04_Lab_3_Decision_trees_linear_regression_solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introductory applied machine learning (INFR10069) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 3: Decision trees and linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the first part of this lab we perform Decision trees classification on the [German credit](http://archive.ics.uci.edu/ml/datasets/Statlog+%28German+Credit+Data%29) data set. In the second part we learn how to train simple linear regression model by using the [CPU performance](https://archive.ics.uci.edu/ml/datasets/Computer+Hardware) data set. Both datasets (`credit.csv` and `cpu.csv`) are located at the `./datasets` directory which is adjacent to this file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's import the packages we will be using throughout this lab:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Import packages\n",
    "from __future__ import division, print_function # Imports from __future__ since we're running Python 2\n",
    "import os\n",
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.tree import DecisionTreeClassifier, export_graphviz\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, r2_score\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Decision Trees\n",
    "One of the great advantages of decision trees is their interpretability. The rules learnt for classification are easy for a person to follow, unlike the opaque \"black box\" of many other methods, such as neural networks. We demonstrate the utility of this using a German credit data set. You can read a description of this dataset at the [UCI site](http://archive.ics.uci.edu/ml/datasets/Statlog+%28German+Credit+Data%29). The task is to predict whether a loan approval is good or bad credit risk based on 20 attributes. We've simplified the data set somewhat, particularly making attribute names and values more meaningful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Download the dataset and save it in a directory called `datasets` in the same folder that your notebooks live. Alternatively, you can save the dataset in any folder you wish and modify the `data_path` variable below accordingly. We will load our data into a pandas DataFrame structure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the dataset\n",
    "data_path = os.path.join(os.getcwd(), 'datasets', 'credit.csv')\n",
    "credit = pd.read_csv(data_path, delimiter = ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.1 ==========\n",
    "Display the number of data points and attributes in the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples: 1001, number of attributes: 21\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "print('Number of samples: {}, number of attributes: {}'.format(credit.shape[0], credit.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.2 ==========\n",
    "Get a feeling of the data by using pandas `describe()` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Duration</th>\n",
       "      <th>CreditAmount</th>\n",
       "      <th>InstallmentRate</th>\n",
       "      <th>ResidentSince</th>\n",
       "      <th>Age</th>\n",
       "      <th>NumCreditsAtBank</th>\n",
       "      <th>Dependents</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1001.000000</td>\n",
       "      <td>1.001000e+03</td>\n",
       "      <td>1001.000000</td>\n",
       "      <td>1001.000000</td>\n",
       "      <td>1001.000000</td>\n",
       "      <td>1001.000000</td>\n",
       "      <td>1001.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>20.882118</td>\n",
       "      <td>-9.957330e+05</td>\n",
       "      <td>-7.019980</td>\n",
       "      <td>2.842158</td>\n",
       "      <td>35.217782</td>\n",
       "      <td>0.406593</td>\n",
       "      <td>0.969031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>12.070878</td>\n",
       "      <td>3.160708e+07</td>\n",
       "      <td>316.165715</td>\n",
       "      <td>1.106825</td>\n",
       "      <td>15.398264</td>\n",
       "      <td>31.656714</td>\n",
       "      <td>5.894916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.000000e+09</td>\n",
       "      <td>-10000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-293.000000</td>\n",
       "      <td>-1000.000000</td>\n",
       "      <td>-185.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>12.000000</td>\n",
       "      <td>1.364000e+03</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>27.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>2.319000e+03</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>33.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>24.000000</td>\n",
       "      <td>3.972000e+03</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>42.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>72.000000</td>\n",
       "      <td>1.842400e+04</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Duration  CreditAmount  InstallmentRate  ResidentSince          Age  \\\n",
       "count  1001.000000  1.001000e+03      1001.000000    1001.000000  1001.000000   \n",
       "mean     20.882118 -9.957330e+05        -7.019980       2.842158    35.217782   \n",
       "std      12.070878  3.160708e+07       316.165715       1.106825    15.398264   \n",
       "min       0.000000 -1.000000e+09    -10000.000000       0.000000  -293.000000   \n",
       "25%      12.000000  1.364000e+03         2.000000       2.000000    27.000000   \n",
       "50%      18.000000  2.319000e+03         3.000000       3.000000    33.000000   \n",
       "75%      24.000000  3.972000e+03         4.000000       4.000000    42.000000   \n",
       "max      72.000000  1.842400e+04         4.000000       4.000000    75.000000   \n",
       "\n",
       "       NumCreditsAtBank   Dependents  \n",
       "count       1001.000000  1001.000000  \n",
       "mean           0.406593     0.969031  \n",
       "std           31.656714     5.894916  \n",
       "min        -1000.000000  -185.000000  \n",
       "25%            1.000000     1.000000  \n",
       "50%            1.000000     1.000000  \n",
       "75%            2.000000     1.000000  \n",
       "max            4.000000     2.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "credit.describe(include=[np.number])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CheckingAccount</th>\n",
       "      <th>CreditHistory</th>\n",
       "      <th>Purpose</th>\n",
       "      <th>SavingsAccount</th>\n",
       "      <th>YearsEmployed</th>\n",
       "      <th>PersonalStatus</th>\n",
       "      <th>OtherDebtors</th>\n",
       "      <th>Property</th>\n",
       "      <th>OtherPlans</th>\n",
       "      <th>Housing</th>\n",
       "      <th>Job</th>\n",
       "      <th>Telephone</th>\n",
       "      <th>Foreign</th>\n",
       "      <th>Approve</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "      <td>1001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>none</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>television</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;4</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>car</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>skilled</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>394</td>\n",
       "      <td>530</td>\n",
       "      <td>280</td>\n",
       "      <td>603</td>\n",
       "      <td>339</td>\n",
       "      <td>548</td>\n",
       "      <td>908</td>\n",
       "      <td>333</td>\n",
       "      <td>815</td>\n",
       "      <td>714</td>\n",
       "      <td>631</td>\n",
       "      <td>596</td>\n",
       "      <td>963</td>\n",
       "      <td>701</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       CheckingAccount CreditHistory     Purpose SavingsAccount YearsEmployed  \\\n",
       "count             1001          1001        1001           1001          1001   \n",
       "unique               4             5          10              5             5   \n",
       "top               none    ok_til_now  television           <100            <4   \n",
       "freq               394           530         280            603           339   \n",
       "\n",
       "       PersonalStatus OtherDebtors Property OtherPlans Housing      Job  \\\n",
       "count            1001         1001     1001       1001    1001     1001   \n",
       "unique              5            3        4          3       3        4   \n",
       "top       male_single         none      car       none     own  skilled   \n",
       "freq              548          908      333        815     714      631   \n",
       "\n",
       "       Telephone Foreign Approve  \n",
       "count       1001    1001    1001  \n",
       "unique         2       2       2  \n",
       "top           no     yes    good  \n",
       "freq         596     963     701  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "credit.describe(include=['O'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.3 ==========\n",
    "Display the first 10 data points of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CheckingAccount</th>\n",
       "      <th>Duration</th>\n",
       "      <th>CreditHistory</th>\n",
       "      <th>Purpose</th>\n",
       "      <th>CreditAmount</th>\n",
       "      <th>SavingsAccount</th>\n",
       "      <th>YearsEmployed</th>\n",
       "      <th>InstallmentRate</th>\n",
       "      <th>PersonalStatus</th>\n",
       "      <th>OtherDebtors</th>\n",
       "      <th>ResidentSince</th>\n",
       "      <th>Property</th>\n",
       "      <th>Age</th>\n",
       "      <th>OtherPlans</th>\n",
       "      <th>Housing</th>\n",
       "      <th>NumCreditsAtBank</th>\n",
       "      <th>Job</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>Telephone</th>\n",
       "      <th>Foreign</th>\n",
       "      <th>Approve</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>&lt;0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>ok</td>\n",
       "      <td>furniture</td>\n",
       "      <td>-1.000000e+09</td>\n",
       "      <td>unknown</td>\n",
       "      <td>unemployed</td>\n",
       "      <td>-10000.0</td>\n",
       "      <td>female_single</td>\n",
       "      <td>none</td>\n",
       "      <td>0.0</td>\n",
       "      <td>car</td>\n",
       "      <td>-293.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>-1000.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>-185.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>&lt;0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>critical</td>\n",
       "      <td>television</td>\n",
       "      <td>1.169000e+03</td>\n",
       "      <td>unknown</td>\n",
       "      <td>&gt;=7</td>\n",
       "      <td>4.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>4.0</td>\n",
       "      <td>real_estate</td>\n",
       "      <td>67.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>2.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>1.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>&lt;200</td>\n",
       "      <td>48.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>television</td>\n",
       "      <td>5.951000e+03</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;4</td>\n",
       "      <td>2.0</td>\n",
       "      <td>female</td>\n",
       "      <td>none</td>\n",
       "      <td>2.0</td>\n",
       "      <td>real_estate</td>\n",
       "      <td>22.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>1.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>1.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>bad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>none</td>\n",
       "      <td>12.0</td>\n",
       "      <td>critical</td>\n",
       "      <td>education</td>\n",
       "      <td>2.096000e+03</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;7</td>\n",
       "      <td>2.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>3.0</td>\n",
       "      <td>real_estate</td>\n",
       "      <td>49.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>1.0</td>\n",
