From e2b6c46c6962557df453a86ee14f0da846df5ae8 Mon Sep 17 00:00:00 2001
From: Eanen Cohn <eanenc@gmail.com>
Date: Wed, 18 Jul 2018 15:20:40 -0500
Subject: [PATCH 1/2] added .ipynb_checkpoints to .gitignore

---
 .gitignore                        |   1 +
 predict_credit_card_balance.ipynb | 249 ++++++++++++++++++++++++++++++
 2 files changed, 250 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 predict_credit_card_balance.ipynb

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..763513e
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+.ipynb_checkpoints
diff --git a/predict_credit_card_balance.ipynb b/predict_credit_card_balance.ipynb
new file mode 100644
index 0000000..2aa1eee
--- /dev/null
+++ b/predict_credit_card_balance.ipynb
@@ -0,0 +1,249 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "import statsmodels.api as sm\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.metrics import r2_score\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df = pd.read_csv('balance.txt')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Index(['Unnamed: 0', 'Income', 'Limit', 'Rating', 'Cards', 'Age', 'Education',\n",
+       "       'Gender', 'Student', 'Married', 'Ethnicity', 'Balance'],\n",
+       "      dtype='object')"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.columns"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<class 'pandas.core.frame.DataFrame'>\n",
+      "RangeIndex: 400 entries, 0 to 399\n",
+      "Data columns (total 12 columns):\n",
+      "Unnamed: 0    400 non-null int64\n",
+      "Income        400 non-null float64\n",
+      "Limit         400 non-null int64\n",
+      "Rating        400 non-null int64\n",
+      "Cards         400 non-null int64\n",
+      "Age           400 non-null int64\n",
+      "Education     400 non-null int64\n",
+      "Gender        400 non-null object\n",
+      "Student       400 non-null object\n",
+      "Married       400 non-null object\n",
+      "Ethnicity     400 non-null object\n",
+      "Balance       400 non-null int64\n",
+      "dtypes: float64(1), int64(7), object(4)\n",
+      "memory usage: 37.6+ KB\n"
+     ]
+    }
+   ],
+   "source": [
+    "df.info()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "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>Unnamed: 0</th>\n",
+       "      <th>Income</th>\n",
+       "      <th>Limit</th>\n",
+       "      <th>Rating</th>\n",
+       "      <th>Cards</th>\n",
+       "      <th>Age</th>\n",
+       "      <th>Education</th>\n",
+       "      <th>Gender</th>\n",
+       "      <th>Student</th>\n",
+       "      <th>Married</th>\n",
+       "      <th>Ethnicity</th>\n",
+       "      <th>Balance</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>14.891</td>\n",
+       "      <td>3606</td>\n",
+       "      <td>283</td>\n",
+       "      <td>2</td>\n",
+       "      <td>34</td>\n",
+       "      <td>11</td>\n",
+       "      <td>Male</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Caucasian</td>\n",
+       "      <td>333</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>106.025</td>\n",
+       "      <td>6645</td>\n",
+       "      <td>483</td>\n",
+       "      <td>3</td>\n",
+       "      <td>82</td>\n",
+       "      <td>15</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Asian</td>\n",
+       "      <td>903</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3</td>\n",
+       "      <td>104.593</td>\n",
+       "      <td>7075</td>\n",
+       "      <td>514</td>\n",
+       "      <td>4</td>\n",
+       "      <td>71</td>\n",
+       "      <td>11</td>\n",
+       "      <td>Male</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Asian</td>\n",
+       "      <td>580</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>148.924</td>\n",
+       "      <td>9504</td>\n",
+       "      <td>681</td>\n",
+       "      <td>3</td>\n",
+       "      <td>36</td>\n",
+       "      <td>11</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Asian</td>\n",
+       "      <td>964</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5</td>\n",
+       "      <td>55.882</td>\n",
+       "      <td>4897</td>\n",
+       "      <td>357</td>\n",
+       "      <td>2</td>\n",
+       "      <td>68</td>\n",
+       "      <td>16</td>\n",
+       "      <td>Male</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>Caucasian</td>\n",
+       "      <td>331</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   Unnamed: 0   Income  Limit  Rating  Cards  Age  Education  Gender Student  \\\n",
+       "0           1   14.891   3606     283      2   34         11    Male      No   \n",
+       "1           2  106.025   6645     483      3   82         15  Female     Yes   \n",
+       "2           3  104.593   7075     514      4   71         11    Male      No   \n",
+       "3           4  148.924   9504     681      3   36         11  Female      No   \n",
