Step_6) LGD and EAD Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import data.\n",
    "loan_data_preprocessed_backup = pd.read_csv('data/loan_data_2007_2014_preprocessed.csv')\n",
    "loan_data_preprocessed = loan_data_preprocessed_backup.copy()\n",
    "\n",
    "loan_data_defaults = pd.read_csv('data/loan_data_defaults.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Explore Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(466285, 209)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>installment</th>\n",
       "      <th>...</th>\n",
       "      <th>addr_state:UT</th>\n",
       "      <th>addr_state:VA</th>\n",
       "      <th>addr_state:VT</th>\n",
       "      <th>addr_state:WA</th>\n",
       "      <th>addr_state:WI</th>\n",
       "      <th>addr_state:WV</th>\n",
       "      <th>addr_state:WY</th>\n",
       "      <th>initial_list_status:f</th>\n",
       "      <th>initial_list_status:w</th>\n",
       "      <th>good_bad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1077501</td>\n",
       "      <td>1296599</td>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>10.65</td>\n",
       "      <td>162.87</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>59.83</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 209 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1       id  member_id  loan_amnt  funded_amnt  \\\n",
       "0           0             0  1077501    1296599       5000         5000   \n",
       "1           1             1  1077430    1314167       2500         2500   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... addr_state:UT  \\\n",
       "0           4975.0   36 months     10.65       162.87  ...             0   \n",
       "1           2500.0   60 months     15.27        59.83  ...             0   \n",
       "\n",
       "  addr_state:VA addr_state:VT addr_state:WA addr_state:WI  addr_state:WV  \\\n",
       "0             0             0             0             0              0   \n",
       "1             0             0             0             0              0   \n",
       "\n",
       "  addr_state:WY initial_list_status:f initial_list_status:w good_bad  \n",
       "0             0                     1                     0        1  \n",
       "1             0                     1                     0        0  \n",
       "\n",
       "[2 rows x 209 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(loan_data_preprocessed.shape)\n",
    "loan_data_preprocessed.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(43236, 213)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>Unnamed: 0.1.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>...</th>\n",
       "      <th>addr_state:WA</th>\n",
       "      <th>addr_state:WI</th>\n",
       "      <th>addr_state:WV</th>\n",
       "      <th>addr_state:WY</th>\n",
       "      <th>initial_list_status:f</th>\n",
       "      <th>initial_list_status:w</th>\n",
       "      <th>good_bad</th>\n",
       "      <th>recovery_rate</th>\n",
       "      <th>CCF</th>\n",
       "      <th>recovery_rate_0_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.046832</td>\n",
       "      <td>0.817416</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>1071795</td>\n",
       "      <td>1306957</td>\n",
       "      <td>5600</td>\n",
       "      <td>5600</td>\n",
       "      <td>5600.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>21.28</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.033761</td>\n",
       "      <td>0.971068</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 213 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1  Unnamed: 0.1.1       id  member_id  loan_amnt  \\\n",
       "0           1             1               1  1077430    1314167       2500   \n",
       "1           8             8               8  1071795    1306957       5600   \n",
       "\n",
       "   funded_amnt  funded_amnt_inv        term  int_rate  ...  addr_state:WA  \\\n",
       "0         2500           2500.0   60 months     15.27  ...              0   \n",
       "1         5600           5600.0   60 months     21.28  ...              0   \n",
       "\n",
       "  addr_state:WI addr_state:WV addr_state:WY initial_list_status:f  \\\n",
       "0             0             0             0                     1   \n",
       "1             0             0             0                     1   \n",
       "\n",
       "  initial_list_status:w  good_bad recovery_rate       CCF recovery_rate_0_1  \n",
       "0                     0         0      0.046832  0.817416                 1  \n",
       "1                     0         0      0.033761  0.971068                 1  \n",
       "\n",
       "[2 rows x 213 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(loan_data_defaults.shape)\n",
    "loan_data_defaults.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LGD Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Splitting Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LGD model stage 1 datasets: recovery rate 0 or greater than 0.\n",
    "lgd_inputs_stage_1_train, lgd_inputs_stage_1_test, lgd_targets_stage_1_train, lgd_targets_stage_1_test = train_test_split(loan_data_defaults.drop(['good_bad', 'recovery_rate','recovery_rate_0_1', 'CCF'], axis = 1), loan_data_defaults['recovery_rate_0_1'], test_size = 0.2, random_state = 42)\n",
    "# Takes a set of inputs and a set of targets as arguments. Splits the inputs and the targets into four dataframes:\n",
    "# Inputs - Train, Inputs - Test, Targets - Train, Targets - Test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparing the Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "features_all = ['grade:A',\n",
    "'grade:B',\n",
    "'grade:C',\n",
    "'grade:D',\n",
    "'grade:E',\n",
    "'grade:F',\n",
    "'grade:G',\n",
    "'home_ownership:MORTGAGE',\n",
    "'home_ownership:NONE',\n",
    "'home_ownership:OTHER',\n",
    "'home_ownership:OWN',\n",
    "'home_ownership:RENT',\n",
    "'verification_status:Not Verified',\n",
    "'verification_status:Source Verified',\n",
    "'verification_status:Verified',\n",
    "'purpose:car',\n",
    "'purpose:credit_card',\n",
    "'purpose:debt_consolidation',\n",
    "'purpose:educational',\n",
    "'purpose:home_improvement',\n",
    "'purpose:house',\n",
    "'purpose:major_purchase',\n",
    "'purpose:medical',\n",
    "'purpose:moving',\n",
    "'purpose:other',\n",
    "'purpose:renewable_energy',\n",
    "'purpose:small_business',\n",
    "'purpose:vacation',\n",
    "'purpose:wedding',\n",
    "'initial_list_status:f',\n",
    "'initial_list_status:w',\n",
    "'term_int',\n",
    "'emp_length_int',\n",
    "'mths_since_issue_d',\n",
    "'mths_since_earliest_cr_line',\n",
    "'funded_amnt',\n",
    "'int_rate',\n",
    "'installment',\n",
    "'annual_inc',\n",
    "'dti',\n",
    "'delinq_2yrs',\n",
    "'inq_last_6mths',\n",
    "'mths_since_last_delinq',\n",
    "'mths_since_last_record',\n",
    "'open_acc',\n",
    "'pub_rec',\n",
    "'total_acc',\n",
    "'acc_now_delinq',\n",
    "'total_rev_hi_lim']\n",
    "# List of all independent variables for the models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "features_reference_cat = ['grade:G',\n",
    "'home_ownership:RENT',\n",
    "'verification_status:Verified',\n",
    "'purpose:credit_card',\n",
    "'initial_list_status:f']\n",
    "# List of the dummy variable reference categories. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_1_train = lgd_inputs_stage_1_train[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(34588, 44)\n"
     ]
    }
   ],
   "source": [
    "lgd_inputs_stage_1_train = lgd_inputs_stage_1_train.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories.\n",
    "\n",
    "print(lgd_inputs_stage_1_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "grade:A                                0\n",
       "grade:B                                0\n",
       "grade:C                                0\n",
       "grade:D                                0\n",
       "grade:E                                0\n",
       "grade:F                                0\n",
       "home_ownership:MORTGAGE                0\n",
       "home_ownership:NONE                    0\n",
       "home_ownership:OTHER                   0\n",
       "home_ownership:OWN                     0\n",
       "verification_status:Not Verified       0\n",
       "verification_status:Source Verified    0\n",
       "purpose:car                            0\n",
       "purpose:debt_consolidation             0\n",
       "purpose:educational                    0\n",
       "purpose:home_improvement               0\n",
       "purpose:house                          0\n",
       "purpose:major_purchase                 0\n",
       "purpose:medical                        0\n",
       "purpose:moving                         0\n",
       "purpose:other                          0\n",
       "purpose:renewable_energy               0\n",
       "purpose:small_business                 0\n",
       "purpose:vacation                       0\n",
       "purpose:wedding                        0\n",
       "initial_list_status:w                  0\n",
       "term_int                               0\n",
       "emp_length_int                         0\n",
       "mths_since_issue_d                     0\n",
       "mths_since_earliest_cr_line            0\n",
       "funded_amnt                            0\n",
       "int_rate                               0\n",
       "installment                            0\n",
       "annual_inc                             0\n",