       "      <td>unskilled</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>&lt;0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>furniture</td>\n",
       "      <td>7.882000e+03</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;7</td>\n",
       "      <td>2.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>guarantor</td>\n",
       "      <td>4.0</td>\n",
       "      <td>savings</td>\n",
       "      <td>45.0</td>\n",
       "      <td>none</td>\n",
       "      <td>free</td>\n",
       "      <td>1.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>&lt;0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>past_delays</td>\n",
       "      <td>car_new</td>\n",
       "      <td>4.870000e+03</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;4</td>\n",
       "      <td>3.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>4.0</td>\n",
       "      <td>unknown</td>\n",
       "      <td>53.0</td>\n",
       "      <td>none</td>\n",
       "      <td>free</td>\n",
       "      <td>2.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>bad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>none</td>\n",
       "      <td>36.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>education</td>\n",
       "      <td>9.055000e+03</td>\n",
       "      <td>unknown</td>\n",
       "      <td>&lt;4</td>\n",
       "      <td>2.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>4.0</td>\n",
       "      <td>unknown</td>\n",
       "      <td>35.0</td>\n",
       "      <td>none</td>\n",
       "      <td>free</td>\n",
       "      <td>1.0</td>\n",
       "      <td>unskilled</td>\n",
       "      <td>2.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>none</td>\n",
       "      <td>24.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>furniture</td>\n",
       "      <td>2.835000e+03</td>\n",
       "      <td>&lt;1000</td>\n",
       "      <td>&gt;=7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>4.0</td>\n",
       "      <td>savings</td>\n",
       "      <td>53.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>1.0</td>\n",
       "      <td>skilled</td>\n",
       "      <td>1.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>&lt;200</td>\n",
       "      <td>36.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>car_used</td>\n",
       "      <td>6.948000e+03</td>\n",
       "      <td>&lt;100</td>\n",
       "      <td>&lt;4</td>\n",
       "      <td>2.0</td>\n",
       "      <td>male_single</td>\n",
       "      <td>none</td>\n",
       "      <td>2.0</td>\n",
       "      <td>car</td>\n",
       "      <td>35.0</td>\n",
       "      <td>none</td>\n",
       "      <td>rent</td>\n",
       "      <td>1.0</td>\n",
       "      <td>management</td>\n",
       "      <td>1.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>none</td>\n",
       "      <td>12.0</td>\n",
       "      <td>ok_til_now</td>\n",
       "      <td>television</td>\n",
       "      <td>3.059000e+03</td>\n",
       "      <td>&gt;=1000</td>\n",
       "      <td>&lt;7</td>\n",
       "      <td>2.0</td>\n",
       "      <td>male_divorced</td>\n",
       "      <td>none</td>\n",
       "      <td>4.0</td>\n",
       "      <td>real_estate</td>\n",
       "      <td>61.0</td>\n",
       "      <td>none</td>\n",
       "      <td>own</td>\n",
       "      <td>1.0</td>\n",
       "      <td>unskilled</td>\n",
       "      <td>1.0</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  CheckingAccount  Duration CreditHistory     Purpose  CreditAmount  \\\n",
       "0              <0       0.0            ok   furniture -1.000000e+09   \n",
       "1              <0       6.0      critical  television  1.169000e+03   \n",
       "2            <200      48.0    ok_til_now  television  5.951000e+03   \n",
       "3            none      12.0      critical   education  2.096000e+03   \n",
       "4              <0      42.0    ok_til_now   furniture  7.882000e+03   \n",
       "5              <0      24.0   past_delays     car_new  4.870000e+03   \n",
       "6            none      36.0    ok_til_now   education  9.055000e+03   \n",
       "7            none      24.0    ok_til_now   furniture  2.835000e+03   \n",
       "8            <200      36.0    ok_til_now    car_used  6.948000e+03   \n",
       "9            none      12.0    ok_til_now  television  3.059000e+03   \n",
       "\n",
       "  SavingsAccount YearsEmployed  InstallmentRate PersonalStatus OtherDebtors  \\\n",
       "0        unknown    unemployed         -10000.0  female_single         none   \n",
       "1        unknown           >=7              4.0    male_single         none   \n",
       "2           <100            <4              2.0         female         none   \n",
       "3           <100            <7              2.0    male_single         none   \n",
       "4           <100            <7              2.0    male_single    guarantor   \n",
       "5           <100            <4              3.0    male_single         none   \n",
       "6        unknown            <4              2.0    male_single         none   \n",
       "7          <1000           >=7              3.0    male_single         none   \n",
       "8           <100            <4              2.0    male_single         none   \n",
       "9         >=1000            <7              2.0  male_divorced         none   \n",
       "\n",
       "   ResidentSince     Property    Age OtherPlans Housing  NumCreditsAtBank  \\\n",
       "0            0.0          car -293.0       none     own           -1000.0   \n",
       "1            4.0  real_estate   67.0       none     own               2.0   \n",
       "2            2.0  real_estate   22.0       none     own               1.0   \n",
       "3            3.0  real_estate   49.0       none     own               1.0   \n",
       "4            4.0      savings   45.0       none    free               1.0   \n",
       "5            4.0      unknown   53.0       none    free               2.0   \n",
       "6            4.0      unknown   35.0       none    free               1.0   \n",
       "7            4.0      savings   53.0       none     own               1.0   \n",
       "8            2.0          car   35.0       none    rent               1.0   \n",
       "9            4.0  real_estate   61.0       none     own               1.0   \n",
       "\n",
       "          Job  Dependents Telephone Foreign Approve  \n",
       "0     skilled      -185.0       yes      no    good  \n",
       "1     skilled         1.0       yes     yes    good  \n",
       "2     skilled         1.0        no     yes     bad  \n",
       "3   unskilled         2.0        no     yes    good  \n",
       "4     skilled         2.0        no     yes    good  \n",
       "5     skilled         2.0        no     yes     bad  \n",
       "6   unskilled         2.0       yes     yes    good  \n",
       "7     skilled         1.0        no     yes    good  \n",
       "8  management         1.0       yes     yes    good  \n",
       "9   unskilled         1.0        no     yes    good  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "pd.set_option('display.max_columns', None)\n",
    "credit.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pd.set_option('display.max_columns', 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.4 ==========\n",
    "When presented with a dataset, it is usually a good idea to visualise it first. By using seaborn's [pairplot](https://seaborn.github.io/generated/seaborn.pairplot.html?highlight=pairplot#seaborn.pairplot) function, try visualising a scatter plot of the `Age` and `Duration` variables. You can use the `Approve` variable as the `hue` parameter to visualise results separately for each class. Do you notice anything unusual?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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RC//2RDtbN1XxavPos9QB7ty+lqf2nQBcfOLBUr53Znzi2ZXVV7BqzSoADp/N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\nzArABdvMzKwAXLDNzMwK4P8Diqz2nn1uBmoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117a2a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "g = sns.pairplot(data=credit, vars=['Duration', 'Age'], hue='Approve', size=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "There is a data point with negative age. This doesn't make sense whatsoever and this data point has been clearly corrupted with noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.5 ==========\n",
    "In the previous point you should have found a data point, which seems to be corrupted, as some of its values are nonsensical. Even a single point like this can significantly affect the performance of a classifier. How do you think it would affect Decision trees? How about Naive Bayes? A good way to check this is to test the performance of each classifier before and after removing this datapoint."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "Naive Bayes fits Gaussian distributions and thus is very sensitive to outliers. Decision trees is expected to be less affected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.6 ==========\n",
    "Now we want to remove this instance from the dataset by using a filter. We want to remove all instances, where the age of an applicant is lower than 0 years, as this suggests that the instance is corrupted. Use logical indexing to get rid of these instances without creating a new dataframe. Display the number of data points after any outliers have been removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of data points after removal of outliers: 1000\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "credit = credit[credit['Age']>0]\n",
    "print('Number of data points after removal of outliers: {}'.format(credit.shape[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.7 ==========\n",
    "\n",
    "You might have noticed that most of the attributes in the dataset are in fact discrete. Now we want to know which variables exactly are discrete (both categorical and numerical, look [here](http://stats.stackexchange.com/questions/206/what-is-the-difference-between-discrete-data-and-continuous-data) if you are unsure about the difference) and which are continuous variables. In order to do so, we will inspect the number of possible values that each attribute can take. \n",
    "\n",
    "Display the number of values each attributes takes in the dataset. *Hint: As a first step, you want to loop over the columns of the DataFrame. Then you might find the numpy `unique` function quite useful.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of values for attribute CheckingAccount: 4 -- ['<0' '<200' '>=200' 'none']\n",
      "Number of values for attribute Duration: 33\n",
      "Number of values for attribute CreditHistory: 5 -- ['critical' 'ok' 'ok_at_this_bank' 'ok_til_now' 'past_delays']\n",
      "Number of values for attribute Purpose: 10 -- ['appliances' 'business' 'car_new' 'car_used' 'education' 'furniture'\n",
      " 'others' 'repairs' 'retraining' 'television']\n",
      "Number of values for attribute CreditAmount: 921\n",
      "Number of values for attribute SavingsAccount: 5 -- ['<100' '<1000' '<500' '>=1000' 'unknown']\n",
      "Number of values for attribute YearsEmployed: 5 -- ['<1' '<4' '<7' '>=7' 'unemployed']\n",
      "Number of values for attribute InstallmentRate: 4 -- [ 1.  2.  3.  4.]\n",
      "Number of values for attribute PersonalStatus: 4 -- ['female' 'male_divorced' 'male_married' 'male_single']\n",
      "Number of values for attribute OtherDebtors: 3 -- ['co' 'guarantor' 'none']\n",
      "Number of values for attribute ResidentSince: 4 -- [ 1.  2.  3.  4.]\n",
      "Number of values for attribute Property: 4 -- ['car' 'real_estate' 'savings' 'unknown']\n",
      "Number of values for attribute Age: 53\n",
      "Number of values for attribute OtherPlans: 3 -- ['bank' 'none' 'stores']\n",
      "Number of values for attribute Housing: 3 -- ['free' 'own' 'rent']\n",
      "Number of values for attribute NumCreditsAtBank: 4 -- [ 1.  2.  3.  4.]\n",