+       "4           5   55.882   4897     357      2   68         16    Male      No   \n",
+       "\n",
+       "  Married  Ethnicity  Balance  \n",
+       "0     Yes  Caucasian      333  \n",
+       "1     Yes      Asian      903  \n",
+       "2      No      Asian      580  \n",
+       "3      No      Asian      964  \n",
+       "4     Yes  Caucasian      331  "
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.head()"
+   ]
+  }
+ ],
+ "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": "3.6.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From 2d0b2f6a0077f27e77239f965261db0ba98997c7 Mon Sep 17 00:00:00 2001
From: Eanen Cohn <eanenc@gmail.com>
Date: Wed, 18 Jul 2018 16:02:36 -0500
Subject: [PATCH 2/2] Finished

---
 predict_credit_card_balance.ipynb | 639 +++++++++++++++++++++++++++++-
 1 file changed, 633 insertions(+), 6 deletions(-)

diff --git a/predict_credit_card_balance.ipynb b/predict_credit_card_balance.ipynb
index 2aa1eee..879b6e7 100644
--- a/predict_credit_card_balance.ipynb
+++ b/predict_credit_card_balance.ipynb
@@ -17,7 +17,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -37,7 +37,7 @@
        "      dtype='object')"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -48,7 +48,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -215,7 +215,7 @@
        "4     Yes  Caucasian      331  "
       ]
      },
-     "execution_count": 7,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -223,6 +223,633 @@
    "source": [
     "df.head()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "y = df.Balance"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = df.drop(columns=['Balance'])\n",
+    "X = pd.get_dummies(X)\n",
+    "X = sm.add_constant(X)\n",
+    "X.head()\n",
+    "#X = df.drop(columns=['Gender_Male', 'Student_No', 'Married_No', 'Ethnicity_Asian'])\n",
+    "X = X.drop(columns=['Gender_Female','Student_No','Married_No','Ethnicity_Asian'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "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>const</th>\n",
+       "      <th>Unnamed: 0</th>\n",
+       "      <th>Income</th>\n",
+       "      <th>Limit</th>\n",
+       "      <th>Rating</th>\n",
+       "      <th>Cards</th>\n",
+       "      <th>Age</th>\n",
+       "      <th>Education</th>\n",
+       "      <th>Gender_ Male</th>\n",
+       "      <th>Student_Yes</th>\n",
+       "      <th>Married_Yes</th>\n",
+       "      <th>Ethnicity_African American</th>\n",
+       "      <th>Ethnicity_Caucasian</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>14.891</td>\n",
+       "      <td>3606</td>\n",
+       "      <td>283</td>\n",
+       "      <td>2</td>\n",
+       "      <td>34</td>\n",
+       "      <td>11</td>\n",
+       "      <td>1</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>1.0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>106.025</td>\n",
+       "      <td>6645</td>\n",
+       "      <td>483</td>\n",
+       "      <td>3</td>\n",
+       "      <td>82</td>\n",
+       "      <td>15</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>104.593</td>\n",
+       "      <td>7075</td>\n",
+       "      <td>514</td>\n",
+       "      <td>4</td>\n",
+       "      <td>71</td>\n",
+       "      <td>11</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>148.924</td>\n",
+       "      <td>9504</td>\n",
+       "      <td>681</td>\n",
+       "      <td>3</td>\n",
+       "      <td>36</td>\n",
+       "      <td>11</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>5</td>\n",
+       "      <td>55.882</td>\n",
+       "      <td>4897</td>\n",
+       "      <td>357</td>\n",
+       "      <td>2</td>\n",
+       "      <td>68</td>\n",
+       "      <td>16</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   const  Unnamed: 0   Income  Limit  Rating  Cards  Age  Education  \\\n",
+       "0    1.0           1   14.891   3606     283      2   34         11   \n",
+       "1    1.0           2  106.025   6645     483      3   82         15   \n",
+       "2    1.0           3  104.593   7075     514      4   71         11   \n",
+       "3    1.0           4  148.924   9504     681      3   36         11   \n",
+       "4    1.0           5   55.882   4897     357      2   68         16   \n",
+       "\n",
+       "   Gender_ Male  Student_Yes  Married_Yes  Ethnicity_African American  \\\n",
+       "0             1            0            1                           0   \n",
+       "1             0            1            1                           0   \n",
+       "2             1            0            0                           0   \n",
+       "3             0            0            0                           0   \n",
+       "4             1            0            1                           0   \n",
+       "\n",
+       "   Ethnicity_Caucasian  \n",
+       "0                    1  \n",
+       "1                    0  \n",
+       "2                    0  \n",
+       "3                    0  \n",
