JP Morgan Quantitative training task4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load Libreries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy import stats \n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "from matplotlib import pyplot\n",
    "from scipy.stats import norm\n",
    "import datetime as dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import data\n",
    "Loans_df = pd.read_csv(\"Task 3 and 4_Loan_Data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>customer_id</th>\n",
       "      <th>credit_lines_outstanding</th>\n",
       "      <th>loan_amt_outstanding</th>\n",
       "      <th>total_debt_outstanding</th>\n",
       "      <th>income</th>\n",
       "      <th>years_employed</th>\n",
       "      <th>fico_score</th>\n",
       "      <th>default</th>\n",
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       "      <td>1345.827718</td>\n",
       "      <td>1768.826187</td>\n",
       "      <td>23448.32631</td>\n",
       "      <td>6</td>\n",
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       "      <td>2553.733144</td>\n",
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       "      <td>697</td>\n",
       "      <td>0</td>\n",
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       "      <th>9996</th>\n",
       "      <td>6184073</td>\n",
       "      <td>1</td>\n",
       "      <td>4146.239304</td>\n",
       "      <td>5458.163525</td>\n",
       "      <td>79969.50521</td>\n",
       "      <td>8</td>\n",
       "      <td>615</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>6694516</td>\n",
       "      <td>2</td>\n",
       "      <td>3088.223727</td>\n",
       "      <td>4813.090925</td>\n",
       "      <td>38192.67591</td>\n",
       "      <td>5</td>\n",
       "      <td>596</td>\n",
       "      <td>0</td>\n",
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       "      <th>9998</th>\n",
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       "      <td>1043.099660</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      customer_id  credit_lines_outstanding  loan_amt_outstanding  \\\n",
       "0         8153374                         0           5221.545193   \n",
       "1         7442532                         5           1958.928726   \n",
       "2         2256073                         0           3363.009259   \n",
       "3         4885975                         0           4766.648001   \n",
       "4         4700614                         1           1345.827718   \n",
       "...           ...                       ...                   ...   \n",
       "9995      3972488                         0           3033.647103   \n",
       "9996      6184073                         1           4146.239304   \n",
       "9997      6694516                         2           3088.223727   \n",
       "9998      3942961                         0           3288.901666   \n",
       "9999      5533570                         1           1917.652480   \n",
       "\n",
       "      total_debt_outstanding       income  years_employed  fico_score  default  \n",
       "0                3915.471226  78039.38546               5         605        0  \n",
       "1                8228.752520  26648.43525               2         572        1  \n",
       "2                2027.830850  65866.71246               4         602        0  \n",
       "3                2501.730397  74356.88347               5         612        0  \n",
       "4                1768.826187  23448.32631               6         631        0  \n",
       "...                      ...          ...             ...         ...      ...  \n",
       "9995             2553.733144  42691.62787               5         697        0  \n",
       "9996             5458.163525  79969.50521               8         615        0  \n",
       "9997             4813.090925  38192.67591               5         596        0  \n",
       "9998             1043.099660  50929.37206               2         647        0  \n",
       "9999             3050.248203  30611.62821               6         757        0  \n",
       "\n",
       "[10000 rows x 8 columns]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10000 entries, 0 to 9999\n",
      "Data columns (total 8 columns):\n",
      " #   Column                    Non-Null Count  Dtype  \n",
      "---  ------                    --------------  -----  \n",
      " 0   customer_id               10000 non-null  int64  \n",
      " 1   credit_lines_outstanding  10000 non-null  int64  \n",
      " 2   loan_amt_outstanding      10000 non-null  float64\n",
      " 3   total_debt_outstanding    10000 non-null  float64\n",
      " 4   income                    10000 non-null  float64\n",
      " 5   years_employed            10000 non-null  int64  \n",
      " 6   fico_score                10000 non-null  int64  \n",
      " 7   default                   10000 non-null  int64  \n",
      "dtypes: float64(3), int64(5)\n",
      "memory usage: 625.1 KB\n"
     ]
    }
   ],
   "source": [
    "Loans_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>customer_id</th>\n",
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       "      <td>1.000000e+04</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.974577e+06</td>\n",
       "      <td>1.461200</td>\n",
       "      <td>4159.677034</td>\n",
       "      <td>8718.916797</td>\n",
       "      <td>70039.901401</td>\n",
       "      <td>4.552800</td>\n",
       "      <td>637.557700</td>\n",
       "      <td>0.185100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.293890e+06</td>\n",
       "      <td>1.743846</td>\n",
       "      <td>1421.399078</td>\n",
       "      <td>6627.164762</td>\n",