      "Number of values for attribute Job: 4 -- ['management' 'skilled' 'unemployed' 'unskilled']\n",
      "Number of values for attribute Dependents: 2 -- [ 1.  2.]\n",
      "Number of values for attribute Telephone: 2 -- ['no' 'yes']\n",
      "Number of values for attribute Foreign: 2 -- ['no' 'yes']\n",
      "Number of values for attribute Approve: 2 -- ['bad' 'good']\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "for column in credit:\n",
    "    unique_vals = np.unique(credit[column])\n",
    "    nr_vals = len(unique_vals)\n",
    "    if nr_vals < 11:\n",
    "        print('Number of values for attribute {}: {} -- {}'.format(column, nr_vals, unique_vals))\n",
    "    else:\n",
    "        print('Number of values for attribute {}: {}'.format(column, nr_vals)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems like the variables `Duration`, `CreditAmount` and `Age` are continuous and all the rest are discrete. The discrete variables are not in a very convenient format though. Ideally we would want the discrete attributes to take values between `0` and `n_values-1`. Scikit-learn has a handy [`LabelEncoder`](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html#sklearn.preprocessing.LabelEncoder) implementation which can do that for us. You are encouraged to read its documentation.\n",
    "\n",
    "Now we will create a new DataFrame called `credit_clean` and convert all the discrete variables from `credit` by using a `LabelEncoder`. Remember, we want to change the discrete variables only, so we will have to exclude the `CreditAmount`, `Age` and `Duration` attributes. Also, we don't really mind if the target variable is categorical, so we won't be transforming the `Approve` attribute either. Execute the cell below and make sure you understand what it does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "le_dict = dict() # Initialise an empty dictionary to keep all LabelEncoders\n",
    "credit_clean = credit.copy(deep=True) # Make a copy of the DataFrame\n",
    "# Loop over attributes by excluding the ones that are continuous and the target variable\n",
    "for column in credit_clean.drop(['CreditAmount', 'Age', 'Duration', 'Approve'], axis=1):  \n",
    "    le = LabelEncoder().fit(credit[column]) # Initialise the LabelEncoder and fit\n",
    "    credit_clean[column] = le.transform(credit[column]) # Transform data and save in credit_clean DataFrame\n",
    "    le_dict[column] = le # Store the LabelEncdoer in dictionary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.8 ==========\n",
    "Display the first 10 data points of the clean data. Does it look like what you expected?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CheckingAccount</th>\n",
       "      <th>Duration</th>\n",
       "      <th>CreditHistory</th>\n",
       "      <th>Purpose</th>\n",
       "      <th>CreditAmount</th>\n",
       "      <th>SavingsAccount</th>\n",
       "      <th>YearsEmployed</th>\n",
       "      <th>InstallmentRate</th>\n",
       "      <th>PersonalStatus</th>\n",
       "      <th>OtherDebtors</th>\n",
       "      <th>ResidentSince</th>\n",
       "      <th>Property</th>\n",
       "      <th>Age</th>\n",
       "      <th>OtherPlans</th>\n",
       "      <th>Housing</th>\n",
       "      <th>NumCreditsAtBank</th>\n",
       "      <th>Job</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>Telephone</th>\n",
       "      <th>Foreign</th>\n",
       "      <th>Approve</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>1169.0</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>67.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>48.0</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>5951.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>bad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2096.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>49.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>7882.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>45.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>4870.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>53.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>bad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>9055.0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>24.0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>2835.0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>53.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>6948.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>12.0</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>3059.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>61.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>good</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5234.0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>bad</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    CheckingAccount  Duration  CreditHistory   ...     Telephone  Foreign  Approve\n",
       "1                 0       6.0              0   ...             1        1     good\n",
       "2                 1      48.0              3   ...             0        1      bad\n",
       "3                 3      12.0              0   ...             0        1     good\n",
       "4                 0      42.0              3   ...             0        1     good\n",
       "5                 0      24.0              4   ...             0        1      bad\n",
       "6                 3      36.0              3   ...             1        1     good\n",
       "7                 3      24.0              3   ...             0        1     good\n",
       "8                 1      36.0              3   ...             1        1     good\n",
       "9                 3      12.0              3   ...             0        1     good\n",
       "10                1      30.0              0   ...             0        1      bad\n",
       "\n",
       "[10 rows x 21 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "credit_clean.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.9 ==========\n",
    "Store the input features (i.e. attributes) into a matrix `X` and the target variable (`Approve`) into a vector `y`. Remember to not include the target variable into `X`. *Hint: You can either use pandas `as_matrix()` or `values`.* \n",
    "\n",
    "Display the shapes of `X` and `y`. Confirm that you have 20 input features, one target variable and 1000 data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X shape: (1000, 20)\n",
      "y shape: (1000,)\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "X = credit_clean.drop('Approve', axis=1).as_matrix() # Input features (attributes)\n",
    "y = credit_clean['Approve'].as_matrix() # Target vector\n",
    "print('X shape: {}'.format(np.shape(X)))\n",
    "print('y shape: {}'.format(np.shape(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hold-out validation\n",
    "In the next step we will be using a Decision Tree classifier model. To get an accurate estimate of the model's classification performance we will use hold-out validation. Familiriase yourself with the logic behind [`train_test_split CV`](http://scikit-learn.org/stable/modules/cross_validation.html#cross-validation-evaluating-estimator-performance) (also called `Hold-out` validation) and [how it is used](http://scikit-learn.org/0.16/modules/generated/sklearn.cross_validation.train_test_split.html) in `Scikit-learn`. Execute the cell below to create your training/testing sets by assigning 10% of the data to the test set (and convince yourself you understand what is going on)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.9, test_size=0.1, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.10 ==========\n",
    "Confirm that `X_train` and `X_test` matrices are subsets of `X` by displaying the number of rows in the three matrices (no need to make use of set theory)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of instances in X: 1000\n",
      "Number of instances in X_train: 900\n",
      "Number of instances in X_test: 100\n",
      "Number of instances in X_train and X_test together: 1000\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "print('Number of instances in X: {}'.format(np.shape(X)[0]))\n",
    "print('Number of instances in X_train: {}'.format(X_train.shape[0]))\n",
    "print('Number of instances in X_test: {}'.format(X_test.shape[0]))\n",
    "print('Number of instances in X_train and X_test together: {}'.format(X_train.shape[0] + X_test.shape[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.11 ==========\n",
    "Now we will train a Decision Tree classifier on the training data. Read about [Decision Tree classifiers](http://scikit-learn.org/stable/modules/tree.html) in `Scikit-learn` and how they are [used](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier). \n",
    "Create a `DecisionTreeClassifier` instance and train it by using training data only (i.e. `X_train` and `y_tain`). Set the `criterion` attribute to `entropy` in order to measure the quality of splits by using the information gain. Use the default settings for the rest of parameters. By default, trees are grown to full depth; this means that very fine splits are made involving very few data points. Not only does this make the trees hard to visualise (they'll be deep), but also we could be overfitting the data. For now, we arbitrarily choose a depth of 2 for our tree, but this is a parameter we could tune."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='entropy', max_depth=2,\n",
       "            max_features=None, max_leaf_nodes=None, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            presort=False, random_state=1337, splitter='best')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "dt = DecisionTreeClassifier(criterion='entropy', max_depth=2, random_state=1337)\n",
    "dt.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have mentioned in the class that decision trees have the advantage of being interpretable by humans. Now we visualise the decision tree we have just trained. Scikit-learn can export the tree in a `.dot` format. To visualise the tree, open the output .dot file with an editor, copy its content and paste into [this online .dot renderer](http://dreampuf.github.io/GraphvizOnline/) (you can double click on the tree once it has been produced to view it in full screen)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import tree\n",
    "from sklearn.externals.six import StringIO\n",
    "with open(\"tree.dot\", 'w') as f:\n",
    "    f = export_graphviz(dt, out_file=f,\n",
    "                        feature_names=credit_clean.drop('Approve', axis=1).columns,  \n",
    "                        class_names=credit_clean['Approve'].unique(),  \n",
    "                        filled=True, rounded=True,  \n",
    "                        special_characters=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.12 ==========\n",
    "Inspect the tree. Describe what it shows. Which attribute yields the highest information gain and what is its critical value?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "Below is a png of the tree produced. It shows that we will classify a loan as `bad` if the `CheckingAccount in (2, 3)` i.e. is '>=200' or 'none', and even worse if `OtherPlans in (1, 2)` i.e. is 'none' or 'stores'.\n",
    "\n",
    "The attribute with highest information gain is the one at the top of the tree - `CheckingAccount`. Its critical value is 1.5. To trace back the original values we have to make use of the associated LabelEncoder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['<0' '<200' '>=200' 'none']\n"
     ]
    }
   ],
   "source": [