       "dti                                    0\n",
       "delinq_2yrs                            0\n",
       "inq_last_6mths                         0\n",
       "mths_since_last_delinq                 0\n",
       "mths_since_last_record                 0\n",
       "open_acc                               0\n",
       "pub_rec                                0\n",
       "total_acc                              0\n",
       "acc_now_delinq                         0\n",
       "total_rev_hi_lim                       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgd_inputs_stage_1_train.isnull().sum()\n",
    "# Check for missing values. We check whether the value of each row for each column is missing or not,\n",
    "# then sum accross columns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stage 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# P values for sklearn logistic regression.\n",
    "\n",
    "# Class to display p-values for logistic regression in sklearn.\n",
    "\n",
    "from sklearn import linear_model\n",
    "import scipy.stats as stat\n",
    "\n",
    "class LogisticRegression_with_p_values:\n",
    "    \n",
    "    def __init__(self,*args,**kwargs):#,**kwargs):\n",
    "        self.model = linear_model.LogisticRegression(*args,**kwargs)#,**args)\n",
    "\n",
    "    def fit(self,X,y):\n",
    "        self.model.fit(X,y)\n",
    "        \n",
    "        #### Get p-values for the fitted model ####\n",
    "        denom = (2.0 * (1.0 + np.cosh(self.model.decision_function(X))))\n",
    "        denom = np.tile(denom,(X.shape[1],1)).T\n",
    "        F_ij = np.dot((X / denom).T,X) ## Fisher Information Matrix\n",
    "        Cramer_Rao = np.linalg.inv(F_ij) ## Inverse Information Matrix\n",
    "        sigma_estimates = np.sqrt(np.diagonal(Cramer_Rao))\n",
    "        z_scores = self.model.coef_[0] / sigma_estimates # z-score for eaach model coefficient\n",
    "        p_values = [stat.norm.sf(abs(x)) * 2 for x in z_scores] ### two tailed test for p-values\n",
    "        \n",
    "        self.coef_ = self.model.coef_\n",
    "        self.intercept_ = self.model.intercept_\n",
    "        #self.z_scores = z_scores\n",
    "        self.p_values = p_values\n",
    "        #self.sigma_estimates = sigma_estimates\n",
    "        #self.F_ij = F_ij"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_lgd_st_1 = LogisticRegression_with_p_values()\n",
    "# We create an instance of an object from the 'LogisticRegression' class.\n",
    "reg_lgd_st_1.fit(lgd_inputs_stage_1_train, lgd_targets_stage_1_train)\n",
    "# Estimates the coefficients of the object from the 'LogisticRegression' class\n",
    "# with inputs (independent variables) contained in the first dataframe\n",
    "# and targets (dependent variables) contained in the second dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['grade:A' 'grade:B' 'grade:C' 'grade:D' 'grade:E' 'grade:F'\n",
      " 'home_ownership:MORTGAGE' 'home_ownership:NONE' 'home_ownership:OTHER'\n",
      " 'home_ownership:OWN' 'verification_status:Not Verified'\n",
      " 'verification_status:Source Verified' 'purpose:car'\n",
      " 'purpose:debt_consolidation' 'purpose:educational'\n",
      " 'purpose:home_improvement' 'purpose:house' 'purpose:major_purchase'\n",
      " 'purpose:medical' 'purpose:moving' 'purpose:other'\n",
      " 'purpose:renewable_energy' 'purpose:small_business' 'purpose:vacation'\n",
      " 'purpose:wedding' 'initial_list_status:w' 'term_int' 'emp_length_int'\n",
      " 'mths_since_issue_d' 'mths_since_earliest_cr_line' 'funded_amnt'\n",
      " 'int_rate' 'installment' 'annual_inc' 'dti' 'delinq_2yrs'\n",
      " 'inq_last_6mths' 'mths_since_last_delinq' 'mths_since_last_record'\n",
      " 'open_acc' 'pub_rec' 'total_acc' 'acc_now_delinq' 'total_rev_hi_lim']\n"
     ]
    }
   ],
   "source": [
    "feature_name = lgd_inputs_stage_1_train.columns.values\n",
    "# Stores the names of the columns of a dataframe in a variable.\n",
    "print(feature_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>-5.558221e-05</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-6.795707e-06</td>\n",
       "      <td>9.999356e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-5.294391e-05</td>\n",
       "      <td>9.993798e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-1.123227e-04</td>\n",
       "      <td>9.986388e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>2.304027e-05</td>\n",
       "      <td>9.997320e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>grade:E</td>\n",
       "      <td>1.497238e-05</td>\n",
       "      <td>9.998421e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>grade:F</td>\n",
       "      <td>6.745851e-05</td>\n",
       "      <td>9.993811e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>home_ownership:MORTGAGE</td>\n",
       "      <td>-3.149680e-05</td>\n",
       "      <td>9.990085e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>home_ownership:NONE</td>\n",
       "      <td>8.221090e-07</td>\n",
       "      <td>9.999992e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>home_ownership:OTHER</td>\n",
       "      <td>7.256036e-07</td>\n",
       "      <td>9.999985e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>home_ownership:OWN</td>\n",
       "      <td>-1.885950e-06</td>\n",
       "      <td>9.999635e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>verification_status:Not Verified</td>\n",
       "      <td>-3.758344e-05</td>\n",
       "      <td>9.989990e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>verification_status:Source Verified</td>\n",
       "      <td>-1.552916e-04</td>\n",
       "      <td>9.954469e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>purpose:car</td>\n",
       "      <td>1.246058e-05</td>\n",
       "      <td>9.999143e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>purpose:debt_consolidation</td>\n",
       "      <td>-1.291673e-04</td>\n",
       "      <td>9.965982e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>purpose:educational</td>\n",
       "      <td>1.677313e-06</td>\n",
       "      <td>9.999953e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>purpose:home_improvement</td>\n",
       "      <td>1.009488e-05</td>\n",
       "      <td>9.998587e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>purpose:house</td>\n",
       "      <td>1.067563e-05</td>\n",
       "      <td>9.999401e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>purpose:major_purchase</td>\n",
       "      <td>1.862645e-05</td>\n",
       "      <td>9.998275e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>purpose:medical</td>\n",
       "      <td>2.171841e-06</td>\n",
       "      <td>9.999836e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>purpose:moving</td>\n",
       "      <td>3.829696e-06</td>\n",
       "      <td>9.999744e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>purpose:other</td>\n",
       "      <td>4.115872e-05</td>\n",
       "      <td>9.993759e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>purpose:renewable_energy</td>\n",
       "      <td>2.980485e-06</td>\n",
       "      <td>9.999930e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>purpose:small_business</td>\n",
       "      <td>4.792752e-05</td>\n",
       "      <td>9.994621e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>purpose:vacation</td>\n",
       "      <td>4.403543e-06</td>\n",
       "      <td>9.999756e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>purpose:wedding</td>\n",
       "      <td>1.079062e-05</td>\n",
       "      <td>9.999411e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>initial_list_status:w</td>\n",
       "      <td>-7.045037e-04</td>\n",
       "      <td>9.791259e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>term_int</td>\n",
       "      <td>-6.283961e-04</td>\n",
       "      <td>8.015743e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>emp_length_int</td>\n",
       "      <td>-2.398829e-04</td>\n",
       "      <td>9.375519e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>mths_since_issue_d</td>\n",
       "      <td>1.717075e-02</td>\n",
       "      <td>5.344334e-87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>mths_since_earliest_cr_line</td>\n",
       "      <td>-1.549782e-03</td>\n",
       "      <td>1.380369e-26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>funded_amnt</td>\n",
       "      <td>2.062960e-05</td>\n",
       "      <td>3.843097e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>int_rate</td>\n",
       "      <td>6.381448e-04</td>\n",
       "      <td>9.124077e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>installment</td>\n",
       "      <td>-2.941314e-04</td>\n",
       "      <td>3.423448e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>annual_inc</td>\n",
       "      <td>-1.897291e-07</td>\n",
       "      <td>5.763106e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>dti</td>\n",
       "      <td>-4.488850e-03</td>\n",
       "      <td>5.797179e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>delinq_2yrs</td>\n",
       "      <td>-5.957514e-05</td>\n",
       "      <td>9.967562e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>inq_last_6mths</td>\n",
       "      <td>2.088708e-04</td>\n",
       "      <td>9.822345e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>mths_since_last_delinq</td>\n",
       "      <td>-7.701858e-04</td>\n",
       "      <td>1.284782e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>mths_since_last_record</td>\n",
       "      <td>-4.352028e-03</td>\n",