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       "      <td>1.566862</td>\n",
       "      <td>60.657906</td>\n",
       "      <td>0.388398</td>\n",
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       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000324e+06</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>46.783973</td>\n",
       "      <td>31.652732</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>408.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.977661e+06</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3154.235371</td>\n",
       "      <td>4199.836020</td>\n",
       "      <td>56539.867903</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>597.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.989502e+06</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4052.377228</td>\n",
       "      <td>6732.407217</td>\n",
       "      <td>70085.826330</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>638.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.967210e+06</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>5052.898103</td>\n",
       "      <td>11272.263740</td>\n",
       "      <td>83429.166133</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>679.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.999789e+06</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>10750.677810</td>\n",
       "      <td>43688.784100</td>\n",
       "      <td>148412.180500</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>850.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "        customer_id  credit_lines_outstanding  loan_amt_outstanding  \\\n",
       "count  1.000000e+04              10000.000000          10000.000000   \n",
       "mean   4.974577e+06                  1.461200           4159.677034   \n",
       "std    2.293890e+06                  1.743846           1421.399078   \n",
       "min    1.000324e+06                  0.000000             46.783973   \n",
       "25%    2.977661e+06                  0.000000           3154.235371   \n",
       "50%    4.989502e+06                  1.000000           4052.377228   \n",
       "75%    6.967210e+06                  2.000000           5052.898103   \n",
       "max    8.999789e+06                  5.000000          10750.677810   \n",
       "\n",
       "       total_debt_outstanding         income  years_employed    fico_score  \\\n",
       "count            10000.000000   10000.000000    10000.000000  10000.000000   \n",
       "mean              8718.916797   70039.901401        4.552800    637.557700   \n",
       "std               6627.164762   20072.214143        1.566862     60.657906   \n",
       "min                 31.652732    1000.000000        0.000000    408.000000   \n",
       "25%               4199.836020   56539.867903        3.000000    597.000000   \n",
       "50%               6732.407217   70085.826330        5.000000    638.000000   \n",
       "75%              11272.263740   83429.166133        6.000000    679.000000   \n",
       "max              43688.784100  148412.180500       10.000000    850.000000   \n",
       "\n",
       "            default  \n",
       "count  10000.000000  \n",
       "mean       0.185100  \n",
       "std        0.388398  \n",
       "min        0.000000  \n",
       "25%        0.000000  \n",
       "50%        0.000000  \n",
       "75%        0.000000  \n",
       "max        1.000000  "
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     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "Loans_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rating map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a rating map that maps the FICO score of the borrowers to a rating where a lower rating signifies a better credit score.\n",
    "The process of doing this is known as quantization.\n",
    "Creating six buckets for FICO scores ranging from 300 to 850. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "d = {range(800,851):1,range(750,800):2,range(700,750):3,\n",
    "     range(650,700):4,range(600,650):5,range(300,600):6 }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{range(800, 851): 1,\n",
       " range(750, 800): 2,\n",
       " range(700, 750): 3,\n",
       " range(650, 700): 4,\n",
       " range(600, 650): 5,\n",
       " range(300, 600): 6}"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "Loans_df['Rating'] = Loans_df['fico_score'].apply(lambda x: next((v for k, v in d.items() if x in k), 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.generic.SeriesGroupBy object at 0x000000001D2D5190>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df.groupby('fico_score')['default']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>customer_id</th>\n",
       "      <th>credit_lines_outstanding</th>\n",
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       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4700614</td>\n",
       "      <td>1</td>\n",
       "      <td>1345.827718</td>\n",
       "      <td>1768.826187</td>\n",
       "      <td>23448.32631</td>\n",
       "      <td>6</td>\n",
       "      <td>631</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>3972488</td>\n",
       "      <td>0</td>\n",
       "      <td>3033.647103</td>\n",
       "      <td>2553.733144</td>\n",
       "      <td>42691.62787</td>\n",
       "      <td>5</td>\n",
       "      <td>697</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>6184073</td>\n",
       "      <td>1</td>\n",
       "      <td>4146.239304</td>\n",
       "      <td>5458.163525</td>\n",
       "      <td>79969.50521</td>\n",
       "      <td>8</td>\n",
       "      <td>615</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>6694516</td>\n",
       "      <td>2</td>\n",
       "      <td>3088.223727</td>\n",