    "print(le_dict['CheckingAccount'].classes_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The critical value for the `CheckingAccount` attribute is thus <200."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eVigWMABgWJ96UFrhf/TqOn1Wlbre7ARP2lpeukKcyJ11yI+t5YxalW/Qd9gA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\nYXtnoi0rqPDLs73rO0MHkOUuudLqY7fl6gdfnXS0k7flLayslIM+1X7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SlXF9R14XALaZ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tvLyi5sejV5d6XAUAiubMOdtnXXPzo0jTAFRF/s/vd4Hh/ivO4sVBGKnF0RTZWgdt9DMJXdYF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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='tree.png') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "N.B. You should query the validity of this tree. The categories here are being treated as numeric, i.e. ordinal. Is 'none' really greater than '>=200' in the `CheckingAccount` attribute...no not really! This is a drawback of the CART method implemented by scikit learn. One way to force the tree to think of these categories as separate is to use a `OnehotEncoder` but, in practice, because the tree can separate the classes it needs by using multiple splitting conditions, this isn't usually a problem. An example of where it is a problem would be if an important condition was if `CheckingAccount` was  '<0' or 'none'. This tree **can't** make a single branch that contains this condition - if you used a `OnehotEncoder` it could."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.13 ==========\n",
    "Tree-based estimators (i.e. decision trees and random forests) can be used to compute feature importances. The importance of a feature is computed as the (normalized) total reduction of entropy (or other used `criterion`) brought by that feature. Find the relevant attribute of the classifier you just trained and display feature importances along with their names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Importance of feature CheckingAccount:, 0.752\n",
      "Importance of feature Duration:, 0.154\n",
      "Importance of feature CreditHistory:, 0.000\n",
      "Importance of feature Purpose:, 0.000\n",
      "Importance of feature CreditAmount:, 0.000\n",
      "Importance of feature SavingsAccount:, 0.000\n",
      "Importance of feature YearsEmployed:, 0.000\n",
      "Importance of feature InstallmentRate:, 0.000\n",
      "Importance of feature PersonalStatus:, 0.000\n",
      "Importance of feature OtherDebtors:, 0.000\n",
      "Importance of feature ResidentSince:, 0.000\n",
      "Importance of feature Property:, 0.000\n",
      "Importance of feature Age:, 0.000\n",
      "Importance of feature OtherPlans:, 0.094\n",
      "Importance of feature Housing:, 0.000\n",
      "Importance of feature NumCreditsAtBank:, 0.000\n",
      "Importance of feature Job:, 0.000\n",
      "Importance of feature Dependents:, 0.000\n",
      "Importance of feature Telephone:, 0.000\n",
      "Importance of feature Foreign:, 0.000\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "for i, column in enumerate(credit_clean.drop('Approve', axis=1)):\n",
    "    print('Importance of feature {}:, {:.3f}'.format(column, dt.feature_importances_[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.14 ==========\n",
    "Now we want to evaluate the performance of the classifier on unseen data. Use the trained model to predict the target variables for the test data set. Display the classification accuracy for both the training and test data sets. What do you observe? Are you surprised by the results?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification accuracy on training set: 0.731\n",
      "Classification accuracy on test set: 0.730\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "prediction_train = dt.predict(X=X_train)\n",
    "prediction_test = dt.predict(X=X_test)\n",
    "print('Classification accuracy on training set: {:.3f}'.format(accuracy_score(y_train,prediction_train)))\n",
    "print('Classification accuracy on test set: {:.3f}'.format(accuracy_score(y_test,prediction_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "The decision tree classifier is not overfitting. The classification accuracy is similar for training and test. The decision tree has provided a very simple way to interpret the data - splitting it into 4 bins and applying a class to each bin. Clearly this is an oversimplification: even in the training data, the leaves of the tree contain many examples of the 'incorrect' class.\n",
    "\n",
    "**However, the very astute will make an observation:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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cFxHTgLXAio5EJXWRupP5gcCTgbOBQ4Ev8Jv36bcAMymJflPL9l6GuM9mt9zYsVtOg8nM\n9/R7fh+wsDPRSN2p7mT+ALC2uuL+UUQ8BBzcsr/vftpmSlLvv32P7JYbO3bLNZtfxKSJr+7R7KuB\n5wJExEHAAcBXq3vpUO6nrQLuBk6OiH2qwTRHAGtqjk2SpAmh1ivzzLwlIk6JiO8Ak4BXAeuB61vv\np2XmrohYSkn+kygD5B6uMzZJkiaK2qemZebrB9i8cIDjllOqR0mSpL1g0RhJkhrOZC5JUsOZzCVJ\najiTuSRJDWcylySp4UzmkiQ1nMlckqSGM5lLktRwJnNJkhrOZC5JUsOZzCVJajiTuSRJDWcylySp\n4UzmkiQ1nMlckqSGM5lLktRwUzsdgKRmi4jXAy8EpgEfBO4EbgB2Amsyc3HnopO6g1fmkoYtIhYA\nJ2bmScBC4MnA1cAVmbkAmBwR53QwRKkrmMwljcSZwJqI+DzwBeCLwLzMXFXtvxU4rVPBSd3CbnZJ\nI3Eg5Wr8bOBQSkJvvUjYAswa6iSzZ+/P1KlTBj2mp2f68KPUI+bMmc7cuTM6HYZGmclc0kg8AKzN\nzO3AjyLiIeDglv0zgAeHOklPz9Yh32jjxt7hxqgWGzf2smHDlk6HoWEY7EuY3eySRmI18FyAiDgI\nOAD4anUvHeAsYNUeXitplHhlLmnYMvOWiDglIr4DTAJeBawHro+IacBaYEUHQ5S6gslc0ohk5usH\n2LxwrOOQulntyTwi7gE2VU//DXgbA8xBjYhFwCXANmBJZt5Sd2ySJE0EtSbziNgXIDNPbdl2M2UO\n6qqIWFbNQb0LuBSYB+wPrI6I2zJzW53xSZI0EdR9ZX40cEBEfBmYAlzJo+egnkG5Sl9djYjdHBH3\nAUcB99QcnyRJjVd3Mt8KvDszl0fE4ZTkPall/xZgJmX6yqaW7b0MMTfVealjx3mpkjS+1Z3MfwT8\nGCAz74uIByhd6X365qBupiT1/tv3yHmpY8d5qc3mFzFp4qt7nvmfAu+FR+agzgRuG2AO6t3AyRGx\nT0TMAo4A1tQcmyRJE0LdV+bLgY9FxCrKffELKRWjfmMOambuioillAIUkygD5B6uOTZJkiaEWpN5\nNRr9/AF2LRzg2OWU5C9JkvaC5VwlSWo4k7kkSQ1nMpckqeFM5pIkNZzJXJKkhjOZS5LUcCZzSZIa\nzmQuSVLDmcwlSWo4k7kkSQ1nMpckqeHqXmhF0gQXEfcAm6qn/wa8DbiBsrjSmsxc3KHQpK7hlbmk\nYYuIfQEy89Tqv4uAqykrHy4AJkfEOR0NUuoCXplLGomjgQMi4svAFOBKYF5mrqr23wqcDtzcofik\nruCVuaSR2Aq8OzPPBF4FfAKY1LJ/CzCrE4FJ3cQrc0kj8SPgxwCZeV9EPADMa9k/A3hwqJPMnr0/\nU6dOGfSYnp7pIwhTfebMmc7cuTM6HYZGmclc0kj8KXAksDgiDgJmArdFxILM/DpwFrByqJP09Gwd\n8o02buwdYaiC8nvcsGFLp8PQMAz2JcxkLmkklgMfi4hVlNHrFwIPANdHxDRgLbCic+FJ3cFkLmnY\nMnMbcP4AuxaOcShSV3MAnCRJDWcylySp4UzmkiQ1nMlckqSGq30AXEQ8DvgucBqwgwFqNkfEIuAS\nYBuwJDNvqTsuSZImilqvzCNiKvAhSpUoGKBmc0Q8HrgUOBF4LvD2akqLJElqQ93d7O8BlgE/o5R4\nHKhm8/HA6szcnpmbgfuAo2qOS5KkCaO2ZB4RFwK/yMzb2V2rufX9tlCqRc1g9/KJAL1Yy1mSpLbV\nec/85cDOiDidsrLSx4G5Lfv7ajZvpiT1/tsHZS3nsWMtZ0ka32pL5tV9cQAiYiXwSuDdETE/M+9k\nd83mu4ElEbEPsB9wBLBmqPNby3nsWMu52fwiJk18Y13O9TLgutaazZm5KyKWAqsp3fFXZObDYxyX\nJEmNNSbJPDNPbXm6cID9yykLNkiSpL1k0RhJkhqurWQeEdcMsO3G0Q9HkiTtrUG72SPieuBQ4LiI\neHrLrmk4fUySpHFhqHvmbwUOAT4AvKll+3bKADZJktRhgybzzFwPrAeOjoiZlKvxvgIw04GNdQYn\nSZKG1tZo9oi4HLgceKBl8y5KF7wkSeqgdqemXQwclpkb6gxGkiTtvXanpv0Eu9QlSRqX2r0yvw9Y\nHRF3AA/1bczMN9cSlaTGiIjHAd8FTgN2ADcAO4E1mbm4g6FJXaPdK/P/BL4E/JoyAK7vP0ldLCKm\nAh8C+hZLuJpSknkBMDkizulYcFIXaevKPDPfNPRRkrrQe4BllAGyk4B5mbmq2ncrcDpwc4dik7pG\nu6PZd1JGr7f6WWY+afRDktQEEXEh8IvMvD0irqg2t/b2bcHiUtKYaPfK/JEGWq14di5wYl1BSWqE\nlwM7I+J04Gjg48Dclv0zgAfbOdHs2fszdeqUQY/p6Zk+zDDVas6c6S6LOwHt9appmbkN+ExEXFlD\nPJIaorovDkBErAReCbw7IuZn5p3AWcDKds7V07N1yGM2buwdZqRqtXFjLxs2bOl0GBqGwb6EtdvN\nfkHL00nA0wHXHJfU32XAdVUP3lpgRYfjkbpCu1fmv9/yeBdwP3De6IcjqYky89SWpws7FYfUrdq9\nZ/7y6pt2VK9Zk5nba41MkiS1pd31zI+lFI65EfgY8JOIOKHOwCRJUnva7WZfCpyXmd8GiIhnAdcA\nx9cVmCRJak+7FeCm9yVygMy8C3hMPSFJkqS90W4y39haljEizuU3l0OVJEkd0m43+yXAFyNiOWVq\n2i7gpNqikiRJbWv3yvwsykIKT6FMU9uA008kSRoX2k3mlwDPzsxfZub3gWOBS+sLS5IktavdbvZp\n/GbFt4d59MIrjxIRk4HrKPPTd1LKPf6aAdY7johFlC8N24AlmXlLm7FJktTV2k3mnwdWRsRN1fM/\noL1lDV8A7MrMkyNiAfA2yj33KzJzVUQsqwbW3UW50p8H7A+sjojbqjrwkiRpEG11s2fm6yhzzQM4\nFFiamVe18bqbKVfbUO639zDwesfHA6szc3tmbqYUqDlqb34QSZK6VdurpmXmCoaxaEJm7oyIGyjL\npr6Ekrz7bAFmUpZK3NSyvRfXQZYkqS17vQTqcGTmhRHxOOBuYL+WXX3rHW+mJPX+2/fI9Y/Hjusf\nS9L4Vmsyj4jzgYMz8x3AQ8AO4LsRsSAzv87u9Y7vBpZExD6UZH8EsGawc7v+8dhx/eNm84uYNPHV\nfWX+WeBjEfH16r3+AvghcH3reseZuSsilgKr2T1AzvXSJUlqQ63JPDO3MvC65wsHOHY5sLzOeCRJ\nmojaLRojSZLGKZO5JEkNZzKXJKnhxmRqmtRqx44drF+/rtNhNN4hhxzKlCmDT8+U1B1M5hpz69ev\n46rPvJnpB84c+mANqPf+zbzlJW/gsMMO72gce7P+gqT6mMzVEdMPnMmsJ8zudBgaubbWX6hKO0uq\niffMJQ1bm+svnNaJ2KRuYjKXNCIt6y8sBT5JuTLvswXXWZBqZze7pBFrY/2FQbnWwthxrYWJyWQu\nadj2Yv2FQbnWwthxrYXmGuxLmMlc0ki0tf5CB+OTuoLJXNKw7c36C5Lq4wA4SZIazmQuSVLDmcwl\nSWo4k7kkSQ1nMpckqeFM5pIkNZzJXJKkhjOZS5LUcCZzSZIazgpwkqRh2bFjB+vXr+t0GI13yCGH\nMmXK4AsNDcVkLkkalvXr13HVZ97M9ANndjqUxuq9fzNveckbOOyww0d0HpO5JGnYph84k1lPmN3p\nMLpebck8IqYCHwUOAfYBlgD/CtwA7ATWZObi6thFwCXANmBJZt5SV1ySJE00dQ6AOx+4PzPnA88F\nrgWuBq7IzAXA5Ig4JyIeD1wKnFgd9/Zq6URJktSGOrvZbwI+Uz2eAmwH5mXmqmrbrcAZlKv01Zm5\nHdgcEfcBRwH31BibJEkTRm3JvFrnmIiYQUnqVwLvaTlkCzATmAFsatneC8yqKy5JkiaaWgfARcST\ngM8C12bmP0TEu1p2zwAeBDZTknr/7YOaPXt/pk4dfCh/T8/0vY5ZjzZnznTmzp0xaufzcxkdo/25\nSGquOgfAPR74MrA4M++oNt8bEfMz807gLGAlcDewJCL2AfYDjgDWDHX+np6tQ8awcWPvMKNXq40b\ne9mwYcuonk8j1+7nYsKXJr46r8wvBx4LXBURbwB2AX8JXFMNcFsLrMjMXRGxFFgNTKIMkHu4xrgk\nSZpQ6rxn/mrg1QPsWjjAscuB5XXFIknSRGbRGEnDtjf1JCTVx4VWJI1EW/UkOhmg1A1M5pJG4ibg\nqurxnupJnNaJwKRuYje7pGFrs56EdSOkmpnMJY1Im/UkBmXdiLEzmvUJ/ExGx2h8JiZzScO2F/Uk\nBmXdiLEzmnUj/ExGx2jUjDCZSxqJtupJdDA+qSuYzCUN297Uk5BUH0ezS5LUcCZzSZIazmQuSVLD\nmcwlSWo4k7kkSQ1nMpckqeFM5pIkNZzJXJKkhjOZS5LUcCZzSZIazmQuSVLDmcwlSWo4k7kkSQ1n\nMpckqeFM5pIkNZzJXJKkhpta9xtExAnAOzLz9yPiMOAGYCewJjMXV8csAi4BtgFLMvOWuuOSJGmi\nqPXKPCL+GrgO2LfadDVwRWYuACZHxDkR8XjgUuBE4LnA2yNiWp1xSZI0kdTdzf5j4EUtz4/NzFXV\n41uB04HjgdWZuT0zNwP3AUfVHJckSRNGrck8Mz8HbG/ZNKnl8RZgJjAD2NSyvReYVWdckiRNJLXf\nM+9nZ8vjGcCDwGZKUu+/fVCzZ+/P1KlTBj2mp2f6MEJUf3PmTGfu3Bmjdj4/l9Ex2p/LcLUzLkZS\nvcY6mX8vIuZn5p3AWcBK4G5gSUTsA+wHHAGsGepEPT1bh3yzjRt7RxatgPJ73LBhy6ieTyPX7udS\nZ8KvxsX8CaVHDXaPi1kVEcsi4pzMvLm2ACQBYz817TLgzRHxDWAasCIzfw4sBVYDX6H8IXh4jOOS\nNDxDjYs5bexDkrpP7VfmmfnvwEnV4/uAhQMcsxxYXncskkZXZn4uIp7Ssqn/uBjHv0hjYKy72SVN\nbAONixmSY2DGzmiOtfAzGR2j8ZmYzCWNpoHGxQzJMTBjZzTHwPiZjI7RGP9iMpc0mi4DrqsKP60F\nVnQ4HqkrmMwljUg742Ik1cuFViRJajiTuSRJDWcylySp4UzmkiQ1nMlckqSGM5lLktRwJnNJkhrO\nZC5JUsOZzCVJajiTuSRJDWcylySp4UzmkiQ1nMlckqSGM5lLktRwJnNJkhrOZC5JUsOZzCVJajiT\nuSRJDWcylySp4UzmkiQ13NROB9AnIiYBHwSOBh4CLs7MdZ2NStLesi1LY288XZmfC+ybmScBlwNX\ndzgeScNjW5bG2HhK5icDXwLIzG8Dx3U2HEnDZFuWxti46WYHZgKbWp5vj4jJmblzJCf95aYNI4uq\ny9X1++u9f3Mt5+0W4/z3V0tbBtvzSNXx+xvn/xbHvdH6/U3atWvXqJxopCLivcC3MnNF9fwnmfnk\nDoclaS/ZlqWxN5662b8BPA8gIp4F/Etnw5E0TLZlaYyNp272zwGnR8Q3qucv72QwkobNtiyNsXHT\nzS5JkoZnPHWzS5KkYTCZS5LUcCZzSZIazmTeAFHc0ek4JpqIeFlEvG0Yr/uvOuLRxGdbrodt2WTe\nJI5UHD/8LDQS/vsZPybMZzGepqZNKBHxGODjwBOB/wDmA88HrgG2UxagWJSZ/xERrwXOA7YBd2bm\n5RHxBOAT1el+Ptbxd5GTIuIrwAzgTcB+wGJK29gFvAh4EPgI8DRgHbBvZ0JVJ9iWG6Or27JX5vW5\nBFiXmacAfwM8nvKP6M8y8/eBZcD7IuIZwIuBZ2Xms4HDI+L5wJXAJzPzOcDnO/EDdInezDwNOBu4\nFjgceF5mzgfWAmdS/gi0Lhyyf6eCVUfYlpuhq9uyybw+vwt8EyAzE9gAHJSZfdWw7gSeDgRwV0vd\n6tXV9sOB71Tb+opvaPStBsjMDZR64tuBGyPio8CRwDTgqVSfRWb+FPhpZ0JVh9iWm6Gr27LJvD5r\ngJMAIuIw4EDgPyPiyGr/QiCBHwInRMTkah3o+dX2f+17PXD8GMbdbY4HqLpCZwF/CbwUuJjSfTqJ\nls8iIg7vT8GyAAAAzElEQVQCDu5IpOoU23IzdHVb9p55fZYDN0TE14CfAL+idNddGxFQvjVelJnr\nI+Imyjf/ScDqzLw5IlYDn4iI84B/68QP0CUeExFfBQ4ALgJeAdxF+Xw2Uq7AboyI0yPiW5TP8hcd\ni1adYFtuhq5uy5ZzrUlEnAhMz8zbI+J3gFsz8/BOxyVp79iW1QRemddnHfCpiHgj5ff8Zx2OR9Lw\n2JY17nllLklSwzkATpKkhjOZS5LUcCZzSZIazmQuSVLDmcwlSWo4k7kkSQ333/xFQn2FCGIvAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a854710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(8,4))\n",
    "sns.countplot(y_train, ax=ax1)\n",
    "ax1.set_title('Training set', size=12)\n",
    "ax1.set_xlabel(' ')\n",
    "sns.countplot(y_test, ax=ax2)\n",
    "ax2.set_xlabel(' ')\n",
    "ax2.set_ylabel('')\n",
    "ax2.set_title('Validation set', size=12)\n",
    "fig.suptitle('Target distribution', size=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dummy classifier of predicting everything as 'good' **will beat this model (75% accuracy)!** It is worse than the baseline."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.15 =========="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit another `DecisionTreeClassifier` but this time grow it to full depth (i.e. remove the max_depth condition. Display the classification accuracy for training and test data as above. Again, what do you observe and are you surprised?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification accuracy on training set: 1.000\n",
      "Classification accuracy on test set: 0.660\n"
     ]
    }
   ],
   "source": [
    "dt_fulldepth = DecisionTreeClassifier(criterion='entropy', random_state=1337)\n",
    "dt_fulldepth.fit(X_train, y_train)\n",