       "      <td>1.639999e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>open_acc</td>\n",
       "      <td>-1.756136e-03</td>\n",
       "      <td>5.921493e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>pub_rec</td>\n",
       "      <td>-7.953811e-05</td>\n",
       "      <td>9.983910e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>total_acc</td>\n",
       "      <td>-4.630170e-03</td>\n",
       "      <td>1.399017e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>acc_now_delinq</td>\n",
       "      <td>2.686354e-06</td>\n",
       "      <td>9.999878e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>total_rev_hi_lim</td>\n",
       "      <td>-6.439478e-06</td>\n",
       "      <td>5.925663e-20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Feature name  Coefficients      p_values\n",
       "0                             Intercept -5.558221e-05           NaN\n",
       "1                               grade:A -6.795707e-06  9.999356e-01\n",
       "2                               grade:B -5.294391e-05  9.993798e-01\n",
       "3                               grade:C -1.123227e-04  9.986388e-01\n",
       "4                               grade:D  2.304027e-05  9.997320e-01\n",
       "5                               grade:E  1.497238e-05  9.998421e-01\n",
       "6                               grade:F  6.745851e-05  9.993811e-01\n",
       "7               home_ownership:MORTGAGE -3.149680e-05  9.990085e-01\n",
       "8                   home_ownership:NONE  8.221090e-07  9.999992e-01\n",
       "9                  home_ownership:OTHER  7.256036e-07  9.999985e-01\n",
       "10                   home_ownership:OWN -1.885950e-06  9.999635e-01\n",
       "11     verification_status:Not Verified -3.758344e-05  9.989990e-01\n",
       "12  verification_status:Source Verified -1.552916e-04  9.954469e-01\n",
       "13                          purpose:car  1.246058e-05  9.999143e-01\n",
       "14           purpose:debt_consolidation -1.291673e-04  9.965982e-01\n",
       "15                  purpose:educational  1.677313e-06  9.999953e-01\n",
       "16             purpose:home_improvement  1.009488e-05  9.998587e-01\n",
       "17                        purpose:house  1.067563e-05  9.999401e-01\n",
       "18               purpose:major_purchase  1.862645e-05  9.998275e-01\n",
       "19                      purpose:medical  2.171841e-06  9.999836e-01\n",
       "20                       purpose:moving  3.829696e-06  9.999744e-01\n",
       "21                        purpose:other  4.115872e-05  9.993759e-01\n",
       "22             purpose:renewable_energy  2.980485e-06  9.999930e-01\n",
       "23               purpose:small_business  4.792752e-05  9.994621e-01\n",
       "24                     purpose:vacation  4.403543e-06  9.999756e-01\n",
       "25                      purpose:wedding  1.079062e-05  9.999411e-01\n",
       "26                initial_list_status:w -7.045037e-04  9.791259e-01\n",
       "27                             term_int -6.283961e-04  8.015743e-01\n",
       "28                       emp_length_int -2.398829e-04  9.375519e-01\n",
       "29                   mths_since_issue_d  1.717075e-02  5.344334e-87\n",
       "30          mths_since_earliest_cr_line -1.549782e-03  1.380369e-26\n",
       "31                          funded_amnt  2.062960e-05  3.843097e-02\n",
       "32                             int_rate  6.381448e-04  9.124077e-01\n",
       "33                          installment -2.941314e-04  3.423448e-01\n",
       "34                           annual_inc -1.897291e-07  5.763106e-01\n",
       "35                                  dti -4.488850e-03  5.797179e-03\n",
       "36                          delinq_2yrs -5.957514e-05  9.967562e-01\n",
       "37                       inq_last_6mths  2.088708e-04  9.822345e-01\n",
       "38               mths_since_last_delinq -7.701858e-04  1.284782e-01\n",
       "39               mths_since_last_record -4.352028e-03  1.639999e-12\n",
       "40                             open_acc -1.756136e-03  5.921493e-01\n",
       "41                              pub_rec -7.953811e-05  9.983910e-01\n",
       "42                            total_acc -4.630170e-03  1.399017e-03\n",
       "43                       acc_now_delinq  2.686354e-06  9.999878e-01\n",
       "44                     total_rev_hi_lim -6.439478e-06  5.925663e-20"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "# Creates a dataframe with a column titled 'Feature name' and row values contained in the 'feature_name' variable.\n",
    "summary_table['Coefficients'] = np.transpose(reg_lgd_st_1.coef_)\n",
    "# Creates a new column in the dataframe, called 'Coefficients',\n",
    "# with row values the transposed coefficients from the 'LogisticRegression' object.\n",
    "summary_table.index = summary_table.index + 1\n",
    "# Increases the index of every row of the dataframe with 1.\n",
    "summary_table.loc[0] = ['Intercept', reg_lgd_st_1.intercept_[0]]\n",
    "# Assigns values of the row with index 0 of the dataframe.\n",
    "summary_table = summary_table.sort_index()\n",
    "# Sorts the dataframe by index.\n",
    "p_values = reg_lgd_st_1.p_values\n",
    "# We take the result of the newly added method 'p_values' and store it in a variable 'p_values'.\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "# We add the value 'NaN' in the beginning of the variable with p-values.\n",
    "summary_table['p_values'] = p_values\n",
    "# In the 'summary_table' dataframe, we add a new column, called 'p_values', containing the values from the 'p_values' variable.\n",
    "summary_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_1_test = lgd_inputs_stage_1_test[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_1_test = lgd_inputs_stage_1_test.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd_stage_1 = reg_lgd_st_1.model.predict(lgd_inputs_stage_1_test)\n",
    "# Calculates the predicted values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, ..., 0, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_lgd_stage_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_proba_lgd_stage_1 = reg_lgd_st_1.model.predict_proba(lgd_inputs_stage_1_test)\n",
    "# Calculates the predicted probability values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.3907724 , 0.6092276 ],\n",
       "       [0.38899655, 0.61100345],\n",
       "       [0.5450988 , 0.4549012 ],\n",
       "       ...,\n",
       "       [0.52010829, 0.47989171],\n",
       "       [0.41123402, 0.58876598],\n",
       "       [0.45310323, 0.54689677]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_proba_lgd_stage_1\n",
    "# This is an array of arrays of predicted class probabilities for all classes.\n",
    "# In this case, the first value of every sub-array is the probability for the observation to belong to the first class, i.e. 0,\n",
    "# and the second value is the probability for the observation to belong to the first class, i.e. 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_proba_lgd_stage_1 = y_hat_test_proba_lgd_stage_1[: ][: , 1]\n",
    "# Here we take all the arrays in the array, and from each array, we take all rows, and only the element with index 1,\n",
    "# that is, the second element.\n",
    "# In other words, we take only the probabilities for being 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6092276 , 0.61100345, 0.4549012 , ..., 0.47989171, 0.58876598,\n",
       "       0.54689677])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_proba_lgd_stage_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_1_test_temp = lgd_targets_stage_1_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_1_test_temp.reset_index(drop = True, inplace = True)\n",
    "# We reset the index of a dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_actual_predicted_probs = pd.concat([lgd_targets_stage_1_test_temp, pd.DataFrame(y_hat_test_proba_lgd_stage_1)], axis = 1)\n",
    "# Concatenates two dataframes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_actual_predicted_probs.columns = ['lgd_targets_stage_1_test', 'y_hat_test_proba_lgd_stage_1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_actual_predicted_probs.index = lgd_inputs_stage_1_test.index\n",
    "# Makes the index of one dataframe equal to the index of another dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>lgd_targets_stage_1_test</th>\n",
       "      <th>y_hat_test_proba_lgd_stage_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21362</th>\n",
       "      <td>1</td>\n",
       "      <td>0.609228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8768</th>\n",
       "      <td>1</td>\n",
       "      <td>0.611003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11903</th>\n",
       "      <td>0</td>\n",
       "      <td>0.454901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42973</th>\n",
       "      <td>1</td>\n",
       "      <td>0.547883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29933</th>\n",
       "      <td>0</td>\n",
       "      <td>0.415082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       lgd_targets_stage_1_test  y_hat_test_proba_lgd_stage_1\n",
       "21362                         1                      0.609228\n",
       "8768                          1                      0.611003\n",
       "11903                         0                      0.454901\n",
       "42973                         1                      0.547883\n",