       "      <td>4813.090925</td>\n",
       "      <td>38192.67591</td>\n",
       "      <td>5</td>\n",
       "      <td>596</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>3942961</td>\n",
       "      <td>0</td>\n",
       "      <td>3288.901666</td>\n",
       "      <td>1043.099660</td>\n",
       "      <td>50929.37206</td>\n",
       "      <td>2</td>\n",
       "      <td>647</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>5533570</td>\n",
       "      <td>1</td>\n",
       "      <td>1917.652480</td>\n",
       "      <td>3050.248203</td>\n",
       "      <td>30611.62821</td>\n",
       "      <td>6</td>\n",
       "      <td>757</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      customer_id  credit_lines_outstanding  loan_amt_outstanding  \\\n",
       "0         8153374                         0           5221.545193   \n",
       "1         7442532                         5           1958.928726   \n",
       "2         2256073                         0           3363.009259   \n",
       "3         4885975                         0           4766.648001   \n",
       "4         4700614                         1           1345.827718   \n",
       "...           ...                       ...                   ...   \n",
       "9995      3972488                         0           3033.647103   \n",
       "9996      6184073                         1           4146.239304   \n",
       "9997      6694516                         2           3088.223727   \n",
       "9998      3942961                         0           3288.901666   \n",
       "9999      5533570                         1           1917.652480   \n",
       "\n",
       "      total_debt_outstanding       income  years_employed  fico_score  \\\n",
       "0                3915.471226  78039.38546               5         605   \n",
       "1                8228.752520  26648.43525               2         572   \n",
       "2                2027.830850  65866.71246               4         602   \n",
       "3                2501.730397  74356.88347               5         612   \n",
       "4                1768.826187  23448.32631               6         631   \n",
       "...                      ...          ...             ...         ...   \n",
       "9995             2553.733144  42691.62787               5         697   \n",
       "9996             5458.163525  79969.50521               8         615   \n",
       "9997             4813.090925  38192.67591               5         596   \n",
       "9998             1043.099660  50929.37206               2         647   \n",
       "9999             3050.248203  30611.62821               6         757   \n",
       "\n",
       "      default  Rating  \n",
       "0           0       5  \n",
       "1           1       6  \n",
       "2           0       5  \n",
       "3           0       5  \n",
       "4           0       5  \n",
       "...       ...     ...  \n",
       "9995        0       4  \n",
       "9996        0       5  \n",
       "9997        0       6  \n",
       "9998        0       5  \n",
       "9999        0       2  \n",
       "\n",
       "[10000 rows x 9 columns]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,5))\n",
    "sns.countplot(x=Loans_df['Rating'],hue=Loans_df['default'])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Rating  default\n",
       "1       1             1\n",
       "2       1             7\n",
       "1       0            33\n",
       "3       1            62\n",
       "2       0           243\n",
       "4       1           263\n",
       "5       1           558\n",
       "6       1           960\n",
       "3       0          1182\n",
       "6       0          1663\n",
       "4       0          2475\n",
       "5       0          2553\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df.groupby('Rating')['default'].value_counts().sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "Loans_df['ratio_income_Totdebt'] = Loans_df['income']/Loans_df['total_debt_outstanding']\n",
    "Loans_df['ratio_income_loan_amt'] = Loans_df['income']/Loans_df['loan_amt_outstanding']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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>customer_id</th>\n",
       "      <th>credit_lines_outstanding</th>\n",
       "      <th>loan_amt_outstanding</th>\n",
       "      <th>total_debt_outstanding</th>\n",
       "      <th>income</th>\n",
       "      <th>years_employed</th>\n",
       "      <th>fico_score</th>\n",
       "      <th>default</th>\n",
       "      <th>Rating</th>\n",
       "      <th>ratio_income_Totdebt</th>\n",
       "      <th>ratio_income_loan_amt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8153374</td>\n",
       "      <td>0</td>\n",
       "      <td>5221.545193</td>\n",
       "      <td>3915.471226</td>\n",
       "      <td>78039.38546</td>\n",
       "      <td>5</td>\n",
       "      <td>605</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>19.931033</td>\n",
       "      <td>14.945650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7442532</td>\n",
       "      <td>5</td>\n",
       "      <td>1958.928726</td>\n",
       "      <td>8228.752520</td>\n",
       "      <td>26648.43525</td>\n",
       "      <td>2</td>\n",
       "      <td>572</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>3.238454</td>\n",
       "      <td>13.603576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2256073</td>\n",
       "      <td>0</td>\n",
       "      <td>3363.009259</td>\n",
       "      <td>2027.830850</td>\n",
       "      <td>65866.71246</td>\n",
       "      <td>4</td>\n",
       "      <td>602</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>32.481364</td>\n",