    "prediction_train2 = dt_fulldepth.predict(X=X_train)\n",
    "prediction_test2 = dt_fulldepth.predict(X=X_test)\n",
    "print('Classification accuracy on training set: {:.3f}'.format(accuracy_score(y_train,prediction_train2)))\n",
    "print('Classification accuracy on test set: {:.3f}'.format(accuracy_score(y_test,prediction_test2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "This is a classic case of overfitting. The tree is allowed to grow to full depth and perfectly fit the training data. The result is that the test accuracy is much lower than the train; in fact it is less accurate than the very simple depth 2 tree! It's important to note that, when grown to full depth, decision tree classifiers can perfectly separate the training data (if no two datapoints are identical but have different classes). Performance on unseen data is likely to be much lower."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.16 ==========\n",
    "By using seaborn's heatmap function, plot the normalised confusion matrices for both the training and test data sets **for the max_depth=2 decision tree from question 1.11**. Make sure you label axes appropriately. *Hint: You can make use of the `plot_confusion_matrix` function introduced in Lab_2.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_confusion_matrix(cm, classes=None, title='Confusion matrix'):\n",
    "    \"\"\"Plots a confusion matrix.\"\"\"\n",
    "    if classes is not None:\n",
    "        sns.heatmap(cm, xticklabels=classes, yticklabels=classes, vmin=0., vmax=1., annot=True)\n",
    "    else:\n",
    "        sns.heatmap(cm, vmin=0., vmax=1.)\n",
    "    plt.title(title)\n",
    "    plt.ylabel('True label')\n",
    "    plt.xlabel('Predicted label')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIk1GHtf6yLv61vo4MP52jpn9EJgKVBFdWHwxgdhERBITcOWj3hr180CaaF2P44hmf9RI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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a903e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cm = confusion_matrix(y_train, prediction_train)\n",
    "cm_norm = cm/cm.sum(axis=1)[:, np.newaxis]\n",
    "plt.figure()\n",
    "plot_confusion_matrix(cm_norm, classes=dt.classes_, title='Training confusion')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b160f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cm = confusion_matrix(y_test, prediction_test)\n",
    "cm_norm = cm/cm.sum(axis=1)[:, np.newaxis]\n",
    "plt.figure()\n",
    "plot_confusion_matrix(cm_norm, classes=dt.classes_, title='Test confusion')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**N.B. it will be obvious if you have plotted the full depth decision tree as the training confusion matrix with be the identity**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.17 ==========\n",
    "\n",
    "Finally we will create a [`Random decision forest`](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) classifier and compare the performance of this classifier to that of the decision tree. The random decision forest is an ensemble classifier that consists of many decision trees and outputs the class that is the mode of the class's output by individual trees. Start with `n_estimators = 100`, use the `entropy` criterion and the same train/test split as before. Plot the classification accuracy of the random forest model on the test set and show the confusion matrix. How does the random decision forest compare performance wise to the decision tree?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification accuracy on test set: 0.790\n"
     ]
    },
    {
     "data": {
      "image/png": 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K1NJYLwMnQ90odAYwGPgScCJwJdFKuZnAZe5eaWbnEm0WtJZotd36tPePItrl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b4fa710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "rf = RandomForestClassifier(n_estimators=100, criterion='entropy')\n",
    "rf.fit(X_train, y_train)\n",
    "prediction_test = rf.predict(X=X_test)\n",
    "print('Classification accuracy on test set: {:.3f}'.format(accuracy_score(y_test,prediction_test)))\n",
    "cm = confusion_matrix(y_test, prediction_test)\n",
    "cm_norm = cm/cm.sum(axis=1)[:, np.newaxis]\n",
    "plt.figure()\n",
    "plot_confusion_matrix(cm_norm, classes=rf.classes_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.18 ==========\n",
    "How high can you get the performance of the classifier by changing the max depth of the trees (`max_depth`), or the `max_features` parameters? Try a few values just to get a look. *Don't do a grid search or anything in-depth, just get a feel*. Try the same settings twice...do you get the same accuracy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification accuracy on test set with max features = 1 and max_depth = None: 0.770\n",
      "Classification accuracy on test set with max features = 1 and max_depth = 2: 0.750\n",
      "Classification accuracy on test set with max features = 1 and max_depth = 5: 0.750\n",
      "Classification accuracy on test set with max features = 1 and max_depth = 10: 0.780\n",
      "Classification accuracy on test set with max features = sqrt and max_depth = None: 0.760\n",
      "Classification accuracy on test set with max features = sqrt and max_depth = 2: 0.750\n",
      "Classification accuracy on test set with max features = sqrt and max_depth = 5: 0.770\n",
      "Classification accuracy on test set with max features = sqrt and max_depth = 10: 0.750\n",
      "Classification accuracy on test set with max features = log2 and max_depth = None: 0.760\n",
      "Classification accuracy on test set with max features = log2 and max_depth = 2: 0.750\n",
      "Classification accuracy on test set with max features = log2 and max_depth = 5: 0.770\n",
      "Classification accuracy on test set with max features = log2 and max_depth = 10: 0.750\n"
     ]
    },
    {
     "data": {
      "image/png": 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KGpGISBFlMplEHykNlcRLwN2nAoeWOw4RkVLRm8nSQUm8BMzsE6Auv7+7b1CG\ncEREik6F63RQEi+NnXP+bg7sD7QsTygiIrKiUhIvAXf/LK/XZWb2OnBhOeIRESk6FcVTQUm8BMys\nT05nBtgUaF2mcEREik4Xq6WDknhp5L7NrA74HzCgTLGIiBSdcng6KImXxn3ufl25gxARKRU9hS0d\ndJ94aZxY7gBEREpJT2xLB5XES2OSmT0LjAZqsj3dfXD5QhIRKR61iaeDknhpvJLzt/Z0EVnhKIen\ng5J4EZnZAHe/3d3Pb/rbIiKVq5glcTPLAEOAzYEfgGPcfUKB790AfO3uZxZt5hVObeLFdUq5AxAR\nqUD7AS3dvRcwCLgy/wtmdjyw2fIOLO2UxEVEJLEiX9jWGxgO4O6jgW1yB5rZDsC2wA0lWJSKpur0\n4trUzBarAiK0i9fp2ekisqLIVBe1Ubw9MD2ne56ZVbn7AjNbGziXUFo/uJgzXREoiRfXx8Be5Q5C\nRKTUinx1+gygXU53lbsviH//ElgNeBzoALQ2sw/d/Y5iBlCplMSLa26B56aLiEjjRgH9gfvNbHtg\nbHaAu18DXAPh4mHAlMAXUhIvrlHlDkBEZHko8i1mw4B+ZpY9hh5lZocCbd39pqLOaQWjJF5E7n5S\nuWMQEVkeilmd7u51wMC83h8V+N7tRZvpCkJJXEREEtPDXtJBSVxERJJTFk8FJXEREUlMbzFLByVx\nERFJTAXxdFASFxGRxPQWs3RQEhcRkcSUw9NBz04XERGpUCqJi4hIciqKp4KSuIiIJKar09NBSVxE\nRBJTEk8HtYmLiIhUKJXERUQkMTWJp4OSuIiIJKbq9HRQEhcRkcT0sJd0UBIXEZHklMNTQRe2iYiI\nVCiVxEVEJLGqKpUB00BJXEREklMOTwUlcRERSUwXtqWDzqVEREQqlEriIiKSmEri6aAknhJm9hxQ\nV2iYu/ddzuGIiDROOTwVlMTT43fx/3OBB4FRwHZA/7JFJCLSAD2xLR2UxFPC3R3AzNZy9/ti72Fm\n9vsyhiUiUpiq01NBSTyFzOxo4FWgFzC3zOGIiCxGOTwdlMTT5zDgr8Avgfdj949eXV0dlw4Zykef\nfEbLFs3568kD6bT22vXDXxz9Gjffez/NmlWzz2592W/33aitreX8q//FF1O+om3bNvx54LF06rA2\nEyZO4uJrbwBgnY4dOOvkgXpwxQrg92cfwwbWmblzarnq3OuZMnlq/bBd99mRg47ch+9nzOaph1/g\nyWHP1Q8Vpr67AAANsUlEQVSz7l04+rRf86ffDi5H2BVLF7alg45cKePuU4DhwLPAC+7+dZlDSoXn\nX36VubXzuOXyizhxwGFcfdNt9cPmzZ/P1Tfdxr/+di43XDyYYcOf4tvp0xk24mnatm7NLVdczBnH\nH82l190IwHV33M1JRx7OjX+/kDrqeOnV18u0VFIsvXbdluYtmnPa4Wdzy9V3c/wfB9QPa7fyShxx\n4sGcPuBc/njUefTduzdrrL0aAAcdtQ+nnn88zVs0L1folasqk+wjJaEknjJmdjFwFKEafYCZXVHm\nkFLhrfc/YIettwBgM9uID8aNrx/26aTJrNOxAyu1aUOzZs3YYtONGTP2fT6ZNJle22wJQOefduTT\nSZMB+Ptf/8Tmm3SjtraWr7/9jpXatFn+CyRFtdmW3Xh95FsA+NiP6brpBvXDOqyzFuP9U2Z/XwPA\nR++OZ+PNNwLgi4lTGHzK5cs/4BVAJpNJ9JHSUBJPnz7ufpC7Xw0cCPQud0BpMGt2zSLJtrq6mgUL\nFiwc1nbhsDatWzFr9mxsg/V56dU3ABj74UdM++Zb6urqyGQyTJk6jUNOPI3pM2bSdYP1luuySPG1\nWakNs2bOru+eP39+feL4/LMv6bxhJ1b+STtatmrBFttvRqvWLQH47zOvMX/e/LLELFIMSuLp09zM\nstslQwP3jv/YtG3Tmtk1P9R3L6irq2/HbtumNbNm19QPmz27hpVWass+u+1C29atOO7PZ/HCK6+y\ncZcN6g/sa6+5Bg8MvZYD9uzHlTfeunwXRopu9vezad22VX13VVUVdXXhpzNr5myGXnYHZ191On++\n9GQ+fv8Tpn87s1yhrjAyVZlEHykNJfH0+TcwysyuAkYC95Y5nlTYfJNujHp9DBBK1V06r1s/bL11\nOjHpyynM/H4WtbW1vPn+B/ToZrw/bjzbbtGDoZdeyK69d+Cna68FwOkXXMKkL74EoE3r1lTroraK\n995bznZ9tgKgW4+ufDJuYv2wqqoMXTZenzOOPI+LTr+KTut35P03P8ybgpJMUkri6aCr01PG3a8w\nsxGAATe5+3vljikNdtmhJ6+++TZH//FMAM459SRGvPASNT/MYb/dd+O0Y47kpLMHU0cd+/bbldVX\n/QnNmjXj+r/fwy3/foD2K7XlrFNOAODIXx7A+VdfS/NmzWnVsgVnnXxCORdNimDU06+y1Q49uPLO\ncIX5FWddx857/oxWbVoy/IFnAbj2vkuYO2cuD9z+KDNnzMqbgiq8ElM7dypkslVOkg5m1gm4CtgU\ncOA0d/90ScadMe5dbUxZxC/3121TUtiId+9bpiw8+fHhiY43nfbaQ1m/BFSPmD43AncSHvRyO3Bz\necMREZG0UnV6+rRy94fj3w+a2WlljUZEpBCVq1NBJfH0aWZm3QGy/4uIpI0ubEsHlcTT5/fAzWbW\nEfgcOK7M8YiILCZTxLs6zCwDDAE2B34AjnH3CTnDDwVOAWqBse6uq1EjlcTT5zFgK6A6/v+SmY0z\ns37lDUtEpGT2A1q6ey9gEHBldoCZtQIGAzu5+47AKmamVzRHSuLp8yKwqbt3ALoR3i2+J3BBWaMS\nEclV3Gen9ya8MwJ3Hw1skzNsDtDL3efE7maE0rqgJJ5GnbLvFnf38cC67v4xMK+8YYmILFTkZ6e3\nB6bndM/LPrnS3evcfRqAmf0eaOvuT5dkoSqQ2sTT50szuwT4L+E2symxKl3vFReR9CjutWozgHY5\n3VXuviDbEdvM/w50BQ4o6pwrnEri6XME8AWhCn0ScCTwPXBoGWMSEVlEkUvio4C9AMxse2Bs3vCh\nhDbz/XKq1QWVxFPH3X8A/pnX++VyxCIispwMA/qZ2ajYfVS8Ir0t8Abh9cwvmdlzhGfk/sPdHypP\nqOmiJC4iIollqotXkevudcDAvN4f5fytXNUArRgREUlOL0BJBSVxERFJbAnauWU50IVtIiIiFUol\ncRERSU7PQ08FJXEREUlM1enpoCQuIiLJKYmngpK4iIgkpteLpoOSuIiIJKeSeCooiYuISGJqE08H\nJXEREUlOSTwVlMRFRCQxtYmngx72IiIiUqFUEhcRkeRUnZ4KSuIiIpJYpkoVuWmgJC4iIsmpTTwV\ndColIiJSoVQSFxGRxDIZlQHTQElcRESS04VtqaAkLiIiiemJbemgJC4iIsnpwrZUUBIXEZHEVBJP\nByVxERFJTkk8FZTERUQkOV2dngpK4iIikphegJIOOpUSERGpUCqJi4hIcmoTTwUlcRERSSxTVV3u\nEAQlcRERWQpqE08HtYmLiIhUKJXERUQkObWJp4KSuIiIJKYntqWDkriIiCSnh72kgpK4iIgkpwvb\nUkFJXEREElN1ejooiYuISHKqTk8FJXEREUlMJfF0UBIXEZHkVBJPBSVxEREpKzPLAEOAzYEfgGPc\nfULO8H2As4Fa4FZ3v6ksgaaQTqVERCSxTFUm0acJ+wEt3b0XMAi4MjvAzJrF7t2AnYHjzGyN0ixV\n5VESFxGR5DKZZJ/G9QaGA7j7aGCbnGEbA+PcfYa71wIjgT6lWKRKpCQuIiKJZaqqE32a0B6YntM9\nz8yqGhg2E1i5eEtS2dQmvgJp33UzXS4qixjx7n3lDkFWUC3ar1bM480MoF1Od5W7L8gZ1j5nWDvg\nuyLOu6KpJC4iIuU2CtgLwMy2B8bmDPsA6GJmq5hZC0JV+svLP8R0ytTV1ZU7BhER+RHLuTq9R+x1\nFLA10NbdbzKzvYFzgQxws7tfX55I00dJXEREpEKpOl1ERKRCKYmLiIhUKCVxERGRCqUkLhXJzAaY\n2UVLMd6XpYhHVgwWPFfuOESWlJK4/NjoSk5pivYRqRh62ItUsl5m9jTh4Q/nA62BEwn7dR2wP+Gh\nEEOBTYAJQMvyhCqlYmatgDuADsBkwn3EewPXAPMIL9Q41t0nm9npwMGEF2m86O6DzGxt4K44ua+W\nd/wiy0Ilcalk37v7bkB/4FqgK7CXu/chPCBid0Iiz32xQptyBSslcxwwwd13BM4D1iKcuJ3g7rsA\n1wFXmdlmwEHA9u7+M6BrvP/4r8Dd7r4r8GA5FkBkaSmJSyUbCeDu0wjPVp4H3G5mtwDdgebARsCr\n8XuTgEnlCVVKaGPgvwDu7sA0oKO7Z5/69SKwKWDAKzmP8xwZ+3cl7iOEJ4eJVAwlcalk2wHE6tCV\ngVOAQ4BjCFWoGeB9oFf8XkegU1kilVJ6l4XbeENgdeBzM+seh+8MOPAh0NPMquITwvrE/vX7CHGf\nEqkUahOXStbKzJ4B2gJHA8cDrxBK5N8QSmO3m1k/M3sZmAhMLVu0Uio3A7eZ2fOEbVxDqGK/1swg\n7A9Hu/unZnYfodSeAUa6+0NmNhK4y8wOBj4pxwKILC09dlVEKpqZ7QCs5O5PmVkX4Al371ruuESW\nB5XERaTSTQDuMbNzCce0E8ocj8hyo5K4iIhIhdKFbSIiIhVKSVxERKRCKYmLiIhUKCVxERGRCqWr\n00WKyMw6Ax8B78VeLYDPgaPc/YulnOYAYCd3/62ZPQoc4+5TGvjuecBT7r7ETx4zswXuXpXX71yg\nzt0HNzLeJzGuiUs4nyanKSLJKImLFN/n7r5VtiO+MvVa4IBlnbC792/iKzsBzyac7NLeoqJbW0TK\nTElcpPReBPaB+tLraGBzYEdgT+BUwhPE3gBOdPe5ZvYbwos5phOeQjYzZ/ydCG/b+hfQG5gLXEh4\nQ9s2wE1mtj/h0bPXAasCs4GT3f2tWFvwf4Qn3Y1uKngzOwk4nPDymAXAwfEZ5RngfDPbnPCUtN+5\n+1gzWxO4gfCI2wXAIHdPemIhIktAbeIiJWRmzQmvvhyZ0/sxd98YWBM4FtghltynAWeYWQfgUkKC\n3oHwqtWsbOn390Bbd+8G9APOBu4BXic8YvQ94Hbgj+6+DeGRtPfGca8FbonzbLTa3czaAb8gVJv3\nAB5i0YepeJzOhXF+AP8Abnb3bYF9gaFm1rbxNSUiS0MlcZHi+6mZjSGUVFsQ3pA1KGd49o1ZuwBd\ngFfiCzmaA2MIL+MY5e7/AzCz/wP6xnEy8f+dCKVd3P0rwlvbiM8Kz8SkuS1wa5w2QBszW5XwQpBD\nYr+7gJsaWhB3n2lmhwGHmtlGwB7AmzlfuTl+7wkzu9PM2gO7hVDsgvidamDDBteWiCw1JXGR4luk\nTbyAmvh/NXCfu58KYGZtCIl81zgsa17O39mSeG3uBOPbu3IvMKsGavLa5ju6+zdmtoBYC+fudbG7\nIDPrBDwPXAM8DkwBtmggtmxc1UBfd/8uTqMDofp//4bmIyJLR9XpIsWXaforQEiO+5vZGrG0fD3h\ndaojCa/M7GBmVYTq+Pxpvwj8CiC2QT9PKPXPA5q5+wxgXCxFY2b94jgATwO/if0PJLSlN2RbYJy7\n/wN4jdCGn3uCkZ3+/sCH7l4DPAOcGPtvArwDtF7CdSIiCSiJixRfY1dt1w9z93eA8wlXk48lJOhL\n3H0qoc37GcKrVacXGH8IMNvM3gaeBE5y91nAcOB6M9uekGCPid/5GzHpx2kfaGZvEarHZzQS7wig\n2szeI7zC8xNg/ZxYNjKzNwkX5w2I/U8Gto/zvQc4LMYmIkWmF6CIiIhUKJXERUREKpSSuIiISIVS\nEhcREalQSuIiIiIVSklcRESkQimJi4iIVCglcRERkQqlJC4iIlKh/j+IsMOdmiEhKgAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b43be50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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15fhq5L6xD7AOcAYQedia0NnZycmnncG+XzqEgw47khdfmtjukKwfGbbO6oz+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\nZoU52ZqZmRX2/wHhtKsPQnf1vwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a8f6a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c13c750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mpUP3EZfm+KwDEBFpaXqyVjpUIi7NVDN7HBgPzM33dPdh2YUkIlJeaiNOhxJx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b626610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CN7OfAkcSXnBUDRwan4mfAc41s20IT8s72d0nm9m6wPWExyNXA6Pd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b618f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SLslvXxoRn6wxLDOz/rmKu3JO0F0gIg4EbgfGALNrDsfMbCHOz9VzL+767QOM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\nnKDNzMy6kBO0mZlZF/r/jdQCjw525AgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b755fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CfbPQzcBu0TKMJXSC6t5AHLVQt+w/B+6J1me3RmJPaz8o9HNgQLReziNs67htBqGUeJeZ\nTYyW6fTo/acICWu5jrtNFdXIHAicFR17bgd+5ks7Ir8WnWQUu4lQg/YGMA64zZd2LLvIzAYXfHZT\nwu+iPpsUj3P3CYTj19OEdVfN0r4c9crpcZOyoqLS1PXAFHe/Iu7zIs1RVA1+f1TSlm/BQj+YQ9z9\nwKxjaY5KuQ5aZDlRdfo0QvXWGRmHI7IyrRalGDPbjdBcVbi8+bbxp9090d+5hcs3L3P3Hxa9fwBw\nPqG9+C/uPizJ+TYnKkGLiEiqLFz58Utgrrv3K3i/BaFJdRtCB7axwH7u/lkmgWasLG8hJyIiq7T3\nqecyKsKleu+5+2x3X0Lox7FLqpGVESVoERFJlbuPYNnLr/I6AIWXe80h9K5fLakNuhmbPnKU2idk\nGdde9XTWIUgZuuLJPzXlsj0Atuy2a8nHmzc//O+Kzm82IUnntQe+WsFpNXtK0CIiEiuXa3KOr3ey\nRcPvEG6c0hGYT6jeXm2vEFGCFhGRWLncSmkRzd+UagDh6YbDzOy3hHs45IBh7j6zsQmsypSgRUQk\nde7+IUvv039vwfsjgZFZxVVOlKBFRCRW5copQUsjlKBFRCRWhRJ06pSgRUQk1krqJCaN0CmRiIhI\nGVIJWkREYuWa9ARUWRFK0CIiEktt0OlTghYRkVhqg06fErSIiMSqUIJOnRK0iIjEyqlPceqUoEVE\nJJaquNOnBC0iIrFUxZ0+JWgREYmly6zSp0YFERGRMqQStIiIxNJ10OlTghYRkViVFUrQaVOCFhGR\nWGqDTp9OiURERMqQStAiIhJLbdDpU4IWEZFYulFJ+pSgRUQklm5Ukj4laBERiaVOYulTghYRkViq\n4k6fErSIiMRSFXf6lKBFRCSWqrjTpwQtIiKxdJlV+rTGRUREypBK0CIiEkudxNKnBC0iIrEqVcWd\nOiVoERGJpV7c6dMpkYiISBlSCVpERGKpDTp9StAiIhJLVdzpU4IWEZFYulFJ+pSgRUQklkrQ6VOC\nFhGRWGqDTp8StIiIxFIJOn1K0CIiEivJNmgzywE3AlsBC4GB7j65YPwRwG+BauAv7n5zYjNvRnQd\ntIiIxKrI5Up+leAgoLW79wPOAYYWjb8C2B3YCTjDzNZMdGGaCSVoERFJ207AaAB3Hwf0LRr/BvAd\noG00XJteaOVDCVpERGLlcrmSXyXoAHxdMFxtZoX56G1gPDABeMTdZye3JM2HErSIiMRKuIp7NtC+\ncPLuXgNgZr2B/YBuwIbAumZ2SMKL0ywoQYuISKyKXEXJrxKMBfYFMLPtCSXlvK+B+cAid68FZhGq\nu1c76sUtIiJpGwHsaWZjo+GjzGwAUOXuw8zsVmCMmS0CPgD+mlGcmVKCFhGRWBUJXgYdlYxPKHp7\nUsH4W4Bbkptj86QELSIisXQnsfQpQYuISCzdSSx9StAZMbOZhGv7WgPtgOlAV2CWu2+YYWgiIstR\nCTp96sWdEXfv7O5dgFFAD3fvAWwCjMs2MhERKQcqQWdvI3efDuDuH5vZBlkHVE5qa2u55p/3M/nj\nj2nVoiW/Pewwuqy1dt34/7w6nn89+ywtKivp3rkzpx7607px/5szhxOvupIrjj+Rruusk0X4shId\nfGp/Om/UmerF1dw/9AG+nPklAGt0XIMj/u8IqK2FXI4uG3fm0WGjGDdyHD88fDc232FzKltU8vzD\nL/DKY69kvBTNR2Vpl09JgpSgszfRzO4CXgL6Ee6eI5GxEyawpLqaa085jXc+nMrNDz3IkKMHArB4\nyRKGjx7Fbb87m1YtWnDJXXfy4ttvs32vXnzzzTdc88D9tGnVKuMlkJVhix17UdmyBTeceiPrb7Y+\nBxy/P8MvvBOAuV/N5ZYzQwfgDXpuwN5H7cW4kePYaMuN6LZ5N2449UZatmnJrofumuUiNDtqg06f\nEnT2jgX6Az2Av7v7QxnHU1bemjKZbTfrCUDPbhsyafr0unEtW7TgmlNOo1WLsBt/U1NDy5bh71se\nfogD+u3IvU89mX7QstJtuEV3/GUHYPq70+nao2u9nzvopJ9w9yX3ANCjbw8+mfIJR170K1q3bc3I\nWx9NLd5VgfJz+lRnkb2OQCtgBtDRzM7JOJ6yMm/hQqratKkbrqyooKamBgidVjqusQYAI557loWL\nF7NND+Oxl8bRsX17tjGjtna1vMf+Kq9NVWsWzltYN1zzTc1ynZh6bt+TT6Z8whcffwFA1ZpVdO3R\nlbsu+hv/umYEPz93QKoxi3xbKkFnbwTwDtCb8FzU+dmGU16q2rRhwaJFdcM1tbVUVCw9r6ytreXW\nfz/MjM8/Y/BRRwPw2EsvkcvlGO/OBx/P4LJ77ubiYwbynfbtl5u+NE8L5y2iddvWdcO5itxyJ2Nb\n77E1Y/75XN3w/NnzmDVtFjU1NXw+43OqF1fTrkM75s/WT64UquJOn0rQ2cu5+/GAA3sCnTKOp6z0\n6t6dce9MBGDi1Kl079xlmfFD7/sHS6qrGXL0wLqq7qEnncyVg07iykEnsXGX9Tj750coOa9ipr49\nlc222wwI7cyfTPlkuc+s36MrH74zrW54yltTsW17ANBhrQ60bNNSyflbyH2Lf5IMlaCzV21mbYAq\nwnXR2iYFduq9JeMnOadeew0AZx0+gP+8Op6Fixezadf1eezll+jdfSPOuOF6crkc/XfZhR236F33\nfV27uWp6a8xb9NhmUwZdfSIA/7jiPvr8sA+t2rTipVEv0a5DOxYUVIEDvDvuXbr37s7J159ELpdj\nxLUjsgi92dJvKX05tdFlK3qM2qZANXAqMNbdDy/lu9NHjtLGk2Vce9XTWYcgZeiKJ//U5Ox6/j7n\nlny8uXjUH5XNE6DSWvYWEHpyfw0sQTeIFxER1AZdDi4EtnP37xOug74043hERJZTkcuV/JJkKEFn\nb467fwbg7p8A8zKOR0RkOeoklj5VcWfEzP4Y/dnCzB4BxgA/ABY1/C0RkWyoZJw+JejseNH/ALqL\nmIiUJeXn9ClBZ8Tdh2cdg4hIqXSZVfqUoEVEJJaquNOnBC0iIrGUn9OnBC0iIrFUgk6fLrMSEREp\nQypBi4hILF3fnD4laBERiaVe3OlTghYRkViVFUrQaVMbtIiISBlSCVpERGKpijt9StAiIhJLNdzp\nU4IWEZFYKkGnTwlaRERiKT+nT53EREREypBK0CIiEqsyp/Jc2pSgRUQklqq406cELSIisfSwjPSp\nzkJERKQMqQQtIiKxdJlV+pSgRUQklvJz+pSgRUQkVpIlaDPLATcCWwELgYHuPrlg/LbAldHgJ8Av\n3H1xYgE0E2qDFhGRWBW50l8lOAho7e79gHOAoUXjbwV+7e67AKOBbkkuS3OhBC0iIrFyuVzJrxLs\nREi8uPs4oG9+hJn1AL4AfmtmzwCd3P295Jeo/KmKuwnM7ILGxrv7kLRiERFZmRJug+4AfF0wXG1m\nFe5eA6wN7ACcCEwGHjGzV9z9mUQjaAZUgm6aXMxLRGSVUJHLlfwqwWygfeHko+QMofT8vrtPcvdq\nQkm7b/EEVgcqQTeBu1+U/9vMqoCNgbeAtu4+L7PAREQSlvBlVmOB/YEHzGx7YELBuMnAGma2UdRx\nbGdgWJIzby5Ugk6Ame0OvAE8BKwLTDWzH2cblYhI2RoBLDKzsYTe2qeb2QAzG+juS4BjgHvNbBww\nzd1HZRlsVlSCTsalhE4Po9x9ppntCtwLPJ5tWCIiyUiyAO3utcAJRW9PKhj/DLBdcnNsnlSCTkaF\nu3+SH3D3iVkGIyKStIqKXMkvSYZK0Mn4yMz2B2rNrCMwCJiWcUwiIonRwzLSpxJ0Mo4DjgDWJ3Rw\n6AMcm2lEIiLSrKkEnQB3nwUMMLMOwBJ3X5B1TCIiSVIBOn1K0Akws97AcGCDaPhd4Eh3/yDTwERE\nEqKnWaVPVdzJuBk4z93Xdve1CZcN3JFxTCIiicnlSn9JMpSgk9G28Do9dx9BuJWdiMgqIeF7cUsJ\nVMXdBGa2QfTnG2Z2NnA7UE3oMPZcZoGJiCRMeTd9StBN81+glnDf7d0IvbnzaoFTMohJRCRxuswq\nfUrQTeDu3bOOQUQkDcrP6VOCToCZGeHRaGsQStOVQPfoYeMiIs2e2pbTp05iyfgH8BXwfeB1YB3C\nU61ERERWiBJ0Mirc/ULCc0tfBQ5CN3oXkVWILrNKnxJ0MuabWWvC01i2cfdFQJuMYxIRSYwelpE+\ntUEn42/AvwmXV71gZnsDM7INSUQkOWqDTp9K0Alw9+uBQ9z9M8LlVrcSqrlFRERWiErQTWBmFxQN\nFw72BoakGpCIyEqiAnT6lKCbRrusiKwWVMWdPiXoJnD3i7KOQUQkDcrP6VOCbsY69bH4D8lq5YXp\nN2QdgqyidKvP9ClBi4hILOXn9ClBJ8TMqoCNgQlAO3efl3FIIiKJURt0+nSZVQLM7EfAG8BDwPeA\nqWb242yjEhFJju4klj4l6GT8EdgJ+MrdZwK7AldkG5KISHJyFbmSX5IMJehkVLj7J/kBd5+YZTAi\nIklTCTp9aoNOxkdmtj9Qa2YdgUHAtIxjEhGRZkwl6GQcR7gP9/rAZKAPcGymEYmIJCiXy5X8kmSo\nBJ0Ad58FDMg6DhGRlUVPqUqfEnQCzGwKUFv8vrtvlEE4IiKJU8E4fUrQydit4O+WQH+gdTahiIjI\nqkAJOgHu/mHRW1eY2SvAH7KIR0QkcSpCp04JOgFmtkvBYA7oBbTNKBwRkcSp81f6lKCTUfhUq1rg\nc+DIjGIREUmc8nP6lKCTcZ+735R1ECIiK4vuEJY+XQedjEFZByAisjLpTmLpUwk6GdPN7D/AOGBB\n/k13H5JdSCIiyVEbdPqUoJPxYsHf2otFZJWj/Jw+JegmMLMj3X24u18U/2kRkeYryRK0meWAG4Gt\ngIXAQHefXM/nbgG+cPdzE5t5M6I26KY5NesARESaoYOA1u7eDzgHGFr8ATM7Dtgi7cDKiRK0iIjE\nSriT2E7AaAB3Hwf0LRxpZjsA2wK3JLwYzYqquJuml5ktVy1DaIeu1b24RWRVkatMtBG6A/B1wXC1\nmVW4e42ZfQ+4kFDKPizJmTY3StBN8z6wb9ZBiIisbAn34p4NtC8YrnD3mujvnwJrAY8CnYG2Zvau\nu9+ZZADNgRJ00yyu5z7cIiLSuLHA/sADZrY9MCE/wt2vA66D0BEXsNUxOYMSdFONzToAEZE0JHyZ\n1QhgTzPLH0OPMrMBQJW7D0t0Ts2YEnQTuPtJWccgIpKGJKu43b0WOKHo7Un1fG54YjNthpSgRUQk\nlm5Ukj4laBERiacMnTolaBERiaWnWaVPCVpERGKpAJ0+JWgREYmlp1mlTwlaRERiKT+nT/fiFhER\nKUMqQYuISDwVoVOnBC0iIrHUizt9StAiIhJLCTp9aoMWEREpQypBi4hILDVBp08JWkREYqmKO31K\n0CIiEks3KkmfErSIiMRTfk6dOomJiIiUIZWgRUQkVkWFynNpU4IWEZF4ys+pU4IWEZFY6iSWPp0T\niYiIlCGVoEVEJJZK0OlTgs6ImT0N1NY3zt13TzkcEZHGKT+nTgk6O8dH/18IPAiMBX4A7J9ZRCIi\nDdCdxNKnBJ0Rd3cAM1vX3e+L3h5hZidnGJaISP1UxZ06JegyYGbHAC8B/YDFGYcjIrIc5ef0KUFn\n7wjgPOCnwMRoeLVWW1vLpVdfz6QPptCqVSsuOPNUunbpXDf+v8+/yLC77qVFixYcuPee9N9vbwB+\nftzJrFFVBcB6ndflwrNOZ/LUD/nDVdcBsMF6XbjgzNN0w4VVxBmDT2QT687ixYu5/Lxr+fijT+vG\n7fWTHzLg6IOZM3suox/8DyP/+QQAt//zaubOnQfAzI8+5bLzrs0k9uZIncTSpwSdMXf/xMxGA9PD\noH+RdUxZe3rM8yxesoS/Xj+UCe+8y9CbbmPoxRcAUP3NNwy96TbuvvlaWrduzdEnn8FuO25PVbt2\nANw69LJlpnXD7cM55TdH0WeLXlx4+VCefWEcu+24Q+rLJMnaZY8daNWqJScMOIvNt+zBSecM5NxB\nlwDQoWN7jjnlCI76ySnMmzufq/96Ca88/zpffv4/AE498rwsQ2++1AadOiXojJnZpcCmwBjgSDPb\nxd3PyDgoxpWZAAANR0lEQVSsTL3+1kT6/aAvAL17bsZEn1Q3bsqH09hgvS51JeU+vXvx6ptvse53\nv8vChQs58XfnUVNTw6BjjqR3z83485DzyeVyLFmyhC/+97+670nztuU2mzPuufEATHxzEpttsWnd\nuC7rf4/335nCvLnzAXh3wiR69TFmfjSLNu1ac+WwIVRWVnDrVXcy8c1J9U5flqcSdPqUoLO3i7vv\nCGBm1wAvZhxP5ubNm79MIq2srKSmpoaKigrmzV92XLt2bZkzbx4brr8+vzrsUA7ady+mfTSDk84+\nnwfvHEZFRQUzP53FCWedS/uqKnps3D2LRZKEtVujHXPnzK8b/qb6G3K5HLW1tXw09WO6b7IBHb/T\ngQULFrHNDlsxbcoMFi5YyD23/4uRDzxB125d+PNtgxmw13HU1tZ7taNI5pSgs9fSzCrcvYZwpeFq\nf7SoqmrH/PlLD761tbV17cZV7doxr2Dc/PkLaF+1Bht07ULX9UI79QZd16Njhw58/sWXrPPdtem8\n7jo8eOcwHnz0Ma688VYu+v1qXUGxSpg/dz7tqtrWDVdU5OoS7dw587jusmH84bpzmf3VHPztD/j6\nf7OZ/uHHzJg2E4CPPvyY2V/NYa3vduLzWat9q1JJdJlV+tRbJnv/AMaa2VWEau6/ZxxP5rbqtTlj\nxr0MwJsT32GT7hvWjevebQOmz/iYOXPnsmTJEl6b8BZb9urJQ6MeZ+hNtwHw2edfMG/BfNZeqxOn\n/99FTJvxMRBK2+ogtmp489WJ7LBraAbptZXxwaQP68ZVVFTQo9fGnPSLs7ng9Mvp1r0rb746kf0O\n2ZOTzj4GgLXW6UTbqrZ88dmXmcTfHOUqciW/JBk5Ve9kz8y2AAx4193fLvV782ZMXiU3Xr4X93uT\npwIw+Hen886k91mwcCH999ub5158iVuH300ttRy0z14ceuB+LKmuZvCfhjLz01lU5HKcetwx9O65\nGW9OfIerbx5Gy5YtadO6NReceRprdfpOtgu4Eu21+ylZh5CaMwafyMa2IQCXnnM11msT2rRtwyMP\nPM6vBx3Ozj/ankWLFvP3O0bw7BMvUNmiknMvPY3vdVmHmpoabv7zX3n7Dc92IVIyxh9pctacPnJU\nyceb9ffbR1k6AUrQGTOzrsBVQC/AgdPdfWop311VE7SsuNUpQUvpkkjQHz06uuTjTdd991aCToDq\n+7J3G3AX4SYlw4Hbsw1HRETKgTqJZa+Nuz8c/f2gmZ2eaTQiIvVRmTh1KkFnr4WZ9QbI/y8iUm7U\nSSx9KkFn72TgdjPrAswAjs04HhGR5eQSvALCzHLAjcBWwEJgoLtPLhg/ADgVWAJMcPcTE5t5M6IS\ndPZGAlsDldH/z5nZe2a2Z7ZhiYisNAcBrd29H3AOMDQ/wszaAEOAXd19Z6Cjma2Wj+FVgs7es0Av\nd+8MbEZ4NvQ+wMWZRiUiUqgiV/or3k7AaAB3Hwf0LRi3COjn7oui4RaEUvZqRwk6e13zz4Z29w+A\nDdz9faA627BERJbK5XIlv0rQAfi6YLjazCoA3L3W3T8DMLOTgSp3fzLxBWoG1AadvZlmdhnwPOFS\nq0+i6m09F1pEykeyfb9mA+0LhvO3Owbq2qj/RHiQ0MGJzrkZUQk6e78CPiZUa08Hfg3MBQZkGJOI\nyDISLkGPBfYFMLPtgQlF428ltFEfVFDVvdpRCTpj7r4QKH5q/AtZxCIikpIRwJ5mNjYaPirquV0F\njAeOInSYfZrwAKFr3P2hbELNjhK0iIjEylUmV+Hq7rXACUVvFz6cW7kJrQQRESlFaVXXkiAlaBER\niVVi27IkSJ3EREREypBK0CIiEk/32E6dErSIiMRSFXf6lKBFRCSeEnTqlKBFRCSWHiOZPiVoERGJ\npxJ06pSgRUQkltqg06cELSIi8ZSgU6cELSIisdQGnT7dqERERKQMqQQtIiLxVMWdOiVoERGJlatQ\nhWvalKBFRCSe2qBTp1MiERGRMqQStIiIxMrlVJ5LmxK0iIjEUyex1ClBi4hILN1JLH1K0CIiEk+d\nxFKnBC0iIrFUgk6fErSIiMRTgk6dErSIiMRTL+7UKUGLiEgsPSwjfTolEhERKUMqQYuISDy1QadO\nCVpERGLlKiqzDmG1owQtIiKx1AadPrVBi4iIlCGVoEVEJJ7aoFOnBC0iIrF0J7H0KUGLiEg83agk\ndUrQIiIST53EUqcELSIisVTFnT4laBERiacq7tQpQYuISCyVoNOnBC0iIvFUgk6dErSIiKTKzHLA\njcBWwEJgoLtPLhh/AHA+sAT4i7sPyyTQjOmUSEREYuUqciW/SnAQ0Nrd+wHnAEPzI8ysRTS8B7Ab\ncKyZfTf5JSp/StAiIhIvlyv9FW8nYDSAu48D+haM6wm85+6z3X0JMAbYJenFaQ6UoEVEJFauorLk\nVwk6AF8XDFebWUUD4+YAayazFM2L2qCbsar1NlK3SlnGGH8k6xBkFdWqw1pJHm9mA+0LhivcvaZg\nXIeCce2BrxKcd7OhErSIiKRtLLAvgJltD0woGPcOsImZdTSzVoTq7RfSDzF7udra2qxjEBGR1UhB\nL+4to7eOArYBqtx9mJntB1wI5IDb3f3mbCLNlhK0iIhIGVIVt4iISBlSghYRESlDStAiIiJlSAla\nmgUzO9LM/rgC35u5MuKRVYMFT2cdh0h9lKBlVadekBJH+4iUJd2oRJqTfmb2JOHGBRcBbYFBhP24\nFuhPuKHBrcDmwGSgdTahyspiZm2AO4HOwEeE62T3A64DqgkPX/iNu39kZmcAhxEeuvCsu59jZt8D\n7o4m92na8YuUSiVoaU7muvsewP7A9cCmwL7uvgvh5gZ7EZJ04U3422UVrKw0xwKT3X1nYDCwLuGk\n7ER3/yFwE3CVmW0BHAps7+47AptG19eeB9zj7j8CHsxiAURKoQQtzckYAHf/jHCv3mpguJndAfQG\nWgI9gJeiz00HpmcTqqxEPYHnAdzdgc+ALu6evxvVs0AvwIAXC24hOSZ6f1OifYRwRyuRsqQELc3J\nDwCiKso1gVOBw4GBhGrNHDAR6Bd9rgvQNZNIZWV6i6XbeGNgbWCGmfWOxu8GOPAusJ2ZVUR3rtol\ner9uHyHap0TKkdqgpTlpY2ZPAVXAMcBxwIuEkvSXhFLUcDPb08xeAKYBszKLVlaW24G/mtkzhG28\ngFDtfb2ZQdgfjnH3qWZ2H6G0nQPGuPtDZjYGuNvMDgOmZLEAIqXQrT5FpFkxsx2ANdz9CTPbBBjl\n7ptmHZdI0lSCFpHmZjJwr5ldSDiGnZhxPCIrhUrQIiIiZUidxERERMqQErSIiEgZUoIWEREpQ0rQ\nIiIiZUi9uEWawMy6AZOAt6O3WgEzgKPc/eMVnOaRwK7ufrSZPQIMdPdPGvjsYOAJdy/5jlhmVuPu\nFUXvXQjUuvuQRr43JYprWonziZ2miDRMCVqk6Wa4+9b5geixmNcDBzd1wu6+f8xHdgX+8y0nu6KX\nbuiSD5EUKUGLJO9Z4ACoK3WOA7YCdgb2AU4j3NlqPDDI3Reb2S8JD3H4mnB3rDkF39+V8NSlG4Cd\ngMXAHwhP6uoLDDOz/oTbnd4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119fd7d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UVQ+h3bte9zYXkRVFoTbXRu9ewKyS4Tozq3H3xWb2BeAUQun8W3kutNopeefn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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c2cb0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oEsFsUBKQjvlm1oHwFKzt3X0R0DHlmEREEqMHCGWD+gSk42/AA4RLA180s32B\n6emGJCKSHPUJyAbVBKTA3a8HDnP3OYRLBUcSmgRERESajWoCmpGZ/bZouHBwK2BEswYkItJEVBGQ\nDUoCmpd+FiLSJqg5IBuUBDQjd78o7RhERJqDcoBsUBLQhvQ9cKu0Q5AW5pqTbkw7BGmhfrCSn9dt\ng7NBSYCIiCROOUA2KAlIiZl1AXoBk4DO7v5tyiGJiCRGfQKyQZcIpsDM9gLeAO4H1gE+NrPvphuV\niEhydMfAbFASkI7fAbsCX7n7TGAwcFW6IYmIJCdXkmvUS9KhJCAdJe4+Kz/g7u+kGYyISNJUE5AN\n6hOQjk/NbChQZWarAWcCU1OOSURE2hjVBKRjGOG5AesDU4BtgFNTjUhEJEG5XK5RL0mHagJS4O6z\ngSPTjkNEpKnoyYDZoCQgBWb2EVBVPN7dN0khHBGRxOnkPhuUBKRj94K/y4BDgA7phCIiIm2VkoAU\nuPsnRaOuMrNXgUvSiEdEJHGqCsgEJQEpMLNBBYM5YAugU0rhiIgkTp39skFJQDoKnyZYBXwOHJdS\nLCIiiVMOkA1KAtJxj7vr8W0i0mrpLoDZoPsEpOPMtAMQEWlKumNgNqgmIB3TzOwpYDywID/S3Uek\nF5KISHLUJyAblASk46WCv/VLEZFWRzlANigJaEZmdpy73+7uF9X/bhGR7EqyJsDMcsANwNbAQuBk\nd59Sw/tuBr