+       "4                    1  "
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<caption>OLS Regression Results</caption>\n",
+       "<tr>\n",
+       "  <th>Dep. Variable:</th>         <td>Balance</td>     <th>  R-squared:         </th> <td>   0.955</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.953</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   450.6</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Date:</th>             <td>Wed, 18 Jul 2018</td> <th>  Prob (F-statistic):</th> <td>5.37e-164</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time:</th>                 <td>15:45:12</td>     <th>  Log-Likelihood:    </th> <td> -1615.2</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>No. Observations:</th>      <td>   268</td>      <th>  AIC:               </th> <td>   3256.</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Residuals:</th>          <td>   255</td>      <th>  BIC:               </th> <td>   3303.</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Model:</th>              <td>    12</td>      <th>                     </th>     <td> </td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "               <td></td>                 <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>const</th>                      <td> -477.4417</td> <td>   46.481</td> <td>  -10.272</td> <td> 0.000</td> <td> -568.978</td> <td> -385.906</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Unnamed: 0</th>                 <td>    0.0195</td> <td>    0.058</td> <td>    0.338</td> <td> 0.736</td> <td>   -0.094</td> <td>    0.133</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Income</th>                     <td>   -7.5929</td> <td>    0.310</td> <td>  -24.465</td> <td> 0.000</td> <td>   -8.204</td> <td>   -6.982</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Limit</th>                      <td>    0.2216</td> <td>    0.041</td> <td>    5.454</td> <td> 0.000</td> <td>    0.142</td> <td>    0.302</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Rating</th>                     <td>    0.6277</td> <td>    0.610</td> <td>    1.029</td> <td> 0.304</td> <td>   -0.573</td> <td>    1.829</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Cards</th>                      <td>   21.3910</td> <td>    5.356</td> <td>    3.994</td> <td> 0.000</td> <td>   10.844</td> <td>   31.938</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age</th>                        <td>   -0.5304</td> <td>    0.385</td> <td>   -1.378</td> <td> 0.169</td> <td>   -1.288</td> <td>    0.227</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Education</th>                  <td>   -0.5830</td> <td>    2.067</td> <td>   -0.282</td> <td> 0.778</td> <td>   -4.653</td> <td>    3.487</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Gender_ Male</th>               <td>   22.7738</td> <td>   12.847</td> <td>    1.773</td> <td> 0.077</td> <td>   -2.525</td> <td>   48.073</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Student_Yes</th>                <td>  416.4639</td> <td>   21.706</td> <td>   19.186</td> <td> 0.000</td> <td>  373.718</td> <td>  459.210</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Married_Yes</th>                <td>   -1.9884</td> <td>   13.347</td> <td>   -0.149</td> <td> 0.882</td> <td>  -28.273</td> <td>   24.296</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Ethnicity_African American</th> <td>  -18.2927</td> <td>   18.403</td> <td>   -0.994</td> <td> 0.321</td> <td>  -54.534</td> <td>   17.949</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Ethnicity_Caucasian</th>        <td>   -2.1490</td> <td>   16.086</td> <td>   -0.134</td> <td> 0.894</td> <td>  -33.828</td> <td>   29.530</td>\n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "  <th>Omnibus:</th>       <td>18.586</td> <th>  Durbin-Watson:     </th> <td>   2.018</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  21.032</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Skew:</th>          <td> 0.686</td> <th>  Prob(JB):          </th> <td>2.71e-05</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Kurtosis:</th>      <td> 3.006</td> <th>  Cond. No.          </th> <td>3.99e+04</td>\n",
+       "</tr>\n",
+       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.99e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary.Summary'>\n",
+       "\"\"\"\n",
+       "                            OLS Regression Results                            \n",
+       "==============================================================================\n",
+       "Dep. Variable:                Balance   R-squared:                       0.955\n",
+       "Model:                            OLS   Adj. R-squared:                  0.953\n",
+       "Method:                 Least Squares   F-statistic:                     450.6\n",
+       "Date:                Wed, 18 Jul 2018   Prob (F-statistic):          5.37e-164\n",