       "      <td>19.585647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4885975</td>\n",
       "      <td>0</td>\n",
       "      <td>4766.648001</td>\n",
       "      <td>2501.730397</td>\n",
       "      <td>74356.88347</td>\n",
       "      <td>5</td>\n",
       "      <td>612</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>29.722181</td>\n",
       "      <td>15.599407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4700614</td>\n",
       "      <td>1</td>\n",
       "      <td>1345.827718</td>\n",
       "      <td>1768.826187</td>\n",
       "      <td>23448.32631</td>\n",
       "      <td>6</td>\n",
       "      <td>631</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>13.256433</td>\n",
       "      <td>17.422978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>3972488</td>\n",
       "      <td>0</td>\n",
       "      <td>3033.647103</td>\n",
       "      <td>2553.733144</td>\n",
       "      <td>42691.62787</td>\n",
       "      <td>5</td>\n",
       "      <td>697</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>16.717341</td>\n",
       "      <td>14.072707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>6184073</td>\n",
       "      <td>1</td>\n",
       "      <td>4146.239304</td>\n",
       "      <td>5458.163525</td>\n",
       "      <td>79969.50521</td>\n",
       "      <td>8</td>\n",
       "      <td>615</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>14.651358</td>\n",
       "      <td>19.287238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>6694516</td>\n",
       "      <td>2</td>\n",
       "      <td>3088.223727</td>\n",
       "      <td>4813.090925</td>\n",
       "      <td>38192.67591</td>\n",
       "      <td>5</td>\n",
       "      <td>596</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>7.935166</td>\n",
       "      <td>12.367199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>3942961</td>\n",
       "      <td>0</td>\n",
       "      <td>3288.901666</td>\n",
       "      <td>1043.099660</td>\n",
       "      <td>50929.37206</td>\n",
       "      <td>2</td>\n",
       "      <td>647</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>48.825030</td>\n",
       "      <td>15.485222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>5533570</td>\n",
       "      <td>1</td>\n",
       "      <td>1917.652480</td>\n",
       "      <td>3050.248203</td>\n",
       "      <td>30611.62821</td>\n",
       "      <td>6</td>\n",
       "      <td>757</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>10.035783</td>\n",
       "      <td>15.963074</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      customer_id  credit_lines_outstanding  loan_amt_outstanding  \\\n",
       "0         8153374                         0           5221.545193   \n",
       "1         7442532                         5           1958.928726   \n",
       "2         2256073                         0           3363.009259   \n",
       "3         4885975                         0           4766.648001   \n",
       "4         4700614                         1           1345.827718   \n",
       "...           ...                       ...                   ...   \n",
       "9995      3972488                         0           3033.647103   \n",
       "9996      6184073                         1           4146.239304   \n",
       "9997      6694516                         2           3088.223727   \n",
       "9998      3942961                         0           3288.901666   \n",
       "9999      5533570                         1           1917.652480   \n",
       "\n",
       "      total_debt_outstanding       income  years_employed  fico_score  \\\n",
       "0                3915.471226  78039.38546               5         605   \n",
       "1                8228.752520  26648.43525               2         572   \n",
       "2                2027.830850  65866.71246               4         602   \n",
       "3                2501.730397  74356.88347               5         612   \n",
       "4                1768.826187  23448.32631               6         631   \n",
       "...                      ...          ...             ...         ...   \n",
       "9995             2553.733144  42691.62787               5         697   \n",
       "9996             5458.163525  79969.50521               8         615   \n",
       "9997             4813.090925  38192.67591               5         596   \n",
       "9998             1043.099660  50929.37206               2         647   \n",
       "9999             3050.248203  30611.62821               6         757   \n",
       "\n",
       "      default  Rating  ratio_income_Totdebt  ratio_income_loan_amt  \n",
       "0           0       5             19.931033              14.945650  \n",
       "1           1       6              3.238454              13.603576  \n",
       "2           0       5             32.481364              19.585647  \n",
       "3           0       5             29.722181              15.599407  \n",
       "4           0       5             13.256433              17.422978  \n",
       "...       ...     ...                   ...                    ...  \n",
       "9995        0       4             16.717341              14.072707  \n",
       "9996        0       5             14.651358              19.287238  \n",
       "9997        0       6              7.935166              12.367199  \n",
       "9998        0       5             48.825030              15.485222  \n",
       "9999        0       2             10.035783              15.963074  \n",
       "\n",
       "[10000 rows x 11 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting the PD (probability of default) for the borrowers using new ratings "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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>default</th>\n",