5w918ltvBWTn0Cmte5aQcgIpJBBwMd3H1nYDhwdfEbzGwYsGVzB5Z1SgJERCRxCXcM\n3BUYA+Du44H+hRPNbCdgB+DmJliVVk3NAc1rCzNbrgqL0C+gSs8OEJHWIleaaKeAbsDcguEKMytx\n90ozWwe4gFBbcHiSC20LlAQ0rw+A/dMOQkSkqSV8dcA8oGvBcIm7V8a/fwCsDjwM9AA6mdl77n5H\nkgG0VkoCmtfiGp4bICIidRsHDAXuNbOBwKT8BHe/DrgOQudrwJQANJySgOY1Lu0ARESaQ8KXCI4G\nhphZfh96gpkdCXRx91sSXVIboySgGbn7WWnHICLSHJJsDnD3KuD0otHv1/C+2xNbaBuhJEBERBKn\nmwVlg5IAERFJnrKATFASICIiidNTBLNBSYCIiCROFQHZoCRAREQSp6cIZoOSABERSZxygGzQswNE\nRETaKNUEiIhI8lQVkAlKAkREJHG6OiAblASIiEjilARkg/oEiIiItFGqCRARkcSpS0A2KAkQEZHE\nqTkgG5Sfc4SRAAAOV0lEQVQEiIhI4nSzoGxQEiAiIslTDpAJ6hgoIiLSRqkmQEREEldSonPMLFAS\nICIiyVMOkAlKAkREJHHqGJgNytVERETaKNUEiIhI4lQTkA1KAjLCzJ4Gqmqa5u57NnM4IiJ1Uw6Q\nCUoCsuO0+P8FwH3AOGBHYGhqEYmI1EJ3DMwGJQEZ4e4OYGZru/s9cfRoMzs7xbBERGqm5oBMUBKQ\nQWZ2EvAysDOwOOVwRESWoxwgG5QEZM9RwK+BHwDvxGGJqqqquGrUX5n8yVQ6lJUxfNjJrLv2Wsu8\nZ+GiRZx76ZX8+rST2aBnDyorK7ls5CimzphFSS7Hz085gY3XWzelNZCmcsrwY9io9wYsXlzOjRff\nxuzpc6qn7bbfQIYetQ+VS5bw1P1jefw/zzB46C7sceAuVFVB+w5lbNRnfU7+7nks+HZhimuRHeoY\nmA26RDBj3H0WMAZ4CnjW3b9IOaQW5dlXJrC4vIK/XHwBpx/5Q/50x13LTH9vykecceGlzJg9u3rc\n2AmvkSPHzSPO55TDD+Omu+8pnq1k3I57bEdZWRm/PvFS/n79vRz/4yOWmX7MuT/kotOu5DcnXcZB\nx+xL51U68eyD47hw2JVcdNqVTHn3E0ZdeZcSgMYoyTXuJalQEpAxZnYZcAKhGeA4M/tDyiG1KG++\n9z4Dt+kHwBa9N+XdKR8tM728ooLLf3YeG/bsUT1u0A7b88tTTwRg5pzP6dqlS/MFLM1is21689qL\nkwCY/NYUevXdaJnpn7w/jS5dO9O+QxkQapTyevXdiPU26clT9z/fbPG2BrlcrlEvSYeaA7JnkLvv\nAmBm1wIvpRxPi/LtggWs0qlT9XBpaSmVlZXV9zHfqk9vAKqKLrYsKSnh4htu5rlXJnLpj9TXsrXp\n3KUT879ZUD28ZEkluVyu+mA/bcoMrvzbhSxcsJDxT01Y5oz/kBMO4F8j72/ukEWahWoCsqfMzPLf\nW45a7h3QVnXp1In5C5fuwKsqqxr8IJPzzxjGP/94JZeNHMXCxepv2ZrM/3YBnTp3rB7OlSxNADbY\ndD2227Ufpw/9KacP/Rmrrr4qA/bcHoDOq3Six4br8M5ETyXuLMuV5Br1knQoCciefwLjzOwaYCzw\nj5TjaVH6WW9eeO0NAN56/wN6bbBevZ8Z8/w47rjvAQA6lLWntKSEElVPtir++gdst0toJuq95SZM\n/eDT6mnzv5nPooWLKS+vAGDul/NYpVtoEuq7bR8mvfxO8wfcCigJyAY1B2SMu//BzB4FDLjF3d9O\nO6aWZPCO/Xl50lucev4IAH5z+ik8Nu5FFi5cxEF77V79vsJj/O479ueSG//C6RdewpIllZx33NG0\nLytr5silKY1/egL9Bm7OJaN+BcCfLxrFLvsMoGOnDjx533M88Z9nuWTUcMoXVzDr09k8/cBYANbd\nqMcyVxFIIyiRzoRcVXHjqLRoZrYecA2wBeDAj9z944Z89svXX9aXLcs49aQb0w5BWqh7J9y2Ukfx\nTx8e06j9zXr776usIQVqDsievwB3Em4UdDswKt1wREQkq9QckD0d3f2/8e/7zOxHqUYjIlITnddn\ngmoCsqedmW0FkP9fRKSlUcfAbFBNQPacDYwys57AdODUlOMREVlOroGX5jaEmeWAG4CtgYXAye4+\npWD6kcC5QDkwyd3PSGzhrZxqArLnIWA7oDT+/7yZTTazIemGJSLSZA4GOrj7zsBw4Or8BDPrCIwA\nBrv7bsBqZqZHrDeQkoDseQ7Ywt17AJsB9wH7ARenGpWISKFknx2wK+GZKbj7eKB/wbRFwM7uvigO\ntyPUFkgDKAnInvXc3QHc/UNgA3f/AKhINywRkaUSfnZAN2BuwXBF/s6p7l7l7nMAzOxsoIu7P9Ek\nK9UKqU9A9sw0s8uBFwiXCc6KTQG6z62ItBzJ9vWbB3QtGC5x98r8QOwzcCXQGzg00SW3cqoJyJ5j\ngRmEJoBpwPHAN8CRKcYkIrKMhGsCxgH7A5jZQGBS0fSRhD4DBxc0C0gDqCYgY9x9IfCnotEvphGL\niEgzGQ0MMbNxcfiEeEVAF2AC4fHqz5vZ04SHql3r7nr0YwMoCRARkcTlSpOraHb3KuD0otHvF/yt\nY9kK0oYTEZHk6QFCmaAkQEREEteAdn5pAdQxUEREpI1STYCIiCRPzwPIBCUBIiKSODUHZIOSABER\nSZ6SgExQEiAiIonT44GzQUmAiIgkTzUBmaAkQEREEqc+AdmgJEBERJKnJCATlASIiEji1CcgG3Sz\nIBERkTZKNQEiIpI8NQdkgpIAERFJXK5EFc1ZoCRARESSpz4BmaBUTUREpI1STYCIiCQul9M5ZhYo\nCRARkeSpY2AmKAkQEZHE6Y6B2aAkQEREkqeOgZmgJEBERBKnmoBsUBIgIiLJUxKQCUoCREQkebo6\nIBOUBIiISOL0AKFsUKomIiLSRqkmQEREkqc+AZmgJEBERBKXKylNOwRpACUBIiKSOPUJyAb1CRAR\nEWmjVBMgIiLJU5+ATFASICIiidMdA7NBSYCIiCRPNwvKBCUBIiKSPHUMzAQlASIikjg1B2SDkgAR\nEUmemgMyQUmAiIgkTjUB2aAkQEREkqeagExQEiAiIi2ameWAG4CtgYXAye4+pWD6gcD5QDlwm7vf\nkkqgGaRUTUREEpcryTXqVY+DgQ7uvjMwHLg6P8HM2sXhvYHdgVPNbM2mWavWR0mAiIgkL5dr3Ktu\nuwJjANx9PNC/YFpfYLK7z3P3cmAsMKgpVqk1UhIgIiKJy5WUNupVj27A3ILhCjMrqWXa18Cqya1J\n66Y+AW1I9212VHddWca9E3ZMOwRppdp3Wz3J/c08oGvBcIm7VxZM61YwrSvwVYLLbtVUEyAiIi3d\nOGB/ADMbCEwqmPYusKmZrWZm7QlNAS82f4jZlKuqqko7BhERkVoVXB3QL446Adge6OLut5jZAcAF\nQA4Y5e43pRNp9igJEBERaaPUHCAiItJGKQkQERFpo5QEiIiItFFKAqRVMrPjzOx3K/C5mU0Rj7QO\nFjyddhwiSVESILIs9ZSV+qiMSKuhmwVJa7azmT1BuHnIRUAn4ExCua8CDiHcVGQksDkwBeiQTqjS\nVMysI3AH0AP4lHAd+QHAdUAF4YE0p7j7p2b2E+BwwoNonnP34Wa2DnBXnN1nzR2/SFNSTYC0Zt+4\n+97AUOB6oDewv7sPItxgZB9CIlD4YJLOaQUrTeZUYIq77wZcCKxNSPzOcPc9gBuBa8xsS+D7wEB3\n3wXoHa8//zXwd3ffC7gvjRUQaSpKAqQ1Gwvg7nMI9xavAG43s1uBrYAyoA/wcnzfNGBaOqFKE+oL\nvADg7g7MAXq6e/6uc88BWwAGvFRwO9qxcXxvYhkh3LlOpNVQEiCt2Y4AsTp3VeBc4AjgZEIVcA54\nB9g5vq8nsF4qkUpTeoul33EvYA1gupltFafvDjjwHjDAzEriHeoGxfHVZYRYpkRaC/UJkNaso5k9\nCXQBTgKGAS8RagS+JJwN3m5mQ8zsRWAqMDu1aKWpjAL+ambPEL7jBYQmguvNDEJ5OMndPzazewi1\nBjlgrLvfb2ZjgbvM7HDgozRWQKSp6LbBItKqmdlOwCru/riZbQo84u69045LpCVQTYCItHZTgLvN\n7ALCPu+MlOMRaTFUEyAiItJGqWOgiIhIG6UkQEREpI1SEiAiItJGKQkQERFpo3R1gEgzMrMNgfeB\nt+Oo9sB04AR3n7GC8zwOGOzuJ5rZg8DJ7j6rlvdeCDzu7g2+852ZVbp7SdG4C4Aqdx9Rx+c+inFN\nbeBy6p2niCRLSYBI85vu7tvlB+Ijj68HDl3ZGbv70HreMhh4qpGzXdFLiHTpkUgLpyRAJH3PAQdC\n9dnzeGBrYDdgP+A8wh3sJgBnuvtiMzuG8GCbuYS74H1d8PnBhKfd/RnYFVgMXEJ4QmJ/4BYzO4Rw\n6+Qbge7AfOAcd3891lb8jXCnxfH1BW9mZwFHEx6+VAkcHu/RnwMuMrOtCXfpO83dJ5nZWsDNhFs0\nVwLD3b2xiYmIJEB9AkRSZGZlhEfXji0Y/ZC79wXWAk4Bdoo1B3OAn5pZD+AKwgF+J8KjkvPyZ99n\nA13cfTNgCHA+cDfwKuEWuW8DtwM/c/f+hFsq/yN+9nrg1rjMOpsNzKwrcBCh2r8fcD/L3ozH43wu\nicsDuBYY5e47AN8DRppZl7q3lIg0BdUEiDS/dc1sIuFMuT3hCXXDC6bnn1i3B7Ap8FJ8oE0ZMJHw\nMJtx7v45gJn9DdgzfiYX/x9MONvG3T8jPDWReK/8XDzo7gDcFucN0NnMuhMeqHNEHHcXcEttK+Lu\nX5vZUcCRZtYH2Bd4reAto+L7HjGzO82sG7B3CMUuju8pBXrVurVEpMkoCRBpfsv0CajBgvh/KXCP\nu58HYGadCYnAXnFaXkXB3/magPLCGcan5xV20CsFFhT1Tejp7l+aWSWxltDdq+JwjcxsPeAZ4Drg\nYWAWsE0tseXjKgX2dPev4jx6EJovDqltOSLSNNQcINL8cvW/BQgH10PMbM14tn4T4XHIYwmPvO1h\nZiWE5oTieT8H/BAgtsE/Q6h1qADaufs8YHI8i8fMhsTPADwBHBPHH0boS1CbHYDJ7n4t8AqhD0Nh\ngpKf/yHAe+6+AHgSODOO3xx4E+jUwG0iIglSEiDS/OrqNV89zd3fBC4i9OafRDjAX+7uswlt/k8S\nHo08t4bP3wDMN7M3gMeAs9z9W2AMcJOZDSQcoE+O77mUmDTEeR9mZq8Tqvfn1RHvo0Cpmb1NeATv\nR8DGBbH0MbPXCJ0bj4vjzwEGxuXeDRwVYxORZqYHCImIiLRRqgkQERFpo5QEiIiItFFKAkRERNoo\nJQEiIiJtlJIAERGRNkpJgIiISBulJEBERKSNUhIgIiLSRv0/qAMRO1oQjWwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b6f39d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mw5iTtZmZVeKbopTjZG1mZtU4WxfjZG1mZpX4qVvlOFmbmVklLliX42RtZmaV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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b055490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QcwlVj88TOhQ9GZc5n9DWc6GZvRynHeDftk3/mbAfPbToLIHF3z8K/Rv4Y6y+HUzoHPMy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\nOQVrERGRMvf/HT4kBiAy//sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b149ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LXFiO8oiIlIRS8kxQIC8BMxueGMwBA4BOZSqOiEhJqBNbNiiQl0byKWh1wAfA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\nIhVMgVxERKSC/T8tCHeYlnkM0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e66d750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "from itertools import product\n",
    "n_estimators = 500\n",
    "max_features = [1, 'sqrt', 'log2']\n",
    "max_depths = [None, 2, 5, 10]\n",
    "for f, d in product(max_features, max_depths): # with product we can iterate through all possible combinations\n",
    "    rf = RandomForestClassifier(n_estimators=n_estimators, \n",
    "                                criterion='entropy', \n",
    "                                max_features=f, \n",
    "                                max_depth=d, \n",
    "                                n_jobs=2,\n",
    "                                random_state=1337)\n",
    "    rf.fit(X_train, y_train)\n",
    "    prediction_test = rf.predict(X=X_test)\n",
    "    print('Classification accuracy on test set with max features = {} and max_depth = {}: {:.3f}'.format(f, d, accuracy_score(y_test,prediction_test)))\n",
    "    cm = confusion_matrix(y_test, prediction_test)\n",
    "    cm_norm = cm/cm.sum(axis=1)[:, np.newaxis]\n",
    "    plt.figure()\n",
    "    plot_confusion_matrix(cm_norm, classes=rf.classes_, title='Confusion matrix accuracy on test set with max features = {} and max_depth = {}: {:.3f}'.format(f, d, accuracy_score(y_test,prediction_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "N.B. Observing these confusion matrices you'll see something very important - for some configurations, the Random Forest **always predicts the majority class**. This highlights (again) the importance of always checking performance against a dummy classifier!!!\n",
    "\n",
    "Additionally, if you want to reproduce your results, you must set the random seed (you can do this with the `random_state` argument). Random forests are...random!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.19 ==========\n",
    "Compare the feature importances as estimated with the decision tree and random forest classifiers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Importance of feature CheckingAccount, DT: 0.752, RF: 0.110\n",
      "Importance of feature Duration, DT: 0.154, RF: 0.092\n",
      "Importance of feature CreditHistory, DT: 0.000, RF: 0.058\n",
      "Importance of feature Purpose, DT: 0.000, RF: 0.064\n",
      "Importance of feature CreditAmount, DT: 0.000, RF: 0.103\n",
      "Importance of feature SavingsAccount, DT: 0.000, RF: 0.056\n",
      "Importance of feature YearsEmployed, DT: 0.000, RF: 0.054\n",
      "Importance of feature InstallmentRate, DT: 0.000, RF: 0.046\n",
      "Importance of feature PersonalStatus, DT: 0.000, RF: 0.035\n",
      "Importance of feature OtherDebtors, DT: 0.000, RF: 0.020\n",
      "Importance of feature ResidentSince, DT: 0.000, RF: 0.041\n",
      "Importance of feature Property, DT: 0.000, RF: 0.051\n",
      "Importance of feature Age, DT: 0.000, RF: 0.089\n",
      "Importance of feature OtherPlans, DT: 0.094, RF: 0.033\n",
      "Importance of feature Housing, DT: 0.000, RF: 0.035\n",
      "Importance of feature NumCreditsAtBank, DT: 0.000, RF: 0.029\n",
      "Importance of feature Job, DT: 0.000, RF: 0.035\n",
      "Importance of feature Dependents, DT: 0.000, RF: 0.017\n",
      "Importance of feature Telephone, DT: 0.000, RF: 0.023\n",
      "Importance of feature Foreign, DT: 0.000, RF: 0.009\n"
     ]
    },
    {
     "data": {
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WqNkbGpZfB1w3qs2vgGdXn50kSZPnTYgkSZIkSbWwAJUkSZIk1cICVJIkSZJU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\nkiRJkiRJkiRJ7hf+P5QQoC2HqjDoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b546850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "rf = RandomForestClassifier(n_estimators=500, \n",
    "                            criterion='entropy', \n",
    "                            max_features=1, \n",
    "                            max_depth=10, \n",
    "                            n_jobs=2)\n",
    "rf.fit(X_train, y_train)\n",
    "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6))\n",
    "xx = np.arange(len(dt.feature_importances_))\n",
    "ax1.bar(xx, dt.feature_importances_)\n",
    "ax1.set_xticks(xx + .5)\n",
    "ax1.set_xticklabels(credit_clean.drop('Approve', axis=1).columns, rotation='vertical')\n",
    "ax1.set_title('Decision tree depth 2 importances')\n",
    "ax2.bar(xx, rf.feature_importances_)\n",
    "ax2.set_xticks(xx + .5)\n",
    "ax2.set_xticklabels(credit_clean.drop('Approve', axis=1).columns, rotation='vertical')\n",
    "ax2.set_title('Random forest max features=1 , max depth=10')\n",
    "\n",
    "for i, column in enumerate(credit_clean.drop('Approve', axis=1)):\n",
    "    print('Importance of feature {}, DT: {:.3f}, RF: {:.3f}'.format(column, dt.feature_importances_[i], rf.feature_importances_[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Linear regression\n",
    "In the second part of the lab we use the [CPU performance](https://archive.ics.uci.edu/ml/datasets/Computer+Hardware) dataset for a simple regression task. Famliarise yourself with the dataset before moving on to the next step. Note that the version we will be using is missing the `Model Name` and `PRP` attributes. Our task will be to use the remaining attributes to predict `ERP` values.\n",
    "\n",
    "Download the dataset and save it in a directory called `datasets` in the same folder that your notebooks live. Alternatively, you can save the dataset in any folder you wish and modify the `data_path` variable below accordingly. We will load our data into a pandas DataFrame structure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the dataset\n",
    "data_path = os.path.join(os.getcwd(), 'datasets', 'cpu.csv')\n",
    "cpu = pd.read_csv(data_path, delimiter = ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.1 ==========\n",