       "29933                         0                      0.415082"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_actual_predicted_probs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the Аccuracy of the Мodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "tr = 0.5\n",
    "# We create a new column with an indicator,\n",
    "# where every observation that has predicted probability greater than the threshold has a value of 1,\n",
    "# and every observation that has predicted probability lower than the threshold has a value of 0.\n",
    "df_actual_predicted_probs['y_hat_test_lgd_stage_1'] = np.where(df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'] > tr, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>998</td>\n",
       "      <td>2764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>692</td>\n",
       "      <td>4194</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted    0     1\n",
       "Actual              \n",
       "0          998  2764\n",
       "1          692  4194"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_lgd_stage_1'], rownames = ['Actual'], colnames = ['Predicted'])\n",
    "# Creates a cross-table where the actual values are displayed by rows and the predicted values by columns.\n",
    "# This table is known as a Confusion Matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.115402</td>\n",
       "      <td>0.319611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.080019</td>\n",
       "      <td>0.484968</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted         0         1\n",
       "Actual                       \n",
       "0          0.115402  0.319611\n",
       "1          0.080019  0.484968"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_lgd_stage_1'], rownames = ['Actual'], colnames = ['Predicted']) / df_actual_predicted_probs.shape[0]\n",
    "# Here we divide each value of the table by the total number of observations,\n",
    "# thus getting percentages, or, rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6003700277520814"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(pd.crosstab(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_lgd_stage_1'], rownames = ['Actual'], colnames = ['Predicted']) / df_actual_predicted_probs.shape[0]).iloc[0, 0] + (pd.crosstab(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_lgd_stage_1'], rownames = ['Actual'], colnames = ['Predicted']) / df_actual_predicted_probs.shape[0]).iloc[1, 1]\n",
    "# Here we calculate Accuracy of the model, which is the sum of the diagonal rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve, roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>lgd_targets_stage_1_test</th>\n",
       "      <th>y_hat_test_proba_lgd_stage_1</th>\n",
       "      <th>y_hat_test_lgd_stage_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21362</th>\n",
       "      <td>1</td>\n",
       "      <td>0.609228</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8768</th>\n",
       "      <td>1</td>\n",
       "      <td>0.611003</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11903</th>\n",
       "      <td>0</td>\n",
       "      <td>0.454901</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42973</th>\n",
       "      <td>1</td>\n",
       "      <td>0.547883</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29933</th>\n",
       "      <td>0</td>\n",
       "      <td>0.415082</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       lgd_targets_stage_1_test  y_hat_test_proba_lgd_stage_1  \\\n",
       "21362                         1                      0.609228   \n",
       "8768                          1                      0.611003   \n",
       "11903                         0                      0.454901   \n",
       "42973                         1                      0.547883   \n",
       "29933                         0                      0.415082   \n",
       "\n",
       "       y_hat_test_lgd_stage_1  \n",
       "21362                       1  \n",
       "8768                        1  \n",
       "11903                       0  \n",
       "42973                       1  \n",
       "29933                       0  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_actual_predicted_probs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "fpr, tpr, thresholds = roc_curve(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'])\n",
    "# Returns the Receiver Operating Characteristic (ROC) Curve from a set of actual values and their predicted probabilities.\n",
    "# As a result, we get three arrays: the false positive rates, the true positive rates, and the thresholds.\n",
    "# we store each of the three arrays in a separate variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ROC curve')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(fpr, tpr)\n",
    "# We plot the false positive rate along the x-axis and the true positive rate along the y-axis,\n",
    "# thus plotting the ROC curve.\n",
    "plt.plot(fpr, fpr, linestyle = '--', color = 'k')\n",
    "# We plot a seconary diagonal line, with dashed line style and black color.\n",
    "plt.xlabel('False positive rate')\n",
    "# We name the x-axis \"False positive rate\".\n",
    "plt.ylabel('True positive rate')\n",
    "# We name the x-axis \"True positive rate\".\n",
    "plt.title('ROC curve')\n",
    "# We name the graph \"ROC curve\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6453480122986985"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AUROC = roc_auc_score(df_actual_predicted_probs['lgd_targets_stage_1_test'], df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'])\n",
    "# Calculates the Area Under the Receiver Operating Characteristic Curve (AUROC)\n",
    "# from a set of actual values and their predicted probabilities.\n",
    "AUROC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saving the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump(reg_lgd_st_1, open('models/lgd_model_stage_1.sav', 'wb'))\n",
    "# Here we export our model to a 'SAV' file with file name 'lgd_model_stage_1.sav'."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stage 2 – Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_stage_2_data = loan_data_defaults[loan_data_defaults['recovery_rate_0_1'] == 1]\n",
    "# Here we take only rows where the original recovery rate variable is greater than one,\n",
    "# i.e. where the indicator variable we created is equal to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LGD model stage 2 datasets: how much more than 0 is the recovery rate\n",
    "lgd_inputs_stage_2_train, lgd_inputs_stage_2_test, lgd_targets_stage_2_train, lgd_targets_stage_2_test = train_test_split(lgd_stage_2_data.drop(['good_bad', 'recovery_rate','recovery_rate_0_1', 'CCF'], axis = 1), lgd_stage_2_data['recovery_rate'], test_size = 0.2, random_state = 42)\n",
    "# Takes a set of inputs and a set of targets as arguments. Splits the inputs and the targets into four dataframes:\n",
    "# Inputs - Train, Inputs - Test, Targets - Train, Targets - Test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since the p-values are obtained through certain statistics, we need the 'stat' module from scipy.stats\n",
    "import scipy.stats as stat\n",
    "\n",
    "# Since we are using an object oriented language such as Python, we can simply define our own \n",
    "# LinearRegression class (the same one from sklearn)\n",
    "# By typing the code below we will ovewrite a part of the class with one that includes p-values\n",
    "# Here's the full source code of the ORIGINAL class: https://github.com/scikit-learn/scikit-learn/blob/7b136e9/sklearn/linear_model/base.py#L362\n",
    "\n",
    "\n",
    "class LinearRegression(linear_model.LinearRegression):\n",
    "    \"\"\"\n",
    "    LinearRegression class after sklearn's, but calculate t-statistics\n",
    "    and p-values for model coefficients (betas).\n",
    "    Additional attributes available after .fit()\n",
    "    are `t` and `p` which are of the shape (y.shape[1], X.shape[1])\n",
    "    which is (n_features, n_coefs)\n",
    "    This class sets the intercept to 0 by default, since usually we include it\n",
    "    in X.\n",
    "    \"\"\"\n",
    "    \n",
    "    # nothing changes in __init__\n",
    "    def __init__(self, fit_intercept=True, normalize=False, copy_X=True,\n",
    "                 n_jobs=1):\n",
    "        self.fit_intercept = fit_intercept\n",
    "        self.normalize = normalize\n",
    "        self.copy_X = copy_X\n",
    "        self.n_jobs = n_jobs\n",
    "\n",
    "    \n",
    "    def fit(self, X, y, n_jobs=1):\n",
    "        self = super(LinearRegression, self).fit(X, y, n_jobs)\n",
    "        \n",
    "        # Calculate SSE (sum of squared errors)\n",
    "        # and SE (standard error)\n",
    "        sse = np.sum((self.predict(X) - y) ** 2, axis=0) / float(X.shape[0] - X.shape[1])\n",
    "        se = np.array([np.sqrt(np.diagonal(sse * np.linalg.inv(np.dot(X.T, X))))])\n",
    "\n",
    "        # compute the t-statistic for each feature\n",
    "        self.t = self.coef_ / se\n",
    "        # find the p-value for each feature\n",
    "        self.p = np.squeeze(2 * (1 - stat.t.cdf(np.abs(self.t), y.shape[0] - X.shape[1])))\n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_2_train = lgd_inputs_stage_2_train[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_2_train = lgd_inputs_stage_2_train.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_lgd_st_2 = LinearRegression()\n",
    "# We create an instance of an object from the 'LogisticRegression' class.\n",
    "reg_lgd_st_2.fit(lgd_inputs_stage_2_train, lgd_targets_stage_2_train)\n",