       "      <th>Rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      default  Rating\n",
       "0           0       5\n",
       "1           1       6\n",
       "2           0       5\n",
       "3           0       5\n",
       "4           0       5\n",
       "...       ...     ...\n",
       "9995        0       4\n",
       "9996        0       5\n",
       "9997        0       6\n",
       "9998        0       5\n",
       "9999        0       2\n",
       "\n",
       "[10000 rows x 2 columns]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Loans_df[['default','Rating']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.dummy import DummyClassifier\n",
    "from sklearn.metrics import accuracy_score, f1_score, confusion_matrix, recall_score, roc_auc_score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = Loans_df.drop(['default','fico_score','customer_id'], axis=1)\n",
    "Y = Loans_df['default']\n",
    "id_users = Loans_df['customer_id']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.7, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "# Create, train, and fit a logistic regression model\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "clf_logistic = LogisticRegression(solver='lbfgs').fit(X_train, np.ravel(Y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create predictions of probability for loan status using test data\n",
    "# .predict_proba creates an array of probabilities of default: [[non-defualt-0, default-1]]\n",
    "lr_preds = clf_logistic.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Create dataframes of predictions and true labels\n",
    "lr_preds_df = pd.DataFrame(lr_preds[:,1][0:], columns = ['lr_pred_PD'])\n",
    "true_df = Y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      default    lr_pred_PD\n",
      "0           0  2.044388e-01\n",
      "1           0  9.964434e-09\n",
      "2           0  1.450456e-12\n",
      "3           0  3.162185e-07\n",
      "4           0  1.325936e-06\n",
      "...       ...           ...\n",
      "6995        1  5.090299e-01\n",
      "6996        0  1.286108e-09\n",
      "6997        0  1.531522e-13\n",
      "6998        0  7.607506e-11\n",
      "6999        0  1.332895e-08\n",
      "\n",
      "[7000 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Concatenate and print the two data frames for comparison\n",
    "print(pd.concat([true_df.reset_index(drop = True), lr_preds_df], axis = 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Non-Default / Default predictions at 60% Threshhold: \n",
      "lr_pred_loan_status_60\n",
      "0    5766\n",
      "1    1234\n",
      "Name: count, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Reassign loan status based on the threshold and print the predictions\n",
    "lr_preds_df['lr_pred_loan_status_60'] = lr_preds_df['lr_pred_PD'].apply(lambda x: 1 if x > 0.60 else 0)\n",
    "print(\"Non-Default / Default predictions at 60% Threshhold: \")\n",
    "print(lr_preds_df['lr_pred_loan_status_60'].value_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "default\n",
       "0    5723\n",
       "1    1277\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_test.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix at 60% Threshhold: \n",
      "[[5716    7]\n",
      " [  50 1227]]\n"
     ]
    }
   ],
   "source": [
    "# Print the confusion matrix\n",
    "from sklearn.metrics import confusion_matrix\n",
    "print(\"Confusion Matrix at 60% Threshhold: \")\n",
    "print(confusion_matrix(Y_test, lr_preds_df['lr_pred_loan_status_60']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      " Non-Default       0.99      1.00      1.00      5723\n",
      "     Default       0.99      0.96      0.98      1277\n",
      "\n",
      "    accuracy                           0.99      7000\n",
      "   macro avg       0.99      0.98      0.99      7000\n",
      "weighted avg       0.99      0.99      0.99      7000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Print the classification report\n",
    "from sklearn.metrics import classification_report\n",
    "target_names = ['Non-Default', 'Default']\n",
    "print(classification_report(Y_test, lr_preds_df['lr_pred_loan_status_60'], target_names=target_names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9934285714285714\n"
     ]
    }
   ],
   "source": [
    "# Print the accuracy score the model\n",
    "print(clf_logistic.score(X_test, Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the ROC curve of the probabilities of default\n",
    "from sklearn.metrics import roc_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr_prob_default = lr_preds[:, 1]\n",
    "fallout, sensitivity, thresholds = roc_curve(Y_test, lr_prob_default)\n",
    "plt.plot(fallout, sensitivity, color = 'darkorange')\n",
    "plt.plot([0, 1], [0, 1], linestyle='--')\n",
    "plt.title(\"ROC Chart for LR on PD\")\n",
    "plt.xlabel(\"Fall-out\")\n",
    "plt.ylabel(\"Sensitivity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Fitting the Model to entire dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "Prob_to_default = clf_logistic.predict_proba(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_data = pd.DataFrame(Prob_to_default[:,1][0:].round(decimals = 2), columns = ['Probability _to_Default'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Probability _to_Default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Probability _to_Default\n",
       "0                         0.0\n",
       "1                         1.0\n",
       "2                         0.0\n",
       "3                         0.0\n",
       "4                         0.0\n",
       "...                       ...\n",