+       "Time:                        15:45:12   Log-Likelihood:                -1615.2\n",
+       "No. Observations:                 268   AIC:                             3256.\n",
+       "Df Residuals:                     255   BIC:                             3303.\n",
+       "Df Model:                          12                                         \n",
+       "Covariance Type:            nonrobust                                         \n",
+       "==============================================================================================\n",
+       "                                 coef    std err          t      P>|t|      [0.025      0.975]\n",
+       "----------------------------------------------------------------------------------------------\n",
+       "const                       -477.4417     46.481    -10.272      0.000    -568.978    -385.906\n",
+       "Unnamed: 0                     0.0195      0.058      0.338      0.736      -0.094       0.133\n",
+       "Income                        -7.5929      0.310    -24.465      0.000      -8.204      -6.982\n",
+       "Limit                          0.2216      0.041      5.454      0.000       0.142       0.302\n",
+       "Rating                         0.6277      0.610      1.029      0.304      -0.573       1.829\n",
+       "Cards                         21.3910      5.356      3.994      0.000      10.844      31.938\n",
+       "Age                           -0.5304      0.385     -1.378      0.169      -1.288       0.227\n",
+       "Education                     -0.5830      2.067     -0.282      0.778      -4.653       3.487\n",
+       "Gender_ Male                  22.7738     12.847      1.773      0.077      -2.525      48.073\n",
+       "Student_Yes                  416.4639     21.706     19.186      0.000     373.718     459.210\n",
+       "Married_Yes                   -1.9884     13.347     -0.149      0.882     -28.273      24.296\n",
+       "Ethnicity_African American   -18.2927     18.403     -0.994      0.321     -54.534      17.949\n",
+       "Ethnicity_Caucasian           -2.1490     16.086     -0.134      0.894     -33.828      29.530\n",
+       "==============================================================================\n",
+       "Omnibus:                       18.586   Durbin-Watson:                   2.018\n",
+       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.032\n",
+       "Skew:                           0.686   Prob(JB):                     2.71e-05\n",
+       "Kurtosis:                       3.006   Cond. No.                     3.99e+04\n",
+       "==============================================================================\n",
+       "\n",
+       "Warnings:\n",
+       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
+       "[2] The condition number is large, 3.99e+04. This might indicate that there are\n",
+       "strong multicollinearity or other numerical problems.\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
+    "\n",
+    "# Construct the model\n",
+    "model = sm.OLS(y_train, X_train)\n",
+    "results = model.fit()\n",
+    "results.summary()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "209     772.457011\n",
+       "280     558.077166\n",
+       "33     -125.543453\n",
+       "210     201.978650\n",
+       "93      871.205893\n",
+       "84       46.316345\n",
+       "329     829.205310\n",
+       "94       84.201889\n",
+       "266     202.972656\n",
+       "126    1308.297008\n",
+       "9      1229.827946\n",
+       "361     455.075067\n",
+       "56      469.669575\n",
+       "72      647.422914\n",
+       "132     864.347372\n",
+       "42      461.990332\n",
+       "278     418.832371\n",
+       "376     770.118832\n",
+       "231     713.641921\n",
+       "385     853.793356\n",
+       "77      241.653270\n",
+       "15       60.261937\n",
+       "391     731.201459\n",
+       "271     479.833037\n",
+       "0       423.112502\n",
+       "396     532.075195\n",
+       "114     380.526136\n",
+       "225     987.416792\n",
+       "262     504.910115\n",
+       "104     738.164762\n",
+       "          ...     \n",
+       "16      113.630171\n",
+       "66     1301.173561\n",
+       "153     121.898452\n",
+       "7       892.332955\n",
+       "19     1009.223837\n",
+       "137     306.789959\n",
+       "355    1318.254317\n",
+       "349     561.658261\n",
+       "131     -14.929632\n",
+       "387    -166.795460\n",
+       "292     540.885366\n",
+       "386     434.105353\n",
+       "297     318.350879\n",
+       "60      646.897781\n",
+       "79        3.317042\n",
+       "285    -145.044533\n",
+       "305    -121.206578\n",
+       "281    -200.344143\n",
+       "157     984.233434\n",
+       "109     416.450961\n",
+       "17      445.475619\n",
+       "347    1184.370402\n",
+       "24      -48.245775\n",
+       "175     -45.816077\n",
+       "351     432.314571\n",