    "# Estimates the coefficients of the object from the 'LogisticRegression' class\n",
    "# with inputs (independent variables) contained in the first dataframe\n",
    "# and targets (dependent variables) contained in the second dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_name = lgd_inputs_stage_2_train.columns.values\n",
    "# Stores the names of the columns of a dataframe in a variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>2.406858e-01</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-6.826892e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-5.083556e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-3.748066e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>-2.717310e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>grade:E</td>\n",
       "      <td>-1.315941e-02</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>grade:F</td>\n",
       "      <td>-5.260168e-03</td>\n",
       "      <td>0.275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>home_ownership:MORTGAGE</td>\n",
       "      <td>2.832212e-03</td>\n",
       "      <td>0.061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>home_ownership:NONE</td>\n",
       "      <td>1.459035e-01</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>home_ownership:OTHER</td>\n",
       "      <td>-9.475922e-03</td>\n",
       "      <td>0.644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>home_ownership:OWN</td>\n",
       "      <td>5.000678e-03</td>\n",
       "      <td>0.040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>verification_status:Not Verified</td>\n",
       "      <td>1.056585e-03</td>\n",
       "      <td>0.553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>verification_status:Source Verified</td>\n",
       "      <td>-1.009915e-03</td>\n",
       "      <td>0.535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>purpose:car</td>\n",
       "      <td>-2.995960e-03</td>\n",
       "      <td>0.634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>purpose:debt_consolidation</td>\n",
       "      <td>8.206319e-05</td>\n",
       "      <td>0.965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>purpose:educational</td>\n",
       "      <td>7.625467e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>purpose:home_improvement</td>\n",
       "      <td>-3.702374e-03</td>\n",
       "      <td>0.273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>purpose:house</td>\n",
       "      <td>-3.786803e-03</td>\n",
       "      <td>0.620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>purpose:major_purchase</td>\n",
       "      <td>2.914439e-03</td>\n",
       "      <td>0.538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>purpose:medical</td>\n",
       "      <td>1.078825e-02</td>\n",
       "      <td>0.074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>purpose:moving</td>\n",
       "      <td>1.398692e-02</td>\n",
       "      <td>0.039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>purpose:other</td>\n",
       "      <td>4.841345e-03</td>\n",
       "      <td>0.109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>purpose:renewable_energy</td>\n",
       "      <td>2.420645e-02</td>\n",
       "      <td>0.142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>purpose:small_business</td>\n",
       "      <td>6.212343e-04</td>\n",
       "      <td>0.869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>purpose:vacation</td>\n",
       "      <td>-3.002398e-03</td>\n",
       "      <td>0.731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>purpose:wedding</td>\n",
       "      <td>2.034853e-02</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>initial_list_status:w</td>\n",
       "      <td>1.464671e-02</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>term_int</td>\n",
       "      <td>3.316229e-04</td>\n",
       "      <td>0.020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>emp_length_int</td>\n",
       "      <td>8.727462e-05</td>\n",
       "      <td>0.635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>mths_since_issue_d</td>\n",
       "      <td>-1.521649e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>mths_since_earliest_cr_line</td>\n",
       "      <td>3.418678e-05</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>funded_amnt</td>\n",
       "      <td>-2.186999e-07</td>\n",
       "      <td>0.699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>int_rate</td>\n",
       "      <td>-2.544714e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>installment</td>\n",
       "      <td>-1.037621e-05</td>\n",
       "      <td>0.557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>annual_inc</td>\n",
       "      <td>6.389841e-08</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>dti</td>\n",
       "      <td>1.775655e-04</td>\n",
       "      <td>0.069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>delinq_2yrs</td>\n",
       "      <td>1.757943e-03</td>\n",
       "      <td>0.050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>inq_last_6mths</td>\n",
       "      <td>1.274095e-03</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>mths_since_last_delinq</td>\n",
       "      <td>-1.094747e-06</td>\n",
       "      <td>0.971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>mths_since_last_record</td>\n",
       "      <td>-5.558083e-05</td>\n",
       "      <td>0.181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>open_acc</td>\n",
       "      <td>-1.196505e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>pub_rec</td>\n",
       "      <td>3.447322e-03</td>\n",
       "      <td>0.208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>total_acc</td>\n",
       "      <td>4.766629e-04</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>acc_now_delinq</td>\n",
       "      <td>4.278394e-03</td>\n",
       "      <td>0.658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>total_rev_hi_lim</td>\n",
       "      <td>2.263456e-07</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Feature name  Coefficients  p_values\n",
       "0                             Intercept  2.406858e-01       NaN\n",
       "1                               grade:A -6.826892e-02     0.000\n",
       "2                               grade:B -5.083556e-02     0.000\n",
       "3                               grade:C -3.748066e-02     0.000\n",
       "4                               grade:D -2.717310e-02     0.000\n",
       "5                               grade:E -1.315941e-02     0.002\n",
       "6                               grade:F -5.260168e-03     0.275\n",
       "7               home_ownership:MORTGAGE  2.832212e-03     0.061\n",
       "8                   home_ownership:NONE  1.459035e-01     0.000\n",
       "9                  home_ownership:OTHER -9.475922e-03     0.644\n",
       "10                   home_ownership:OWN  5.000678e-03     0.040\n",
       "11     verification_status:Not Verified  1.056585e-03     0.553\n",
       "12  verification_status:Source Verified -1.009915e-03     0.535\n",
       "13                          purpose:car -2.995960e-03     0.634\n",
       "14           purpose:debt_consolidation  8.206319e-05     0.965\n",
       "15                  purpose:educational  7.625467e-02     0.000\n",
       "16             purpose:home_improvement -3.702374e-03     0.273\n",
       "17                        purpose:house -3.786803e-03     0.620\n",
       "18               purpose:major_purchase  2.914439e-03     0.538\n",
       "19                      purpose:medical  1.078825e-02     0.074\n",
       "20                       purpose:moving  1.398692e-02     0.039\n",
       "21                        purpose:other  4.841345e-03     0.109\n",
       "22             purpose:renewable_energy  2.420645e-02     0.142\n",
       "23               purpose:small_business  6.212343e-04     0.869\n",
       "24                     purpose:vacation -3.002398e-03     0.731\n",
       "25                      purpose:wedding  2.034853e-02     0.006\n",
       "26                initial_list_status:w  1.464671e-02     0.000\n",
       "27                             term_int  3.316229e-04     0.020\n",
       "28                       emp_length_int  8.727462e-05     0.635\n",
       "29                   mths_since_issue_d -1.521649e-03     0.000\n",
       "30          mths_since_earliest_cr_line  3.418678e-05     0.000\n",
       "31                          funded_amnt -2.186999e-07     0.699\n",
       "32                             int_rate -2.544714e-03     0.000\n",
       "33                          installment -1.037621e-05     0.557\n",
       "34                           annual_inc  6.389841e-08     0.001\n",
       "35                                  dti  1.775655e-04     0.069\n",
       "36                          delinq_2yrs  1.757943e-03     0.050\n",
       "37                       inq_last_6mths  1.274095e-03     0.018\n",
       "38               mths_since_last_delinq -1.094747e-06     0.971\n",
       "39               mths_since_last_record -5.558083e-05     0.181\n",
       "40                             open_acc -1.196505e-03     0.000\n",
       "41                              pub_rec  3.447322e-03     0.208\n",
       "42                            total_acc  4.766629e-04     0.000\n",
       "43                       acc_now_delinq  4.278394e-03     0.658\n",
       "44                     total_rev_hi_lim  2.263456e-07     0.000"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "# Creates a dataframe with a column titled 'Feature name' and row values contained in the 'feature_name' variable.\n",