       "9995                      0.0\n",
       "9996                      0.0\n",
       "9997                      0.0\n",
       "9998                      0.0\n",
       "9999                      0.0\n",
       "\n",
       "[10000 rows x 1 columns]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = pd.concat([id_users,X,Y, prob_data], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "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>customer_id</th>\n",
       "      <th>customer_id</th>\n",
       "      <th>credit_lines_outstanding</th>\n",
       "      <th>loan_amt_outstanding</th>\n",
       "      <th>total_debt_outstanding</th>\n",
       "      <th>income</th>\n",
       "      <th>years_employed</th>\n",
       "      <th>Rating</th>\n",
       "      <th>ratio_income_Totdebt</th>\n",
       "      <th>ratio_income_loan_amt</th>\n",
       "      <th>Probability _to_Default</th>\n",
       "      <th>default</th>\n",
       "      <th>Probability _to_Default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8153374</td>\n",
       "      <td>8153374</td>\n",
       "      <td>0</td>\n",
       "      <td>5221.545193</td>\n",
       "      <td>3915.471226</td>\n",
       "      <td>78039.38546</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>19.931033</td>\n",
       "      <td>14.945650</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7442532</td>\n",
       "      <td>7442532</td>\n",
       "      <td>5</td>\n",
       "      <td>1958.928726</td>\n",
       "      <td>8228.752520</td>\n",
       "      <td>26648.43525</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>3.238454</td>\n",
       "      <td>13.603576</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2256073</td>\n",
       "      <td>2256073</td>\n",
       "      <td>0</td>\n",
       "      <td>3363.009259</td>\n",
       "      <td>2027.830850</td>\n",
       "      <td>65866.71246</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>32.481364</td>\n",
       "      <td>19.585647</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4885975</td>\n",
       "      <td>4885975</td>\n",
       "      <td>0</td>\n",
       "      <td>4766.648001</td>\n",
       "      <td>2501.730397</td>\n",
       "      <td>74356.88347</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>29.722181</td>\n",
       "      <td>15.599407</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4700614</td>\n",
       "      <td>4700614</td>\n",
       "      <td>1</td>\n",
       "      <td>1345.827718</td>\n",
       "      <td>1768.826187</td>\n",
       "      <td>23448.32631</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>13.256433</td>\n",
       "      <td>17.422978</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>3972488</td>\n",
       "      <td>3972488</td>\n",
       "      <td>0</td>\n",
       "      <td>3033.647103</td>\n",
       "      <td>2553.733144</td>\n",
       "      <td>42691.62787</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>16.717341</td>\n",
       "      <td>14.072707</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>6184073</td>\n",
       "      <td>6184073</td>\n",
       "      <td>1</td>\n",
       "      <td>4146.239304</td>\n",
       "      <td>5458.163525</td>\n",
       "      <td>79969.50521</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>14.651358</td>\n",
       "      <td>19.287238</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>6694516</td>\n",
       "      <td>6694516</td>\n",
       "      <td>2</td>\n",
       "      <td>3088.223727</td>\n",
       "      <td>4813.090925</td>\n",
       "      <td>38192.67591</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7.935166</td>\n",
       "      <td>12.367199</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>3942961</td>\n",
       "      <td>3942961</td>\n",
       "      <td>0</td>\n",
       "      <td>3288.901666</td>\n",
       "      <td>1043.099660</td>\n",
       "      <td>50929.37206</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>48.825030</td>\n",
       "      <td>15.485222</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>5533570</td>\n",
       "      <td>5533570</td>\n",
       "      <td>1</td>\n",
       "      <td>1917.652480</td>\n",
       "      <td>3050.248203</td>\n",
       "      <td>30611.62821</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>10.035783</td>\n",
       "      <td>15.963074</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      customer_id  customer_id  credit_lines_outstanding  \\\n",
       "0         8153374      8153374                         0   \n",
       "1         7442532      7442532                         5   \n",
       "2         2256073      2256073                         0   \n",
       "3         4885975      4885975                         0   \n",
       "4         4700614      4700614                         1   \n",
       "...           ...          ...                       ...   \n",
       "9995      3972488      3972488                         0   \n",
       "9996      6184073      6184073                         1   \n",
       "9997      6694516      6694516                         2   \n",
       "9998      3942961      3942961                         0   \n",
       "9999      5533570      5533570                         1   \n",
       "\n",
       "      loan_amt_outstanding  total_debt_outstanding       income  \\\n",
       "0              5221.545193             3915.471226  78039.38546   \n",
       "1              1958.928726             8228.752520  26648.43525   \n",
       "2              3363.009259             2027.830850  65866.71246   \n",
       "3              4766.648001             2501.730397  74356.88347   \n",
       "4              1345.827718             1768.826187  23448.32631   \n",
