Understanding Logistic Regression Tables .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding Logistic Regression Tables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the code try to interpret the summary table.\n",
    "\n",
    "### More information about the dataset: \n",
    "Note that <i> interest rate</i> indicates the 3-month interest rate between banks and <i> duration </i> indicates the time since the last contact was made with a given consumer. The <i> previous </i> variable shows whether the last marketing campaign was successful with this customer. The <i>March</i> and <i> May </i> are Boolean variables that account for when the call was made to the specific customer and <i> credit </i> shows if the customer has enough credit to avoid defaulting.\n",
    "\n",
    "<i> Notes: \n",
    "    <li> the first column of the dataset is an index one; </li>\n",
    "    <li> you don't need the graph for this exercise; </li>\n",
    "    <li> the dataset used is much bigger </li>\n",
    "</i>"
   ]
  },
  {
   "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",
    "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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       "  <thead>\n",
       "    <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",
       "      <th>duration</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
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       "      <td>0</td>\n",
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       "      <td>1.334</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>117.0</td>\n",
       "      <td>no</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",
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       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>204.0</td>\n",
       "      <td>no</td>\n",
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       "    <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",
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       "      <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",
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       "      <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",
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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('Bank_data.csv')\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th>march</th>\n",
       "      <th>may</th>\n",
       "      <th>previous</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</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",
    "\n",
    "# Removes the index column thata comes 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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "      <td>518.000000</td>\n",
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       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
       "      <td>518.000000</td>\n",
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       "      <td>518.000000</td>\n",
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       "      <td>mean</td>\n",
       "      <td>2.835776</td>\n",
       "      <td>0.034749</td>\n",
       "      <td>0.266409</td>\n",
       "      <td>0.388031</td>\n",
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       "      <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",
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       "    <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",
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       "    <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",
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       "    <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",
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       "    <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",
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      ],
      "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."
   ]
  },
  {
   "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"
     ]
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "reg_log = sm.Logit(y,x)\n",
    "results_log = reg_log.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "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>10:13:52</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:                        10:13:52   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": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_log.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dependent variable is 'duration'. The model used is a Logit regression (logistic in common lingo), while the method - Maximum Likelihood Estimation (MLE). It has clearly converged after classifyin 518 observations. \n",
    "\n",
    "The Pseudo R-squared is 0.21 which is within the 'acceptable region'. \n",
    "\n",
    "The duration variable is significant and its coefficient is 0.0051.\n",
    "\n",
    "The constant is also significant and equals: -1.70"
   ]
  }
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