    y\n",
       "0             0       117   no\n",
       "1             1       274  yes\n",
       "2             2       167   no\n",
       "3             3       686  yes\n",
       "4             4       157   no\n",
       "..          ...       ...  ...\n",
       "513         513       204   no\n",
       "514         514       806  yes\n",
       "515         515       290   no\n",
       "516         516       473  yes\n",
       "517         517       142   no\n",
       "\n",
       "[518 rows x 3 columns]"
      ]
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "raw_data = pd.read_csv('Example_bank_data.csv')\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to know whether the bank marketing strategy was successful, so we need to transform the outcome variable into 0s and 1s in order to perform a logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "     duration  y\n",
       "0         117  0\n",
       "1         274  1\n",
       "2         167  0\n",
       "3         686  1\n",
       "4         157  0\n",
       "..        ... ..\n",
       "513       204  0\n",
       "514       806  1\n",
       "515       290  0\n",
       "516       473  1\n",
       "517       142  0\n",
       "\n",
       "[518 rows x 2 columns]"
      ]
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   "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",
    "\n",
    "# Removes the index column that came with the data\n",
    "data = data.drop(['Unnamed: 0'], axis = 1)\n",
    "\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"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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       "      <th>duration</th>\n",
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       "      <td>count</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>382.177606</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>344.295990</td>\n",
       "      <td>0.500483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>155.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>266.500000</td>\n",
       "      <td>0.500000</td>\n",
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       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>482.750000</td>\n",
       "      <td>1.000000</td>\n",
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       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>2653.000000</td>\n",
       "      <td>1.000000</td>\n",
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       "          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"
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   ],
   "source": [
    "# Check the descriptive statistics\n",
    "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": "markdown",
   "metadata": {},
   "source": [
    "Run the regression and visualize it on a scatter plot (no need to plot the line)."
   ]
  },
  {
   "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>09:35:53</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:                        09:35:53   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",
    "\n",
    "# Get the regression summary\n",
    "results_log.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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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",
    "\n",
    "# Don't forget to label your axes!\n",
    "plt.xlabel('Duration', fontsize = 20)\n",
    "plt.ylabel('Subscription', fontsize = 20)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}