       "...                    ...                     ...          ...   \n",
       "9995           3033.647103             2553.733144  42691.62787   \n",
       "9996           4146.239304             5458.163525  79969.50521   \n",
       "9997           3088.223727             4813.090925  38192.67591   \n",
       "9998           3288.901666             1043.099660  50929.37206   \n",
       "9999           1917.652480             3050.248203  30611.62821   \n",
       "\n",
       "      years_employed  Rating  ratio_income_Totdebt  ratio_income_loan_amt  \\\n",
       "0                  5       5             19.931033              14.945650   \n",
       "1                  2       6              3.238454              13.603576   \n",
       "2                  4       5             32.481364              19.585647   \n",
       "3                  5       5             29.722181              15.599407   \n",
       "4                  6       5             13.256433              17.422978   \n",
       "...              ...     ...                   ...                    ...   \n",
       "9995               5       4             16.717341              14.072707   \n",
       "9996               8       5             14.651358              19.287238   \n",
       "9997               5       6              7.935166              12.367199   \n",
       "9998               2       5             48.825030              15.485222   \n",
       "9999               6       2             10.035783              15.963074   \n",
       "\n",
       "      Probability _to_Default  default  Probability _to_Default  \n",
       "0                         0.0        0                      0.0  \n",
       "1                         1.0        1                      1.0  \n",
       "2                         0.0        0                      0.0  \n",
       "3                         0.0        0                      0.0  \n",
       "4                         0.0        0                      0.0  \n",
       "...                       ...      ...                      ...  \n",
       "9995                      0.0        0                      0.0  \n",
       "9996                      0.0        0                      0.0  \n",
       "9997                      0.0        0                      0.0  \n",
       "9998                      0.0        0                      0.0  \n",
       "9999                      0.0        0                      0.0  \n",
       "\n",
       "[10000 rows x 13 columns]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting the PD (probability of default) for the borrowers using only new ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = Loans_df['Rating'].to_numpy().reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.7, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create, train, and fit a logistic regression model\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "clf_logistic = LogisticRegression(solver='lbfgs').fit(X_train, np.ravel(Y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create predictions of probability for loan status using test data\n",
    "# .predict_proba creates an array of probabilities of default: [[non-defualt-0, default-1]]\n",
    "lr_preds = clf_logistic.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Create dataframes of predictions and true labels\n",
    "lr_preds_df = pd.DataFrame(lr_preds[:,1][0:], columns = ['lr_pred_PD'])\n",
    "true_df = Y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      default  lr_pred_PD\n",
      "0           0    0.372445\n",
      "1           0    0.372445\n",
      "2           0    0.092889\n",
      "3           0    0.092889\n",
      "4           0    0.017362\n",
      "...       ...         ...\n",
      "6995        1    0.197768\n",
      "6996        0    0.092889\n",
      "6997        0    0.197768\n",
      "6998        0    0.092889\n",
      "6999        0    0.197768\n",
      "\n",
      "[7000 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "# Concatenate and print the two data frames for comparison\n",
    "print(pd.concat([true_df.reset_index(drop = True), lr_preds_df], axis = 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8175714285714286\n"
     ]
    }
   ],
   "source": [
    "# Print the accuracy score the model\n",
    "print(clf_logistic.score(X_test, Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr_prob_default = lr_preds[:, 1]\n",
    "fallout, sensitivity, thresholds = roc_curve(Y_test, lr_prob_default)\n",
    "plt.plot(fallout, sensitivity, color = 'darkorange')\n",
    "plt.plot([0, 1], [0, 1], linestyle='--')\n",
    "plt.title(\"ROC Chart for LR on PD\")\n",
    "plt.xlabel(\"Fall-out\")\n",
    "plt.ylabel(\"Sensitivity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Fitting the Model to entire dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "Prob_to_default = clf_logistic.predict_proba(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_data = pd.DataFrame(Prob_to_default[:,1][0:].round(decimals = 2), columns = ['Probability _to_Default'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = pd.concat([Loans_df, prob_data], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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>customer_id</th>\n",
       "      <th>credit_lines_outstanding</th>\n",
       "      <th>loan_amt_outstanding</th>\n",
       "      <th>total_debt_outstanding</th>\n",
       "      <th>income</th>\n",
       "      <th>years_employed</th>\n",
       "      <th>fico_score</th>\n",
       "      <th>default</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Probability _to_Default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8153374</td>\n",