+       "332     482.857629\n",
+       "167     -80.621889\n",
+       "245    -138.915182\n",
+       "311     823.704040\n",
+       "145     656.921640\n",
+       "Length: 132, dtype: float64"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y_hat = results.predict(X_test)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.9522383003309712"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "r2_score(y_test, y_hat)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,'actual vs. predicted')"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(X_test.Income, y_test, label='true')\n",
+    "plt.scatter(X_test.Income, y_hat, label='predictor')\n",
+    "plt.legend() \n",
+    "plt.title('actual vs. predicted')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,'actual vs. predicted')"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(X_test.Limit, y_test, label='true')\n",
+    "plt.scatter(X_test.Limit, y_hat, label='predictor')\n",
+    "plt.legend() \n",
+    "plt.title('actual vs. predicted')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,'actual vs. predicted')"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(X_test.Cards, y_test, label='true')\n",
+    "plt.scatter(X_test.Cards, y_hat, label='predictor')\n",
+    "plt.legend() \n",
+    "plt.title('actual vs. predicted')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,'actual vs. predicted')"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(X_test.Student_Yes, y_test, label='true')\n",
+    "plt.scatter(X_test.Student_Yes, y_hat, label='predictor')\n",
+    "plt.legend() \n",
+    "plt.title('actual vs. predicted')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,'actual vs. predicted')"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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XXkpFhdUOP+CAA7qtU19fz0knncSAAQOoqKjgi1/8In/7298AKC8v5wtf+ELe5+mEZ2VgjPkbsD2j7E/GmDb779NAj8ZnERkI7GeMecruDfwGmJabyEWGk6mjqm+67z+EN47ghbhM7AqAYshIViwKzTchmlZFxPF/Z0jrbGGrM7fPxBjjaR03evfuTXl5uevyfAhyzOCrwB9T/g8XkedF5K8i8km7bDCQesca7TJHRGSmiDSISMOWLVsCFDVmZLbWm99zXi8Kr58im1lbDLGWikGh5UWIjhBvv/12ly1+yZIlTJo0KW15T2GrJ06cyH333QdY0UydOPXUU7n99ttpa7Pa0Nu3W+3r1BDaxx9/PH/961/ZunUr7e3tLFmyhE9/+tN5n1s2AlEGIvJdoA3ovAKbgEOMMWOB/wPcKyL7AU4q0VUNGmMWG2PqjDF1AwYMCELUZBAnr59CejsVgGKItVQMCi0vQnSEOOqoo/j1r3/N6NGj2b59O5dddlm3de655x7uuusujj32WI455hgeeeQRAG677TZ+9rOfMWHCBHbu3Om4/4svvphDDjmE0aNHc+yxx3LvvfcCVvrMM844g8mTJzNw4EDmz5/P5MmTOfbYYxk3bhxnn3123ueWjZxCWNsDw492DiDbZRcBlwJTjDGOvlEi8hfg28BG4EljzJF2+fnAScaYS7Idu5RCWHcbIINuoaULxtwanPW1WD2ZhJGZnwGsWEt+EtFENRBdjGHFcw1hHcZEzfXr1/PZz36WNWvW5LWfqIg0hLWInA5cC3w6VRGIyABguzGmXUQOwxooftMYs11EPhCRE4BngAuBn+YjQ1ESJ6+fIptZG1SspSiT/oSR3CVx+PAiU3omF9fSJcBJQK2INAI3YHkP9QJW2IMinS6knwLmiUgb0A5caozpHHy+jL2upX8kfZxB6SQuD/uUOc69lKTOTSCYWEuFSMruRpjBA0vZ7XbYsGGJ7RUEgWdlYIw536H4Lpd1fwv81mVZAzDSaZkSQ+LUSwmKAEwMTTuamVq2kmsqljJIttJkarm5bTq/2zEp+8YBEEbwwGXPb2Tlwz/nfu5jUK+tNO2q5daHZwCXF0QhePG0UZwJYqqWBqpTshOXXkoQBDRh6aK+z3JN6530kRYAhshWFlTeyQGVVcBZAQtdGF74/WLmyeK0c5pnFnPz7yuYNvb7oR67d+/ebNu2jf79+6tCyBFjDNu2baN379557UdzICulxS0jXcZAhlpuvR7Z9cMj6dO8qXt59UD6XPtqPhJGRuOcwxlStrV7eUctQ+atDfXYra2tNDY2snv37uwrK93o3bs3Q4YMobKyMq1ccyArihsBTVjq0/xOTuVJYFDZtpzKg6SyspLhw4eHfhzFHVUGSmkRlHdUkXlZAeyuPtixt7O7+mD6RCBPKQ9mR4FGLVVKi6AmLEUdATaEECF9zphHi/RKK2uRXvQ5o/ATDEs+5EYEqDJQSougwl5HGT47pBAhy9on8p32r9PYUUuHERo7avlO+9dZ1j4xGLlzwG/IjZIO4JcnaiZSSo+gvKOi8rIKKffzwsdeY3xbh10rWI4lLW0dBZk7kYmfkBtRTgQsBrRnoChJI6SonXXvr2BB5Z0MKdtKmcCQMstdtu79FXnt1w+DaqqZWraSlVVX8mavC1hZdSVTy1b2GEOq5AP45YkqA0VJGiEFMryu6oGuOQad9JEWrqt6IK/9+uHWo1/nhxmK6YeVd3Lr0a+7blPyAfzyRJWBoiSNkAavD6L7HIOeysNkwtqfUp2hmKqlhQlr3UOZFUNE2ihRZaAoSSOkwWtx6Vm4lYeKD1PYrNOOoLoyPfFLyQXwywMdQFaUJOJn8DpbTKY4BSX0MY8jzAB+pYAqgzzRiTFKIvASkylOQQl9KqYwAviVChqbKA+CTJSiKKESUEymghJCAptSQ2MTFYgoY9orSk6EmEQ+NIopWm4CUGWQB+rK5o6az2JGEcZSckR7E75Rb6I8UFc2ZzSuTPyoP/wKmk1VWlmzqaL+8CsikigEQgrTUSqoMsgDdWVzRmeCxo+rXx7Bta0Xp8Udurb1Yq5+eUTUogVHT2E6lKyomSgPStWVLZsJSM1n8aNpRzMbmcTylvS0nBLAPYmNSTCJ4yIxQpVBnpSaK5uXYGCDaqoZ//6KbvmBV+93SmRylzqDaqrZ6FDx52vSjFVwuFIZFwmJnMxEInK3iGwWkTUpZQeIyAoRed3+3t8uFxFZJCJviMiLIjIuZZuL7PVfF5GLgjsdJZUwwvl6MQH5iSujhEtYJs1YmQSjzjGRcHIdM/gVcHpG2WzgcWPMCOBx+z/AGcAI+zMT+AVYygO4ATgeOA64oVOBKMER1iCuFxOQn7gyfqlffgfvzP0YHTf04525H6N++R2BH6MYmDZ2MPM/P4rBNdUIMLimOpD5MLEyCUaZY6IIyMlMZIz5m4gMyyg+GzjJ/v1r4C/AtXb5b4w1q+1pEakRkYH2uiuMMdsBRGQFloJZ4usMoiamrmxhzYHwZG4okO22fvkdjFx9vaV4BA5mC/1WX089MGHqJYEeqxgIw6QZO5Ogzk3wTRDeRAcZYzYB2N8H2uWDgVQDXqNd5lbeDRGZKSINItKwZcuWAEQNmBi7soXVYpt12hGcU/X3tDjz51T9Pd3cEFKI5UyGPrfQsQcy9LmFgR5HcUdNgsVDmK6l4lBmeijvXmjMYmNMnTGmbsCAAYEKFwgxdmULaw7EtPJVjglQppWv2rtSgWy3BxrnBsKBpvAhl0uVQpoE/aBpML0ThDfRuyIy0BizyTYDbbbLG4GhKesNAZrs8pMyyv8SgByFJ2aubPXL72Docws50GzhAanl8cqxTJbnu7rvtzKDSaddnt9BHp9HRfvutKKK9t3pKRcLFPBsswzgYLorhM1Sy8GBHklxJWbvQCqx8nRKAEH0DJYDnR5BFwGPpJRfaHsVnQDstM1IjwGnisj+9sDxqXZZ8iiQOcQLnfbzg9lCmcAgtvKlshU9t+D94PXlHz3dCoA2d4f1HYIdd8O4WY6zajeMmxX4sRQXYvQOZBIrT6cEkKtr6RLgKeAIEWkUka8BC4BTROR14BT7P8AfgDeBN4BfApcD2APHPwDq7c+8zsHkxBEjVzYn+7lkGOS6WvD5EKOXf8LUS1gz/kbeYQAdRniHAawZf6MOHheSGL0DmcTK0ykB5OpNdL7LoikO6xrgGy77uRu4O5djR0HWmZUxiv9+oNniPBqTSb7d9zglQMH2GrIr/4Ptj1JAYvQOZBLWRLtiRWcgu+DZ3hgTVzY3+3k38m3Bx/jlVyIiJu9AJrNOO8Ix30ipxw5zQ5WBC0nLVbBh3Cz6dfrc2xiTYSoKqgUf05dfUVIp1dhhflFl4ELS7I0Tpl5CPdjeRFvZLLV8NGwKh+9YVVQt+NgERVMSwbTyVUzrNQ96N0KvIVA+B8jyDsR0ImnYqDJwIYn2xkz7ebERd1dBVVQxw0ve5yC2KRI0n4ELXgN76aSWwhFnV0FN6BND/EwKzWci6YtLrVzTc2us7xhEIsgFVQYueAnspRVAYYmz6S7Oiqpk8TMhzu8kuhiHpvGKmol6IFtgr6QNMiedOJvu4qyoShY/+Q385kToqUeREPOS9gx6Iku3TyuAwuIpSF5EaD7sGOJnQpzfSXQxDsvhFVUGbnjo9mkFECzZxl88BcmLCM2HHUP85DfwmRNhV7Wzy4ZbeRxRZeCGh4EkrQCCw9P4S09B8iJm2tjB/GbCWzzd+yre7HUBT/e+it9MeEvNhVHjI0bWsvaJTNyziOG772HinkUsa5+YdZubW89jV0acrF2miptbz/MteqHRMQM3PHT7po0dzOANj3ZFCt0sA9gwbhYTxmYmgys9cnWz9DT+ErOueOo5XtT3Wa43t1PB7q5EOwe/dAMM2z8xNmPFv/vyrz88ju1lLXaSn200mf7c3Dad3+05jrmFEDwAVBm44WUg6cWlTHjpBqBZK4AU/LxQTTuamVq2slvGrN/tmLR3pRglPM88x4tb/puKsvReS9IGEBX/TiGDaqpZvmMSy1smpZUPTpDJWM1EbngZSIpxcpsoWfjYa5zS/te0gd5T2v/ao5vlRX2fdRwPuKjvs3tXilGEzMxzHCwuCXUSNICo+HcKKQaTsSoDN7wMJMXMbBEX6t5f4Vix172/wnWbayrvp09GCO4+0sI1lffvLYhRwvPMc8wMF95FDOL6K97x6xTiZV5S3FEzUU9kC8gWI7NFnLiu6gH60L1iv67qAWC+4zZ9mt/xVh6TIHlO59iNmMT1V7yTT6TTbPOS4o72DPIhRmaLOHEQziYTt3IgVklzvOB2LlYy72h7LYp/iqGF7xftGeSDxvZ3RFx6TNJTxR6zpDnZcD/HoZYLo5JYkt7C94sqg3yJidkiVvip2JOmWBOmvBQlG6oMwqYUY6P7rdiTpFiTpryUZBBhfSFWquL4U1dXZxoaGqIWIzdeXErbI1ekzZptK+9Nxdk/jW+lUcCHsX75Hd0n7Gkye6VUycylAFZvM4+xJxFZbYyp87KuDiCHyK4/znEMn7DrjzE1JRQwDG/98jsYufp6DmYLZfaEvZGrr6d++R2BH0tREkHE85byVgYicoSIvJDyeV9ErhaRuSKyMaX8zJRtrhORN0TkNRE5LV8Z4kpvF3dJt/LIKeDDOPS5hWn5mgGqpYWhzy0M/FiKkgginreU95iBMeY1YAyAiJQDG4GHga8AtxhjfpS6vogcDcwAjgEGAX8WkY8bY9LngBcBTR39GVLW3QWxqaM/sXSYLODDeKDZAg4TtQ40PbifBoSap5RYEvG8paDNRFOAtcaYt3pY52zgPmPMHmPMOuAN4LiA5YgFd1Z9yTGS4Z1VX4pIoizk4+ufY8q/zTLApbw2+7HyQM1TSmyZMoe28t5pRW3lvQvmoRa0MpgBLEn5/00ReVFE7haR/e2ywUCq+mu0y7ohIjNFpEFEGrZs2RKwqOEz5qyZzDEzaeyopcMIjR21zDEzGXPWzKhFc6T+8CtozlBezaaK+sOv6HlDe6A8dayh7ZErelQIG8bNcjzWhnGz/IrviTDNU5oPW8mHZe0Tmd16cVp9Mbv1Yk8htIMgMNdSEakCpgLX2UW/AH6ANSnzB8CPga/iaBzA0aXJGLMYWAyWN1FQsoZKijfOtH5DGFx3Bee9/EvPoZyj5OqXRzC+9eJuYXhXvzyCVVPdt9v1xzn0cRko7+PiBTFh6iXUg22u2cpmqWXD+PDNNWGZp/yGPlaUThY+9hobWz7Bg3wirfypAqXRDXKewRnAc8aYdwE6vwFE5JfAo/bfRmBoynZDgKYA5YiOTNewnRuY8NINrIpzWIIU5XV/R39uZjqTWhalrSJZIjb6HSifMPUSsCv/g+1P2GyWARxM917mZqnN6/idUUyvqUoPwb3wsSpVBnEnJnOBok6jG6SZ6HxSTEQiMjBl2eeAzjn6y4EZItJLRIYDI4CUOMUJJmkhrTNcSTuji04tW5m2WraIjU0d/XMqj5KwzFN+IrUqMaCA7tTZiDqNbiDKQET6AKcAD6UU3ywiL4nIi8Bk4FsAxph/AkuBl4H/Ab5RNJ5ESQtp7aC8+oiVrakTLxEbkzRQPmHqJawZfyPvMIAOI7zDANaMvzFv89R1VQ84huC2IrUqsSVGDbiocyIEYiYyxuwC+meUfbmH9W8Cbgri2LEiYSGtzc5GxwGcQWXbEPA8xjHmrJnMebiNq819XWMNtzKDSTEdKA/DPOUrUqsSPTFqwHW+Z7mkiw0SjU2UQq55e7uRsOBl71LrbD+nlnULzvK8H+saXc55j01JxEB5GPiK1KpET/X+0LzduTwCooyYqsrAJhBvkCCDlxVgUGt+y7nMr7wzzbyxy1Qxv/VcbstxX0E8xHkr4yhJWENAUTLR2EQ2PSXCzoVl7ROZuGcRw3ffw8Q9i/z5CBdoUKthv1Mc/Zob9juluzw5TCjzQ6cy3rijGcNeZezLV78A8nYjRik5Fe+Y5vdyKi9mtGdgE4RbV2C+5j0NanVWLgH0HKwUfy0sb5nUVVZdWc781AErB3dZfnel9TvAii4w18wCyetIkkJwKwBsoj+DHMZ1rPLSQnsGNoNqqplatpI1J4/fAAAgAElEQVSVVVfyZq8LWFl1JVPLVubk1uW5d5Gt5ZptUCugnoOnFH9BeVtkOefAXDNj5B1SMkTREwuIBS3THT3hFrSUnlLXnoHNrUe/zsjVd3aFKhgiW/lh5Z2sOXoYcLKnfXjqXXhpuWbzSvLSc/BIVlt/EN4WHs7ZKcH8XtfM+Z4P5eYh5Vau5EmUPbEAWN4xCVrpNut+ecckFmXfvKjQnoHNhLU/dYxZM2HtTz3vw9OkES8t1ylzrMHHVFIGI41LRexWnhdBJKr3cM5BuWa+i3OgO7dyJU8K1HMMi5rqSpZ3TGJSyyIO23MPk1oWsbxjEjXVlQU5fpxQZdBJAC1gT5NGvBwny2BkQSu8LIrJEx7O2c0FM1fXzPkt5zp2++e3nJvTfhSPBNlzjGAW8Nypx1BZlt5nrCwT5k49JvRjxw1VBp0E0AL2ZIP3eJyevJIKWuEF4SXj5ZyDUDrk4CGlBEOBeo5hMW3sYBaee2zaO7vw3GOT49IcIDpm0ElAfuLZbPD1h1/ByNXXp5mkWkwFZtf79JpbA/2GUH/4FVxXf6irV1LDfqcw+/3uds7VYVV4eXrJOJ1zs6lizeFXMCH1GFAYDyklOIJ4byKeBRzlRK84ocqgkyAnjPVAZpjoHezDPjTTq3WntcLODYx87nuc0v41lrO3Quv0Spo2dnDiKjzPobEDcM2Mekp/KIQ1ATGI/Qbx3iQsjEuxIsYkI01AXV2daWhoiFqMvBk++/dpyRtWVl3pmBqzsaO2eyhp6AoTUcjZuvkeK/OcO0k9H8WFTG8dsFre+U5oC2u/PujMPtet5xhAAMG4hKeOChFZbYyp87Ku9gwKzKCaajamuJoOEmdvmUGyzXHbTgrVtQ1iIl3mOaeWK1kI0I04rP3m21jwm1QpKwl3ey00qgwKjGXi2Vu5NplahjgohE3pQWALGso2lZ4m0nl94TPPGVzOp8RbcY6EZU/3u9+Me5RtfMsLTTua2cikNLMnZE+qlJWwFGmRot5EBSbT4+hnZRd08wxqNlWsOvTynr2SCuSXHUSYDk9eVjFKMhIrgvDWCWq/DvfIGt/6a9pqucb0Ci2pS4zCUycB7RlEQKqJZ+KCama/39a9i7x5LKtmu8x8LmD3NygTT1azlrbinAkrGqqf/Trco2r2cE3F0m6t+lwaC557jrmiA9M5ocogbJxMH5Bf3uECVpyhvaiZaCvOmbC83Pzs1+VeZBvfykZoHmAaVjwnVBmEiVMLftnlIALtdgwkOyAbrXacFJueXqZCxt8pmKumtuLc8eJy62O8ZVn7RBbuWUTT7mYG9a5mVvsRTOtpA5d7FMT4VigOEQVyFy8WVBmEiVMLvqO122qdeYc7u9rZXia3DGVWefAUxHNJW3H+8WE29OUl5nKPmkZdw+CXq2M5ryNnhVfCqDIIkxxMHLnkHQ4yQ1ls0Facf3yYDX15ibncowmjp+fnAhoSgeUXKRECUwYish74AGgH2owxdSJyAHA/MAxYD0w3xrwnIgLcBpwJ7AL+3RjzXFCyxAY304cDZf2GsG6utwlYBQ9HUSg0OYwjWf34XcdbNljeZg6K1W2At+79FXDLla4KOUkt7SDcokuJoHsGk40xqU7zs4HHjTELRGS2/f9a4AxghP05HviF/V1cOHWryyrTxgyAnM0hSQtHofjHU+u2x0aHcTQbOXmJTS1byYKqu2DnHqsgY7uktbSDcIsuJcKeZ3A28Gv796+hqxFxNvAbY/E0UCMiA0OWpfCMnk79qO/zDgPoMMI7DKB+zE1w9s/yigLqyW9fKQo8Zc9ziviaSUYUUKdw69dWLqWaPa7bBZUnvFB4nr+Q4ExtQRJkz8AAfxIRA9xhjFkMHGSM2QRgjNkkIgfa6w4GUpsyjXbZptQdishMYCbAIYccEqCohWHZ8xtZ2fA2V2NADG0dhvsb3uaRjk/wZJ5d7cRFWvTg7VLIeEtJwVPrdvR06te/x9DnFnKg2YqIcfYqSzEnOXmJDdrd3UXU2s4