    "summary_table['Coefficients'] = np.transpose(reg_lgd_st_2.coef_)\n",
    "# Creates a new column in the dataframe, called 'Coefficients',\n",
    "# with row values the transposed coefficients from the 'LogisticRegression' object.\n",
    "summary_table.index = summary_table.index + 1\n",
    "# Increases the index of every row of the dataframe with 1.\n",
    "summary_table.loc[0] = ['Intercept', reg_lgd_st_2.intercept_]\n",
    "# Assigns values of the row with index 0 of the dataframe.\n",
    "summary_table = summary_table.sort_index()\n",
    "# Sorts the dataframe by index.\n",
    "p_values = reg_lgd_st_2.p\n",
    "# We take the result of the newly added method 'p_values' and store it in a variable 'p_values'.\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "# We add the value 'NaN' in the beginning of the variable with p-values.\n",
    "summary_table['p_values'] = p_values.round(3)\n",
    "# In the 'summary_table' dataframe, we add a new column, called 'p_values', containing the values from the 'p_values' variable.\n",
    "summary_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stage 2 – Linear Regression Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_2_test = lgd_inputs_stage_2_test[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_2_test = lgd_inputs_stage_2_test.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['grade:A', 'grade:B', 'grade:C', 'grade:D', 'grade:E', 'grade:F',\n",
       "       'home_ownership:MORTGAGE', 'home_ownership:NONE',\n",
       "       'home_ownership:OTHER', 'home_ownership:OWN',\n",
       "       'verification_status:Not Verified',\n",
       "       'verification_status:Source Verified', 'purpose:car',\n",
       "       'purpose:debt_consolidation', 'purpose:educational',\n",
       "       'purpose:home_improvement', 'purpose:house',\n",
       "       'purpose:major_purchase', 'purpose:medical', 'purpose:moving',\n",
       "       'purpose:other', 'purpose:renewable_energy',\n",
       "       'purpose:small_business', 'purpose:vacation', 'purpose:wedding',\n",
       "       'initial_list_status:w', 'term_int', 'emp_length_int',\n",
       "       'mths_since_issue_d', 'mths_since_earliest_cr_line', 'funded_amnt',\n",
       "       'int_rate', 'installment', 'annual_inc', 'dti', 'delinq_2yrs',\n",
       "       'inq_last_6mths', 'mths_since_last_delinq',\n",
       "       'mths_since_last_record', 'open_acc', 'pub_rec', 'total_acc',\n",
       "       'acc_now_delinq', 'total_rev_hi_lim'], dtype=object)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgd_inputs_stage_2_test.columns.values\n",
    "# Calculates the predicted values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd_stage_2 = reg_lgd_st_2.predict(lgd_inputs_stage_2_test)\n",
    "# Calculates the predicted values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_2_test_temp = lgd_targets_stage_2_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_2_test_temp = lgd_targets_stage_2_test_temp.reset_index(drop = True)\n",
    "# We reset the index of a dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>recovery_rate</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>recovery_rate</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.307996</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               recovery_rate         0\n",
       "recovery_rate       1.000000  0.307996\n",
       "0                   0.307996  1.000000"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([lgd_targets_stage_2_test_temp, pd.DataFrame(y_hat_test_lgd_stage_2)], axis = 1).corr()\n",
    "# We calculate the correlation between actual and predicted values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='recovery_rate', ylabel='Density'>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.distplot(lgd_targets_stage_2_test - y_hat_test_lgd_stage_2)\n",
    "# We plot the distribution of the residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump(reg_lgd_st_2, open('models/lgd_model_stage_2.sav', 'wb'))\n",
    "# Here we export our model to a 'SAV' file with file name 'lgd_model_stage_1.sav'."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combining Stage 1 and Stage 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd_stage_2_all = reg_lgd_st_2.predict(lgd_inputs_stage_1_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.1193906 , 0.09605635, 0.13367631, ..., 0.12078611, 0.11587422,\n",
       "       0.15667447])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_lgd_stage_2_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd = y_hat_test_lgd_stage_1 * y_hat_test_lgd_stage_2_all\n",
    "# Here we combine the predictions of the models from the two stages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.087135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.050119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.007634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.063962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.101121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.123726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.236973</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.087135\n",
       "std       0.050119\n",
       "min      -0.007634\n",
       "25%       0.063962\n",
       "50%       0.101121\n",
       "75%       0.123726\n",
       "max       0.236973"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_lgd).describe()\n",
    "# Shows some descriptive statisics for the values of a column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd = np.where(y_hat_test_lgd < 0, 0, y_hat_test_lgd)\n",
    "y_hat_test_lgd = np.where(y_hat_test_lgd > 1, 1, y_hat_test_lgd)\n",
    "# We set predicted values that are greater than 1 to 1 and predicted values that are less than 0 to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.087137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.050115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.063962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.101121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.123726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.236973</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.087137\n",
       "std       0.050115\n",
       "min       0.000000\n",
       "25%       0.063962\n",
       "50%       0.101121\n",
       "75%       0.123726\n",
       "max       0.236973"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_lgd).describe()\n",
    "# Shows some descriptive statisics for the values of a column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EAD Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Estimation and Interpretation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# EAD model datasets\n",
    "ead_inputs_train, ead_inputs_test, ead_targets_train, ead_targets_test = train_test_split(loan_data_defaults.drop(['good_bad', 'recovery_rate','recovery_rate_0_1', 'CCF'], axis = 1), loan_data_defaults['CCF'], test_size = 0.2, random_state = 42)\n",
    "# Takes a set of inputs and a set of targets as arguments. Splits the inputs and the targets into four dataframes:\n",
    "# Inputs - Train, Inputs - Test, Targets - Train, Targets - Test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Unnamed: 0', 'Unnamed: 0.1', 'Unnamed: 0.1.1', 'id', 'member_id',\n",
       "       'loan_amnt', 'funded_amnt', 'funded_amnt_inv', 'term', 'int_rate',\n",
       "       'installment', 'grade', 'sub_grade', 'emp_title', 'emp_length',\n",
       "       'home_ownership', 'annual_inc', 'verification_status', 'issue_d',\n",
       "       'loan_status', 'pymnt_plan', 'url', 'desc', 'purpose', 'title',\n",
       "       'zip_code', 'addr_state', 'dti', 'delinq_2yrs', 'earliest_cr_line',\n",
       "       'inq_last_6mths', 'mths_since_last_delinq',\n",
       "       'mths_since_last_record', 'open_acc', 'pub_rec', 'revol_bal',\n",
       "       'revol_util', 'total_acc', 'initial_list_status', 'out_prncp',\n",
       "       'out_prncp_inv', 'total_pymnt', 'total_pymnt_inv',\n",
       "       'total_rec_prncp', 'total_rec_int', 'total_rec_late_fee',\n",
       "       'recoveries', 'collection_recovery_fee', 'last_pymnt_d',\n",
       "       'last_pymnt_amnt', 'next_pymnt_d', 'last_credit_pull_d',\n",
       "       'collections_12_mths_ex_med', 'mths_since_last_major_derog',\n",
       "       'policy_code', 'application_type', 'annual_inc_joint', 'dti_joint',\n",
       "       'verification_status_joint', 'acc_now_delinq', 'tot_coll_amt',\n",
       "       'tot_cur_bal', 'open_acc_6m', 'open_il_6m', 'open_il_12m',\n",
       "       'open_il_24m', 'mths_since_rcnt_il', 'total_bal_il', 'il_util',\n",
       "       'open_rv_12m', 'open_rv_24m', 'max_bal_bc', 'all_util',\n",
       "       'total_rev_hi_lim', 'inq_fi', 'total_cu_tl', 'inq_last_12m',\n",
       "       'emp_length_int', 'earliest_cr_line_date',\n",
       "       'mths_since_earliest_cr_line', 'term_int', 'issue_d_date',\n",
       "       'mths_since_issue_d', 'grade:A', 'grade:B', 'grade:C', 'grade:D',\n",
       "       'grade:E', 'grade:F', 'grade:G', 'sub_grade:A1', 'sub_grade:A2',\n",
       "       'sub_grade:A3', 'sub_grade:A4', 'sub_grade:A5', 'sub_grade:B1',\n",
       "       'sub_grade:B2', 'sub_grade:B3', 'sub_grade:B4', 'sub_grade:B5',\n",
       "       'sub_grade:C1', 'sub_grade:C2', 'sub_grade:C3', 'sub_grade:C4',\n",
       "       'sub_grade:C5', 'sub_grade:D1', 'sub_grade:D2', 'sub_grade:D3',\n",
       "       'sub_grade:D4', 'sub_grade:D5', 'sub_grade:E1', 'sub_grade:E2',\n",
       "       'sub_grade:E3', 'sub_grade:E4', 'sub_grade:E5', 'sub_grade:F1',\n",