       "      <td>0</td>\n",
       "      <td>5221.545193</td>\n",
       "      <td>3915.471226</td>\n",
       "      <td>78039.38546</td>\n",
       "      <td>5</td>\n",
       "      <td>605</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7442532</td>\n",
       "      <td>5</td>\n",
       "      <td>1958.928726</td>\n",
       "      <td>8228.752520</td>\n",
       "      <td>26648.43525</td>\n",
       "      <td>2</td>\n",
       "      <td>572</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2256073</td>\n",
       "      <td>0</td>\n",
       "      <td>3363.009259</td>\n",
       "      <td>2027.830850</td>\n",
       "      <td>65866.71246</td>\n",
       "      <td>4</td>\n",
       "      <td>602</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4885975</td>\n",
       "      <td>0</td>\n",
       "      <td>4766.648001</td>\n",
       "      <td>2501.730397</td>\n",
       "      <td>74356.88347</td>\n",
       "      <td>5</td>\n",
       "      <td>612</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4700614</td>\n",
       "      <td>1</td>\n",
       "      <td>1345.827718</td>\n",
       "      <td>1768.826187</td>\n",
       "      <td>23448.32631</td>\n",
       "      <td>6</td>\n",
       "      <td>631</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>3972488</td>\n",
       "      <td>0</td>\n",
       "      <td>3033.647103</td>\n",
       "      <td>2553.733144</td>\n",
       "      <td>42691.62787</td>\n",
       "      <td>5</td>\n",
       "      <td>697</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>6184073</td>\n",
       "      <td>1</td>\n",
       "      <td>4146.239304</td>\n",
       "      <td>5458.163525</td>\n",
       "      <td>79969.50521</td>\n",
       "      <td>8</td>\n",
       "      <td>615</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>6694516</td>\n",
       "      <td>2</td>\n",
       "      <td>3088.223727</td>\n",
       "      <td>4813.090925</td>\n",
       "      <td>38192.67591</td>\n",
       "      <td>5</td>\n",
       "      <td>596</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>3942961</td>\n",
       "      <td>0</td>\n",
       "      <td>3288.901666</td>\n",
       "      <td>1043.099660</td>\n",
       "      <td>50929.37206</td>\n",
       "      <td>2</td>\n",
       "      <td>647</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>5533570</td>\n",
       "      <td>1</td>\n",
       "      <td>1917.652480</td>\n",
       "      <td>3050.248203</td>\n",
       "      <td>30611.62821</td>\n",
       "      <td>6</td>\n",
       "      <td>757</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      customer_id  credit_lines_outstanding  loan_amt_outstanding  \\\n",
       "0         8153374                         0           5221.545193   \n",
       "1         7442532                         5           1958.928726   \n",
       "2         2256073                         0           3363.009259   \n",
       "3         4885975                         0           4766.648001   \n",
       "4         4700614                         1           1345.827718   \n",
       "...           ...                       ...                   ...   \n",
       "9995      3972488                         0           3033.647103   \n",
       "9996      6184073                         1           4146.239304   \n",
       "9997      6694516                         2           3088.223727   \n",
       "9998      3942961                         0           3288.901666   \n",
       "9999      5533570                         1           1917.652480   \n",
       "\n",
       "      total_debt_outstanding       income  years_employed  fico_score  \\\n",
       "0                3915.471226  78039.38546               5         605   \n",
       "1                8228.752520  26648.43525               2         572   \n",
       "2                2027.830850  65866.71246               4         602   \n",
       "3                2501.730397  74356.88347               5         612   \n",
       "4                1768.826187  23448.32631               6         631   \n",
       "...                      ...          ...             ...         ...   \n",
       "9995             2553.733144  42691.62787               5         697   \n",
       "9996             5458.163525  79969.50521               8         615   \n",
       "9997             4813.090925  38192.67591               5         596   \n",
       "9998             1043.099660  50929.37206               2         647   \n",
       "9999             3050.248203  30611.62821               6         757   \n",
       "\n",
       "      default  Rating  Probability _to_Default  \n",
       "0           0       5                     0.20  \n",
       "1           1       6                     0.37  \n",
       "2           0       5                     0.20  \n",
       "3           0       5                     0.20  \n",
       "4           0       5                     0.20  \n",
       "...       ...     ...                      ...  \n",
       "9995        0       4                     0.09  \n",
       "9996        0       5                     0.20  \n",
       "9997        0       6                     0.37  \n",
       "9998        0       5                     0.20  \n",
       "9999        0       2                     0.02  \n",
       "\n",
       "[10000 rows x 10 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model built in this way clearly understimate risk of default for low fico scores or low income/total debt ratio , anyway\n",
    "it could be used to get a \"at priori\" probability of default for a specific rating category"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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