yN93f0Z+by6aneb31JGPUeHKL1pAVXQSpDCYaY5rsCn+FiLzaw7qOnpHdCiyFshisQHXBiFk4Xvj9YubJ4q6B3iGylXlmMdc928FG+4WKe1c7EDy8cEkzQRQKL5P+lj2/0Q4JYbkPuAU/zHTT7daguKVnc5MfN2hXggo90sN+PLlF62THLgIzExljmuzvzcDDwHHAu53mH/t7s716IzA0ZfMhQFNQssSFi1v+O83jByw30lkV6d3QOHe1A8FD8pKkmSAKhZfseZnX7ua26bSY9HZeu1RmH5fyYG7qdIN2k8UTQYUe8bCfaWMHs2r2yaxbcBarZp/cvWGhkx27CEQZiMg+IrJv52/gVGANsBy4yF7tIuAR+/dy4EKxOAHY2WlOKiYGlTl3u51mbMa1qx0IPXm72Lba+3d9nallK7utUtTXxQNexoecrpHJ6Gi3d3RQv/69ng+WmdXOhU43aN9jVUFlNgtiP2HFfkogQZmJDgIetjxGqQDuNcb8j4jUA0tF5GvA20BnXsY/YLmVvoHlWvqVgOSIFburD6ZPc3cd12T6dysr6nDOrt4u0lUeqAmiyMg2PpRpSrqmYim9JL2XVSXtDH1uIeSSH0DKwbR3K87FDdqRoFrjQexHJzt2EUjPwBjzpjHmWPtzjDHmJrt8mzFmijFmhP293S43xphvGGMON8aMMsYkP2uNA33OmEeL9Eor2yO9uJUZaWVRhacuGI7mByFzmCgQE0QhiYkXSqYpyS1HxoHGubyLTLOLgyKgrBJaPsrvnINqjQexnyByfBcJGsI6RJa1T+Q77V9PS87+3fav03vcjNzdQmNS8fjC6YVzzH0Gg8u28mavC3i691X8ZsJb8R08jlHI7UxT0iZqHdfbLM7lXTiZXYA2yugwwg72pd0AzdvJ65ydGgd+WuNB7Wf0dPjWGpi7w/ouQUUAmvYyVCYueMLRE2RwTbV7eGon/KYojHOymFtGZp+dHVEaRk+4yd9vqFWhRIjfNJJmbg3ioKQ7jHDYnnt68FLycc5+ns0sEYBj94zHAE17GRMCmwHpx/0t7v7TTrbaTOLs4hdjL5QJUy+hHrrmHWyWWjaMn5U1n7BbAMTOMS4385Ovc8419Ijb8/xviyJXvsWCmolCJLAMTn4qnqA8NsLCo+dKHCpXR2LuhTJh6iUcPPcNyr6/g4PnvuEpsfz8lnO7Zd3bZaq4uc2qtJuMi5mpEOcc9+e5CFBlECJefMQ94afiiVnLddnzG5m44AmGz/49Exc8wbLnN6bbavsNdd4wJpVrN4KyV8eIhv1OYXbrxWljXLNbL+7y7rq5bXo3ZVGwc47Z81yMqJkoRAJLDOPH/S3IZDF5jj24zS5ueGs7T766haYdzVzU9wtcX347Fe27924Y58o16pDbWe6Jn9AeTgEQU1neMYkqU8a8Pr+lT/M7hT1nTX4UOjqAnBRyrZD9DjqHsB+3gfRM59Jzqv7OvH0iqGiSRpZ7kql8wY5q68FrLVOJTD5yQJfCjjRelMs514/6Ple/PCIv+Yo5JpYOIBcjuQ64BdVyDSB2i9uAeWYz5MGWT/BUnymsmpuDp1WERFaJZLknQcbxrzv0AG6cNipfifPH4XmuP/wKLqw/lGb7WviJZ6UxsfaiyqCYCSJZTAC2Wrdga04kJfxEpJVIlnvi14utkOfkS5FmPM9XL3iiSxF0kqvS0wQ4e9EBZKVnAvCacRpId/MfSkr4iUgD62W5J3692Ap1Tp1KZ+OOZgx7lc6y5zfmtJ8gXLc1Ac5eVBkoPROA14xTsLUvnnBINwVRWSbsamlL9ziKKZFWIlnuiV8vtkKdU1BKJwjX7cDcv4sANRMlhMjs0wGNPTgFW6s79ICuc+pXXclHLW28t6sViL/t1kuegdDIck/8erEV6pyCUjqektcUYB/FgnoTJQDf3iFxDkeRQWChOwpEPh47caVQ5xTkvQ6ikaTeRBbaM0gAvga54h6OIoOk2W4Dm0MSI0I9p5SGyYrqg5lT9QUebPlE12K/rfEg0r8mLoVsSKgySABOFeLUspVcs2spzN3m3OpPWDq/SM0uPinGSiSUc8pomPRp3sSCyjvpW1XBrz88rigUaTGgyiABZFaUU8tWsqDyzr0pNZ1a/Qmbvl+0ttsEmeq84Muk4tAwqWjfzdx+v2Xu9d8PUVolF0rHmyjB+QAyvUOuqVjaLbdyZtCuXdUHO+5rT+V+sbwOXtI7Jo4Y5TwIAt8uoT2lPY3Zc1jKlEbPIGH280y62XJdciunvnQ3t57HNebnaUpjjylHWj+CnTvt9eN1HYrO7JIwU102fE/Qck17CmlKEhJ5XYqF0ugZuL2UD1+amJbJtLGDWTX7ZNYtOIsyDxPBfv3hcd0iUH5ENVW0pW/jIQywY8RRJTuFNNUVoOfre5DfMe1pBhqOOnJKQxm4vXymnUR236fMgfKMUMLlVWkTwQbVVLO8YxKTWhZx2J57mNSyiBo+dN5fD5VTULNFSxI3pS1lwVbaBTJH+Z6glfTcFSVCaSgDL6ETktYyyZwfkvHfaRaqW27cnq5PpGEXko5bizjoRkiBEr/klZ8jybkrSoS8lYGIDBWRJ0XkFRH5p4hcZZfPFZGNIvKC/TkzZZvrROQNEXlNRE7LV4aseOmmQnJaJo/Pg47W9LKO1rSX32lAtmn8NTmHloi9/3+cHQMyW8RS3n2dICrtApmjAhvk9xniRM2V4RLEAHIb8B/GmOdEZF9gtYissJfdYoz5UerKInI0MAM4BhgE/FlEPm6MSW9+Bknm9H0ps1tnGYTRMgnDtdDjy999QPZkGLZ/TvLE2v8/CY4BqZE259Y4r5NvpV3AxC+BDPL7CHGioabDJ29lYIzZBGyyf38gIq8APd2ds4H7jDF7gHUi8gZwHPBUvrL0SOpL6ZYcJOisWmFVVvm8/DmGtY61/3/SvHXCqrT9ZMKLmhyfQw01HT6BjhmIyDBgLPCMXfRNEXlRRO4Wkf3tssFA6hvRiIvyEJGZItIgIg1btmwJTtDM7nu/oblnAPNCWLbcAubfjbX/f8Im1gV539JMJn+opX7U98N/niMk9ubKIiCweQYi0hf4LXC1MeZ9EfkF8AOshFY/AH4MfBVndwLHaHnGmMXAYrAC1QUlKxBM4pdshFVZFTj/bmz9/5OWFzeg++ZkMrmw/lDmf/6xeN6nAIi1ubJICEQZiEglliK4xxjzEIAx5t2U5b8EHrX/NgKp7gRDgKYg5IgdYVZWHpRZMUdjBErCPOJEKZpMYmeuLLIwIxCAMhARAe4CXjHG/CSlfKA9ngDwOWCN/Xs5cK+I/ARrAHkE8Gy+cmQjkooxwsqqJAbcCtxD8oOv5y5LRVOKJpNYRYlNguOCD4LoGUwEvgy8JCIv2GXfAc4XkTFYJqD1wCUAxph/ishS4GUsT6RvhOpJRIAVY66tgRArq2yVTMm0Hgth7vOJr+fOQ0WTRJNJEI2x2Jgrk+a44JEgvIlW4jwO8IcetrkJuCnfY3slkIrRb2sghMrKSyVTiq3HuOHrufNQ0cTOZJKFouulJs1xwSMlMQM5kIqxQLM8veBlVrBbK7FfdaVO3CkQvp47DxVNrD28HAhsFntcJhh6iA2WREoiamkg3eoYtQa8VDJOrcfKMuGjljZ2NCcjz3DsyWI29PXceXQ6iI3JxAOBNMbiZKdPouOCB0qiZ+AUU6WyXPhoT5v3FnKMWgM1fSqzlju1Hvv2rqC1Pd1DV+MM+cRDcDhfsXwKOIekUPgOcJdKjHrmBZunVGBKomeQ6YlQ06eSD3fn2EL22RoIw4spM0adW3lm63H47N87bqfjCD7wYNv35QGTAA+pXAlkjCNGPXMg1o4LfikJZQDpFePEBU/w3q70QG9ZB/bcXlKw7JcOL67ngbMcvZR2NrfmVN5JqF4oReh33SO+40N5oMgqmkDcQpM2wTCBlIwySMW3DTPzJc1ix/TkTeLDFuq3Ug/NCyVO9txCEbPKKe4TDDOVYmc4Dc/yFqmdPk6UxJhBJoHYMCGrHdOT0vFhC/UbVz40L5QI7bmRhTWOkW0/aQmIfMlbpHb6OFGSPYPAWshZTAWeWvBuuWFdc8bm1+0OxQslKHtujqamSP3Xg7Tt52lii90Ewyzn41veIjOfxY2SVAaBTW3PYirwpHSk3Dm3glMilIxziI0ZIAiTiQ9TU+SVoI/KKdOcc+vRrzPhpRvyMrHFaoKhh/sYK3mVLkpSGUBAlWkWO6YnpeMWiSOsCB1hDPQGYc/1McU/aZWKU09m0OqbQbqf9zsPfYcT793HU0OloOEpsj0/Hu5jEsNplAIlqwwCwYOpIKvS6TfUpVXtkic2H8Ia6PViMslWifgwNSWtUnHqyQxkq+O6B5qtafZ0cDd9FSw8hZfnx8N9TFo4jVJBlUEOOHts5GnHLKSXRJgBtnoymXipRHyYmpJWqTj1WJpMLUOku0JoMv27fmczfRUsoqeX58fDfYxVBFKlC1UGHgltsLKQk4yimrjjpRLxoRSTVqk49WRubpvOD6vuopo9XWW7TBU3t6Xf/2ymr4KMIXl5fjzex1iNeSmAKgPPhDpYWSgviah8471UIj6VYqSVSo7jL049mRXln+bL44YxYe1PYWcj71DLf7aey/KOSWnbFsz01dM5eXl+inAGdamgysAjSRusdCSqiTtelVCSXAd9jL+49WQmjD0dO90HTz+/kRUPvQQdEZi+sp2T1+cnSfdR6UKVgUeSNljpSFSttmKcPepz/CVbTyZS01e2c9JWf1GjysAjSRusdCWKVlsRViJmZ6NjRie38lyIzPTlZQKktvqLFlUGHnFrsQG5xVgpVYqsEnmXWg5mi0t5QvE5AVIpDlQZ5IBTsK2iSueneGZ+y7nMr7yTPtLSVbbLVDG/9Vxui1CuvCj0BEglVpRkoLqgCCydn5I4GvY7hdmtF9PYUUuHERo7apndejEN+50StWj+cZvoGMYEyIQTWYDEEImsZyAipwO3AeXAncaYBVHJ4hcvHkbXL3uJJc9soN0YykU4//ih3DhtVNr6TuvUHXpA3oOITpPkoOfBSS/bTD5yAE++uqUg+812zl6ubxjhnWeddgT/Z2kzy1v2uoAK0M/Onud2HC/XYVj/ap5+870ezymT+uV3MPS5hRxotrBZBrBh3CwmTL0kt5OaMoeWh79Jldk756FFelGVMtDv5VqGFU47qGPnK1+xWgTEuKXNCvOgIuXAv4BTgEagHjjfGPOy2zZ1dXWmoaGhQBJ6Y+KCJxw9jAbXVLNq9slcv+wl/vvpt7st/9IJh3S93G7rlJcJ7R177011ZXlO4aYzH1iwUn1ioNVlv47blAkI3dJlpuK0ThD7zXbOXq6v07FzvZa5HLsn+f1eB0g/p0zql9/ByNXXU51ismo2VawZf2NOCuH6ZS/x/rP3ck3FUgbJNppMf25um85+x13AjdNGebqWYV3voI4dhHzZ3vs4ISKrjTF1XtaNykx0HPCGMeZNY0wLcB9wdkSy+CZbXoElzzh7Z6SWu62Tqgggd/OTkwmrtd2kKYLM/Tpu02GyVlRO63jZ7xnmf1lZdSVv9rqAlVVXMrVspes+nPByfcMy5bkdu6fj+L2+2Y439LmFaYoAoFpaGPrcwqz7zTzG8o5JTGpZxGF77mFSyyKWd0zqOraXaxnW9Q7q2EHIVxRzjhyIShkMBlKf7ka7LA0RmSkiDSLSsGVLd8+NqMmWLKbdGKaWrexW4bWn9Mbac+iZ5fKw+Vk36Ie5p/1OLVvJgso7GVK2lTKBIWVbWVB5ZzeF0JNMbtcutTysF9frfUs9Tj7H7Ol4Bxrnd+NA4xwEL9djdJZ7uZZhXe+gjh2EfIElx4oZUSkDRxftbgXGLDbG1Blj6gYMGFAAsXJn2tjBrJp9MusWnMWq2SendTWnla9yrPCmla/qWqdcvHul5/Kw+VnX6zZOCi7X/V5TsTTNEwegj7RwTcVSx3044XbtUsvDenG93rfU4+RzzJ6Ot1mc343NUhvIMTrLvVzLsK53UMcOQj6/mQbjTlTKoBFIdVEYAjRFJEto3NDnQccK74Y+D3b9P/94Z0+N8rL0FzPXh83pga0sF8tG7bJfx23KxBprsHFr0X+uYlVO+x3kEKnTKt/muA8n3K5danlYL67bsXs6jpfr6+d4G8bNotlUpZU1myo2jJuVdb9ejtFZ7uVahnW9gzp2EPKFlj42YqLyJqoHRojIcGAjMAO4ICJZQmP/1s1ZyzsHBYP2Juppkpzbfr1s852qB+hDdwV3074P8az5jOf97paB9Gne1E3uzVKLgKdzdrt2qQOt08YOZvCGR7t72ow93fO1dDv26O1/YuJbP2cgW9lELcv2/yr37j7R9Z55vSe5ehNNmHoJ9WCf41Y2Sy0bxufuTZTtenoJlRFWOI2gjh2UfMUYdTUSbyIAETkTuBXLtfRuY8xNPa0fR2+irNwy0j1xzbfWFF6eIJhbg4NFDxCYu8P7fjKDooEVryjoJOdhHadQ8itKHiTBmwhjzB+MMR83xhyeTREklilzrAoilbgHaHtxqaXE5tZY3y+m2/Bdw13nGgZ79HSr4uw3FBDrO4yKtKfga3Hcr6JEhIajCJOkBWjzEpY5yAikhYhXFFZCn6gSBSlKSKgyCJsoA7TlmHzFU1jmpCm4sBL6RJUoSFFCQpVBseIj+Yrn1m6cIpBmU3hh5VIoxhwNSkmjgeqKFT827aDGAwpFp8LbuQEwexVe6jhHWGMThRrzUJQCoT2DYsWPTTtprV2v2cbC6snEqYekKHmiPYNixU8rP2mtXR3EVZTA0J5B2OQ6iBsUflv5SWrt6iCuogSG9gzCxItNOyyS1sr3w4hTcytPCtnmeihKCGjPIEy82rTDIqhWflS9m2y8/qfcypOAHy8wZS9xfVYTgPYMwqQYbNpR9m6yUQzXNxOd2eyfOD+rCUCVQZgkzVXTiThXTsVwfTMpRgVXKOL8rCYAVQZhksTYRJnEuXIqhuubSTEquEIR52c1AagyCJNiGMSNc+VUDNc3k2IdFC8EcX5WE4AOIIdNklw1nYj7RLSkX99MinFQvFDE/VmNOdozUHqmGFvfcUZNHf7RZzUvtGcQV+LkIldsre84oxPp8kOfVd9ozyCOqItc6VKMg+JKIlBlEEfURS6ZBDFzWE0dSkSomSiOqN04eXidOezF/KemjnCJkwk2RmjPII6oi1zy8NKbU/Nf9Og9cEWVQRxRu3Hy8NKbU/Nf9Og9cCUvZSAiC0XkVRF5UUQeFpEau3yYiDSLyAv25/aUbcaLyEsi8oaILBIRyfckig61GycPL705Nf9Fj94DV/LtGawARhpjRgP/Aq5LWbbWGDPG/lyaUv4LYCYwwv6cnqcMxcno6fCtNTB3h/WtiiDeeOnNqfkvevQeuJKXMjDG/MkY02b/fRro8YqKyEBgP2PMU8YYA/wGmJaPDIoSC7z05tT8Fz16D1wJ0pvoq8D9Kf+Hi8jzwPvA9caY/wUGA6n9sUa7zBERmYnVi+CQQw4JUFRFCYFsXkCdy9STJTr0HriSVRmIyJ+Bgx0WfdcY84i9zneBNuAee9km4BBjzDYRGQ8sE5FjAKfxAeN2bGPMYmAxQF1dnet6ipIY1G00evQeOJJVGRhjPtPTchG5CPgsMMU2/WCM2QPssX+vFpG1wMexegKppqQhQJM/0RVFUZSgyNeb6HTgWmCqMWZXSvkAESm3fx+GNVD8pjFmE/CBiJxgexFdCDySjwyKoihK/uQ7ZvBfQC9ghe0h+rTtOfQpYJ6ItAHtwKXGmO32NpcBvwKqgT/aH0VRFCVC8lIGxpiPuZT/Fvity7IGYGQ+x1UURVGCRWcgK4qiKKoMFEVRFFUGiqIoCqoMFEVRFEDsqQGxR0S2AG9lFNcCWyMQxw9JkhVU3rBRecNF5bU41BgzwMuKiVEGTohIgzGmLmo5vJAkWUHlDRuVN1xU3txRM5GiKIqiykBRFEVJvjJYHLUAOZAkWUHlDRuVN1xU3hxJ9JiBoiiKEgxJ7xkoiqIoAaDKQFEURUmGMhCRoSLypIi8IiL/FJGr7PIDRGSFiLxuf+8ftawAItJbRJ4VkX/Y8n7fLh8uIs/Y8t4vIlVRy5qKiJSLyPMi8qj9P7byish6EXlJRF4QkQa7LJbPA4CI1IjIgyLyqv0cnxhXeUXkCPu6dn7eF5GrYyzvt+z3bI2ILLHfvzg/u1fZsv5TRK62yyK/tolQBlhZ1P7DGHMUcALwDRE5GpgNPG6MGQE8bv+PA3uAk40xxwJjgNNF5ATgh8AttrzvAV+LUEYnrgJeSfkfd3knG2PGpPhnx/V5ALgN+B9jzJHAsVjXOZbyGmNes6/rGGA8sAt4mBjKKyKDgSuBOmPMSKAcmEFMn10RGQl8HTgO6zn4rIiMIA7X1hiTuA9WQpxTgNeAgXbZQOC1qGVzkLUP8BxwPNYMwwq7/ETgsajlS5FzCNZDeDLwKFaK0jjLux6ozSiL5fMA7Aesw3bYiLu8GTKeCqyKq7xYOdQ3AAdgheR/FDgtrs8ucC5wZ8r/7wHXxOHaJqVn0IWIDAPGAs8ABxkrexr294HRSZaObXJ5AdgMrADWAjuMMW32Ko1YD3JcuBXroeyw//cn3vIa4E8islpEZtplcX0eDgO2AP/XNsPdKSL7EF95U5kBLLF/x05eY8xG4EfA21i513cCq4nvs7sG+JSI9BeRPsCZwFBicG0TpQxEpC9W0pyrjTHvRy1PTxhj2o3VzR6C1SU8ymm1wkrljIh8FthsjFmdWuywaizktZlojBkHnIFlNvxU1AL1QAUwDviFMWYs8BExMLFkw7azTwUeiFoWN2zb+tnAcGAQsA/WM5FJLJ5dY8wrWCasFcD/AP/AMoNHTmKUgYhUYimCe4wxD9nF74rIQHv5QKxWeKwwxuwA/oI11lEjIsfog0IAAAGZSURBVJ3Z5YYATVHJlcFEYKqIrAfuwzIV3Up85cUY02R/b8ayZx9HfJ+HRqDRGPOM/f9BLOUQV3k7OQN4zhjzrv0/jvJ+BlhnjNlijGkFHgI+Qbyf3buMMeOMMZ8CtgOvE4NrmwhlIFaC5buAV4wxP0lZtBy4yP59EdZYQuSIyAARqbF/V2M9sK8ATwLn2KvFRl5jzHXGmCHGmGFYZoEnjDFfJKbyisg+IrJv528su/YaYvo8GGPeATaIyBF20RTgZWIqbwrns9dEBPGU923gBBHpY9cTndc2ls8ugIgcaH8fAnwe6xpHf22jHlDxOOgyCaub9yLwgv05E8uu/TiWZn0cOCBqWW15RwPP2/KuAebY5YcBzwJvYHW9e0Utq4PsJwGPxlleW65/2J9/At+1y2P5PNiyjQEa7GdiGbB/zOXtA2wD+qWUxVJe4PvAq/a79v+AXnF9dm15/xdLYf0DmBKXa6vhKBRFUZRkmIkURVGUcFFloCiKoqgyUBRFUVQZKIqiKKgyUBRFUVBloCiKoqDKQFEURQH+P2rnpgW9yx5lAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([-4.79762874e+02,  4.10476414e-02, -7.80739871e+00,  1.90521273e-01,\n",
+       "        1.14248766e+00,  1.78363875e+01, -6.29546793e-01, -1.09830902e+00,\n",
+       "        9.54615446e+00,  4.26167154e+02, -8.78055030e+00, -1.68575176e+01,\n",
+       "       -7.56462490e+00])"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linalg.inv(X.T @ X) @ (X.T@y)"
+   ]
   }
  ],
  "metadata": {