       "       'sub_grade:F2', 'sub_grade:F3', 'sub_grade:F4', 'sub_grade:F5',\n",
       "       'sub_grade:G1', 'sub_grade:G2', 'sub_grade:G3', 'sub_grade:G4',\n",
       "       'sub_grade:G5', 'home_ownership:ANY', 'home_ownership:MORTGAGE',\n",
       "       'home_ownership:NONE', 'home_ownership:OTHER',\n",
       "       'home_ownership:OWN', 'home_ownership:RENT',\n",
       "       'verification_status:Not Verified',\n",
       "       'verification_status:Source Verified',\n",
       "       'verification_status:Verified', 'loan_status:Charged Off',\n",
       "       'loan_status:Current', 'loan_status:Default',\n",
       "       'loan_status:Does not meet the credit policy. Status:Charged Off',\n",
       "       'loan_status:Does not meet the credit policy. Status:Fully Paid',\n",
       "       'loan_status:Fully Paid', 'loan_status:In Grace Period',\n",
       "       'loan_status:Late (16-30 days)', 'loan_status:Late (31-120 days)',\n",
       "       'purpose:car', 'purpose:credit_card', 'purpose:debt_consolidation',\n",
       "       'purpose:educational', 'purpose:home_improvement', 'purpose:house',\n",
       "       'purpose:major_purchase', 'purpose:medical', 'purpose:moving',\n",
       "       'purpose:other', 'purpose:renewable_energy',\n",
       "       'purpose:small_business', 'purpose:vacation', 'purpose:wedding',\n",
       "       'addr_state:AK', 'addr_state:AL', 'addr_state:AR', 'addr_state:AZ',\n",
       "       'addr_state:CA', 'addr_state:CO', 'addr_state:CT', 'addr_state:DC',\n",
       "       'addr_state:DE', 'addr_state:FL', 'addr_state:GA', 'addr_state:HI',\n",
       "       'addr_state:IA', 'addr_state:ID', 'addr_state:IL', 'addr_state:IN',\n",
       "       'addr_state:KS', 'addr_state:KY', 'addr_state:LA', 'addr_state:MA',\n",
       "       'addr_state:MD', 'addr_state:ME', 'addr_state:MI', 'addr_state:MN',\n",
       "       'addr_state:MO', 'addr_state:MS', 'addr_state:MT', 'addr_state:NC',\n",
       "       'addr_state:NE', 'addr_state:NH', 'addr_state:NJ', 'addr_state:NM',\n",
       "       'addr_state:NV', 'addr_state:NY', 'addr_state:OH', 'addr_state:OK',\n",
       "       'addr_state:OR', 'addr_state:PA', 'addr_state:RI', 'addr_state:SC',\n",
       "       'addr_state:SD', 'addr_state:TN', 'addr_state:TX', 'addr_state:UT',\n",
       "       'addr_state:VA', 'addr_state:VT', 'addr_state:WA', 'addr_state:WI',\n",
       "       'addr_state:WV', 'addr_state:WY', 'initial_list_status:f',\n",
       "       'initial_list_status:w'], dtype=object)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ead_inputs_train.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(49, 5)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(features_all),len(features_reference_cat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_train = ead_inputs_train[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_train = ead_inputs_train.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_ead = LinearRegression()\n",
    "# We create an instance of an object from the 'LogisticRegression' class.\n",
    "reg_ead.fit(ead_inputs_train, ead_targets_train)\n",
    "# Estimates the coefficients of the object from the 'LogisticRegression' class\n",
    "# with inputs (independent variables) contained in the first dataframe\n",
    "# and targets (dependent variables) contained in the second dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_name = ead_inputs_train.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>1.109746e+00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-3.030033e-01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-2.364277e-01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-1.720232e-01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>-1.198470e-01</td>\n",
       "      <td>1.970424e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>grade:E</td>\n",
       "      <td>-6.768713e-02</td>\n",
       "      <td>1.918578e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>grade:F</td>\n",
       "      <td>-2.045907e-02</td>\n",
       "      <td>2.748685e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>home_ownership:MORTGAGE</td>\n",
       "      <td>-6.343341e-03</td>\n",
       "      <td>6.050271e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>home_ownership:NONE</td>\n",
       "      <td>-5.539064e-03</td>\n",
       "      <td>9.092582e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>home_ownership:OTHER</td>\n",
       "      <td>-2.426052e-03</td>\n",
       "      <td>6.436926e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>home_ownership:OWN</td>\n",
       "      <td>-1.619582e-03</td>\n",
       "      <td>3.963089e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>verification_status:Not Verified</td>\n",
       "      <td>5.339510e-05</td>\n",
       "      <td>5.528332e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>verification_status:Source Verified</td>\n",
       "      <td>8.967822e-03</td>\n",
       "      <td>5.354622e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>purpose:car</td>\n",
       "      <td>7.904787e-04</td>\n",
       "      <td>6.340924e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>purpose:debt_consolidation</td>\n",
       "      <td>1.264922e-02</td>\n",
       "      <td>9.646959e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>purpose:educational</td>\n",
       "      <td>9.643587e-02</td>\n",
       "      <td>5.368894e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>purpose:home_improvement</td>\n",
       "      <td>1.923044e-02</td>\n",
       "      <td>2.729279e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>purpose:house</td>\n",
       "      <td>1.607120e-02</td>\n",
       "      <td>6.200015e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>purpose:major_purchase</td>\n",
       "      <td>2.984917e-02</td>\n",
       "      <td>5.376877e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>purpose:medical</td>\n",
       "      <td>3.962479e-02</td>\n",
       "      <td>7.391253e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>purpose:moving</td>\n",
       "      <td>4.577630e-02</td>\n",
       "      <td>3.865040e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>purpose:other</td>\n",
       "      <td>3.706744e-02</td>\n",
       "      <td>1.089028e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>purpose:renewable_energy</td>\n",
       "      <td>7.212969e-02</td>\n",
       "      <td>1.423251e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>purpose:small_business</td>\n",
       "      <td>5.128674e-02</td>\n",
       "      <td>8.692143e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>purpose:vacation</td>\n",
       "      <td>1.874863e-02</td>\n",
       "      <td>7.311861e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>purpose:wedding</td>\n",
       "      <td>4.350522e-02</td>\n",
       "      <td>5.539872e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>initial_list_status:w</td>\n",
       "      <td>1.318126e-02</td>\n",
       "      <td>4.662937e-15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>term_int</td>\n",
       "      <td>4.551882e-03</td>\n",
       "      <td>2.042660e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>emp_length_int</td>\n",
       "      <td>-1.591478e-03</td>\n",
       "      <td>6.350976e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>mths_since_issue_d</td>\n",
       "      <td>-4.305274e-03</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>mths_since_earliest_cr_line</td>\n",
       "      <td>-3.634030e-05</td>\n",
       "      <td>1.087757e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>funded_amnt</td>\n",
       "      <td>2.212126e-06</td>\n",
       "      <td>6.992397e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>int_rate</td>\n",
       "      <td>-1.172652e-02</td>\n",
       "      <td>1.887379e-14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>installment</td>\n",
       "      <td>-6.865607e-05</td>\n",
       "      <td>5.568684e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>annual_inc</td>\n",
       "      <td>5.021816e-09</td>\n",
       "      <td>1.308549e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>dti</td>\n",
       "      <td>2.832769e-04</td>\n",
       "      <td>6.897933e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>delinq_2yrs</td>\n",
       "      <td>4.833234e-04</td>\n",
       "      <td>5.043858e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>inq_last_6mths</td>\n",
       "      <td>1.131678e-02</td>\n",
       "      <td>1.819423e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>mths_since_last_delinq</td>\n",
       "      <td>-1.965980e-04</td>\n",
       "      <td>9.708935e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>mths_since_last_record</td>\n",
       "      <td>-5.085639e-05</td>\n",
       "      <td>1.809354e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>open_acc</td>\n",
       "      <td>-2.142130e-03</td>\n",
       "      <td>1.365854e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>pub_rec</td>\n",
       "      <td>6.782062e-03</td>\n",
       "      <td>2.079574e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>total_acc</td>\n",
       "      <td>4.518110e-04</td>\n",
       "      <td>5.133116e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>acc_now_delinq</td>\n",
       "      <td>9.974801e-03</td>\n",
       "      <td>6.583494e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>total_rev_hi_lim</td>\n",
       "      <td>2.166527e-07</td>\n",
       "      <td>2.592628e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Feature name  Coefficients      p_values\n",
       "0                             Intercept  1.109746e+00           NaN\n",
       "1                               grade:A -3.030033e-01  0.000000e+00\n",
       "2                               grade:B -2.364277e-01  0.000000e+00\n",
       "3                               grade:C -1.720232e-01  0.000000e+00\n",
       "4                               grade:D -1.198470e-01  1.970424e-12\n",
       "5                               grade:E -6.768713e-02  1.918578e-03\n",
       "6                               grade:F -2.045907e-02  2.748685e-01\n",
       "7               home_ownership:MORTGAGE -6.343341e-03  6.050271e-02\n",
       "8                   home_ownership:NONE -5.539064e-03  9.092582e-05\n",
       "9                  home_ownership:OTHER -2.426052e-03  6.436926e-01\n",
       "10                   home_ownership:OWN -1.619582e-03  3.963089e-02\n",
       "11     verification_status:Not Verified  5.339510e-05  5.528332e-01\n",
       "12  verification_status:Source Verified  8.967822e-03  5.354622e-01\n",
       "13                          purpose:car  7.904787e-04  6.340924e-01\n",
       "14           purpose:debt_consolidation  1.264922e-02  9.646959e-01\n",
       "15                  purpose:educational  9.643587e-02  5.368894e-09\n",
       "16             purpose:home_improvement  1.923044e-02  2.729279e-01\n",
       "17                        purpose:house  1.607120e-02  6.200015e-01\n",
       "18               purpose:major_purchase  2.984917e-02  5.376877e-01\n",
       "19                      purpose:medical  3.962479e-02  7.391253e-02\n",
       "20                       purpose:moving  4.577630e-02  3.865040e-02\n",
       "21                        purpose:other  3.706744e-02  1.089028e-01\n",
       "22             purpose:renewable_energy  7.212969e-02  1.423251e-01\n",
       "23               purpose:small_business  5.128674e-02  8.692143e-01\n",
       "24                     purpose:vacation  1.874863e-02  7.311861e-01\n",
       "25                      purpose:wedding  4.350522e-02  5.539872e-03\n",
       "26                initial_list_status:w  1.318126e-02  4.662937e-15\n",
       "27                             term_int  4.551882e-03  2.042660e-02\n",
       "28                       emp_length_int -1.591478e-03  6.350976e-01\n",
       "29                   mths_since_issue_d -4.305274e-03  0.000000e+00\n",
       "30          mths_since_earliest_cr_line -3.634030e-05  1.087757e-04\n",
       "31                          funded_amnt  2.212126e-06  6.992397e-01\n",
       "32                             int_rate -1.172652e-02  1.887379e-14\n",
       "33                          installment -6.865607e-05  5.568684e-01\n",
       "34                           annual_inc  5.021816e-09  1.308549e-03\n",
       "35                                  dti  2.832769e-04  6.897933e-02\n",
       "36                          delinq_2yrs  4.833234e-04  5.043858e-02\n",
       "37                       inq_last_6mths  1.131678e-02  1.819423e-02\n",
       "38               mths_since_last_delinq -1.965980e-04  9.708935e-01\n",
       "39               mths_since_last_record -5.085639e-05  1.809354e-01\n",
       "40                             open_acc -2.142130e-03  1.365854e-09\n",
       "41                              pub_rec  6.782062e-03  2.079574e-01\n",
       "42                            total_acc  4.518110e-04  5.133116e-08\n",
       "43                       acc_now_delinq  9.974801e-03  6.583494e-01\n",
       "44                     total_rev_hi_lim  2.166527e-07  2.592628e-08"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "# Creates a dataframe with a column titled 'Feature name' and row values contained in the 'feature_name' variable.\n",
    "summary_table['Coefficients'] = np.transpose(reg_ead.coef_)\n",
    "# Creates a new column in the dataframe, called 'Coefficients',\n",
    "# with row values the transposed coefficients from the 'LogisticRegression' object.\n",
    "summary_table.index = summary_table.index + 1\n",
    "# Increases the index of every row of the dataframe with 1.\n",
    "summary_table.loc[0] = ['Intercept', reg_ead.intercept_]\n",
    "# Assigns values of the row with index 0 of the dataframe.\n",
    "summary_table = summary_table.sort_index()\n",
    "# Sorts the dataframe by index.\n",
    "p_values = reg_lgd_st_2.p\n",
    "# We take the result of the newly added method 'p_values' and store it in a variable 'p_values'.\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "# We add the value 'NaN' in the beginning of the variable with p-values.\n",
    "summary_table['p_values'] = p_values\n",
    "# In the 'summary_table' dataframe, we add a new column, called 'p_values', containing the values from the 'p_values' variable.\n",
    "summary_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_test = ead_inputs_test[features_all]\n",
    "# Here we keep only the variables we need for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_test = ead_inputs_test.drop(features_reference_cat, axis = 1)\n",
    "# Here we remove the dummy variable reference categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['grade:A', 'grade:B', 'grade:C', 'grade:D', 'grade:E', 'grade:F',\n",
       "       'home_ownership:MORTGAGE', 'home_ownership:NONE',\n",
       "       'home_ownership:OTHER', 'home_ownership:OWN',\n",
       "       'verification_status:Not Verified',\n",
       "       'verification_status:Source Verified', 'purpose:car',\n",
       "       'purpose:debt_consolidation', 'purpose:educational',\n",
       "       'purpose:home_improvement', 'purpose:house',\n",
       "       'purpose:major_purchase', 'purpose:medical', 'purpose:moving',\n",
       "       'purpose:other', 'purpose:renewable_energy',\n",
       "       'purpose:small_business', 'purpose:vacation', 'purpose:wedding',\n",
       "       'initial_list_status:w', 'term_int', 'emp_length_int',\n",
       "       'mths_since_issue_d', 'mths_since_earliest_cr_line', 'funded_amnt',\n",
       "       'int_rate', 'installment', 'annual_inc', 'dti', 'delinq_2yrs',\n",
       "       'inq_last_6mths', 'mths_since_last_delinq',\n",
       "       'mths_since_last_record', 'open_acc', 'pub_rec', 'total_acc',\n",
       "       'acc_now_delinq', 'total_rev_hi_lim'], dtype=object)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ead_inputs_test.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_ead = reg_ead.predict(ead_inputs_test)\n",
    "# Calculates the predicted values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_targets_test_temp = ead_targets_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_targets_test_temp = ead_targets_test_temp.reset_index(drop = True)\n",
    "# We reset the index of a dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>CCF</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CCF</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.530654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.530654</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          CCF         0\n",
       "CCF  1.000000  0.530654\n",
       "0    0.530654  1.000000"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([ead_targets_test_temp, pd.DataFrame(y_hat_test_ead)], axis = 1).corr()\n",
    "# We calculate the correlation between actual and predicted values."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='CCF', ylabel='Density'>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.distplot(ead_targets_test - y_hat_test_ead)\n",
    "# We plot the distribution of the residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.736013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.105194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.384774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.661553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.731750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.810625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.161088</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.736013\n",
       "std       0.105194\n",
       "min       0.384774\n",
       "25%       0.661553\n",
       "50%       0.731750\n",
       "75%       0.810625\n",
       "max       1.161088"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_ead).describe()\n",
    "# Shows some descriptive statisics for the values of a column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_ead = np.where(y_hat_test_ead < 0, 0, y_hat_test_ead)\n",
    "y_hat_test_ead = np.where(y_hat_test_ead > 1, 1, y_hat_test_ead)\n",
    "# We set predicted values that are greater than 1 to 1 and predicted values that are less than 0 to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.735992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.105127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.384774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.661553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.731750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.810625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.735992\n",
       "std       0.105127\n",
       "min       0.384774\n",
       "25%       0.661553\n",
       "50%       0.731750\n",
       "75%       0.810625\n",
       "max       1.000000"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_ead).describe()\n",
    "# Shows some descriptive statisics for the values of a column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump(reg_ead, open('models/reg_ead.sav', 'wb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}