    "Display the number of data points and attributes in the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples: 209, number of attributes: 8\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "print('Number of samples: {}, number of attributes: {}'.format(cpu.shape[0], cpu.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.2 ==========\n",
    "Get a feeling of the data by using pandas `describe()` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MYCT</th>\n",
       "      <th>MMIN</th>\n",
       "      <th>MMAX</th>\n",
       "      <th>CACH</th>\n",
       "      <th>CHMIN</th>\n",
       "      <th>CHMAX</th>\n",
       "      <th>ERP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "      <td>209.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>203.822967</td>\n",
       "      <td>2867.980861</td>\n",
       "      <td>11796.153110</td>\n",
       "      <td>25.205742</td>\n",
       "      <td>4.698565</td>\n",
       "      <td>18.267943</td>\n",
       "      <td>99.330144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>260.262926</td>\n",
       "      <td>3878.742758</td>\n",
       "      <td>11726.564377</td>\n",
       "      <td>40.628722</td>\n",
       "      <td>6.816274</td>\n",
       "      <td>25.997318</td>\n",
       "      <td>154.757102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>17.000000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>4000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>28.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>110.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>8000.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>45.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>225.000000</td>\n",
       "      <td>4000.000000</td>\n",
       "      <td>16000.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>101.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1500.000000</td>\n",
       "      <td>32000.000000</td>\n",
       "      <td>64000.000000</td>\n",
       "      <td>256.000000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>1238.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              MYCT          MMIN     ...            CHMAX          ERP\n",
       "count   209.000000    209.000000     ...       209.000000   209.000000\n",
       "mean    203.822967   2867.980861     ...        18.267943    99.330144\n",
       "std     260.262926   3878.742758     ...        25.997318   154.757102\n",
       "min      17.000000     64.000000     ...         0.000000    15.000000\n",
       "25%      50.000000    768.000000     ...         5.000000    28.000000\n",
       "50%     110.000000   2000.000000     ...         8.000000    45.000000\n",
       "75%     225.000000   4000.000000     ...        24.000000   101.000000\n",
       "max    1500.000000  32000.000000     ...       176.000000  1238.000000\n",
       "\n",
       "[8 rows x 7 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "cpu.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.3 ==========\n",
    "Display the first 10 data points of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vendor</th>\n",
       "      <th>MYCT</th>\n",
       "      <th>MMIN</th>\n",
       "      <th>MMAX</th>\n",
       "      <th>CACH</th>\n",
       "      <th>CHMIN</th>\n",
       "      <th>CHMAX</th>\n",
       "      <th>ERP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>adviser</td>\n",
       "      <td>125.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>128.0</td>\n",
       "      <td>199.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>253.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>253.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>253.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>132.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>26.0</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>23.0</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>381.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>23.0</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>381.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>23.0</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>64000.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>749.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>amdahl</td>\n",
       "      <td>23.0</td>\n",
       "      <td>32000.0</td>\n",
       "      <td>64000.0</td>\n",
       "      <td>128.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>1238.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    vendor   MYCT     MMIN     MMAX   CACH  CHMIN  CHMAX     ERP\n",
       "0  adviser  125.0    256.0   6000.0  256.0   16.0  128.0   199.0\n",
       "1   amdahl   29.0   8000.0  32000.0   32.0    8.0   32.0   253.0\n",
       "2   amdahl   29.0   8000.0  32000.0   32.0    8.0   32.0   253.0\n",
       "3   amdahl   29.0   8000.0  32000.0   32.0    8.0   32.0   253.0\n",
       "4   amdahl   29.0   8000.0  16000.0   32.0    8.0   16.0   132.0\n",
       "5   amdahl   26.0   8000.0  32000.0   64.0    8.0   32.0   290.0\n",
       "6   amdahl   23.0  16000.0  32000.0   64.0   16.0   32.0   381.0\n",
       "7   amdahl   23.0  16000.0  32000.0   64.0   16.0   32.0   381.0\n",
       "8   amdahl   23.0  16000.0  64000.0   64.0   16.0   32.0   749.0\n",
       "9   amdahl   23.0  32000.0  64000.0  128.0   32.0   64.0  1238.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "cpu.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.4 ========== \n",
    "You might have noticed that the `vendor` attribute is categorical. This will give problems when using a linear regression model. For now we can simply remove this attribute. Create a new DataFrame called `cpu_clean` by copying `cpu` but omit the `vendor` attribute. Display the number of samples and attributes in the clean dataset as a sanity check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clean dataset, number of samples: 209, number of attributes: 7\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "cpu_clean = cpu.copy(deep=True)\n",
    "cpu_clean=cpu_clean.drop('vendor', axis=1)\n",
    "print('Clean dataset, number of samples: {}, number of attributes: {}'.format(cpu_clean.shape[0], cpu_clean.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.5 ==========\n",
    "Now -as always- we want to perform some exploratory data analysis. Remember that our task is to predict `ERP` values, so it's a good idea to inspect individual scatter plots of the target variable (`ERP`) against our input features. For this purpose we will use once again seaborn's pairplot implementation.\n",
    "\n",
    "Create a series of [pairplots](https://seaborn.github.io/generated/seaborn.pairplot.html?highlight=pairplot#seaborn.pairplot) showing the pairwise relationship of `ERP` and the remaining attributes in the data. You can do so by specifying explicitly the `x_vars` and `y_vars` input arguments in the pairplot. *Hnt: Your final plot will consist of 6 subplots each contaning a scatter plot.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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BA8B9wBLwsrX2jvBrbwc+DMwDd1trH/S6vABdm2qZW1ikp2+cLW21fOXhVyLP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\nkUL+H7UvDJRxNyh6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad01e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "g2 = sns.pairplot(data=cpu, x_vars=['MYCT', 'MMIN', 'MMAX', 'CACH', 'CHMIN', 'CHMAX'], y_vars = 'ERP', size=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.6 ==========\n",
    "* Do you think that ERP should be at least partially predictable from the input attributes?\n",
    "* Do any attributes exhibit significant correlations?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "Yes, it seems that some input features are positively correlated with the target variable so it should be possible to partially predict it. The `MMIN` and `MMAX` features appear to exhibit the strongest correlations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.7 ==========\n",
    "Now we have a feel for the data and we will try fitting a simple linear regression model. Similarly to what we did in the first part of the lab, we want to use cross-validation to evaluate the goodness of the fit.\n",
    "\n",
    "By using the `cpu_clean` dataset extract the raw values for the input features and the target variable and store them in two matrices, called `X` and `y` respectively. \n",
    "\n",
    "Then, split the dataset into training and testing sets by using a 75%-25% split (training/testing).\n",
    "\n",
    "Display the shapes of all matrices involved and double-check that all dimensionalities appear to be as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of instances in X: 209\n",
      "Number of instances in X_train: 156\n",
      "Number of instances in X_test: 53\n",
      "Number of instances in X_train and X_test together: 209\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "X = cpu_clean.drop('ERP', axis=1).as_matrix()\n",
    "y = cpu_clean['ERP'].as_matrix()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, test_size=0.25, random_state=0)\n",
    "\n",
    "print('Number of instances in X: {}'.format(np.shape(X)[0]))\n",
    "print('Number of instances in X_train: {}'.format(X_train.shape[0]))\n",
    "print('Number of instances in X_test: {}'.format(X_test.shape[0]))\n",
    "print('Number of instances in X_train and X_test together: {}'.format(X_train.shape[0] + X_test.shape[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.8 ==========\n",
    "Fit a simple linear regressor by using the [`LinearRegression`](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) model in Scikit-learn. Report the training accuracy by using the `score` attribute. What does this represent?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy: 0.916\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "lm = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "lm.fit(X_train, y_train)\n",
    "print('Training accuracy: {:.3f}'.format(lm.score(X_train, y_train)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer here*\n",
    "\n",
    "The accuracy score represents the coefficient of determination ($R^2$). This is at max 1, but can be negative. It will be 0 if you predict the mean of y for all observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.9 ==========\n",
    "Now report the testing accuracy by using the `score` attribute of the regressor as well as the `r2_score` metric. Confirm that these two yield identical results.\n",
    "\n",
    "How does the accuracy compare to the one reported on the training dataset? Do you think that your model does well on generalising on unseen data? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing accuracy by using score function: 0.857\n",
      "Testing accuracy by using r2_score meric: 0.857\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "print('Testing accuracy by using score function: {:.3f}'.format(lm.score(X_test, y_test)))\n",
    "print('Testing accuracy by using r2_score meric: {:.3f}'.format(r2_score(y_test, lm.predict(X_test))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "The accuracy on the test dataset is very similar to the training accuracy. From that we can conclude that the model has not overfitted the training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.10 ==========\n",
    "Now we want to get a feel for how good the fit is, so we wil plot the measured values against the predicted ones. Make use of the function provided below which takes as input arguments the measured (`y_true`) and predicted (`y_pred`) values of a target variable and produces a scatter plot for the two by also including a straight line going through the origin. \n",
    "\n",
    "Where would you expect the circles to be for a perfect fit?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fit_scatter(y_true, y_pred):\n",
    "    assert y_true.shape == y_pred.shape\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(y_true, y_pred)\n",
    "    ax.plot([y_true.min(), y_true.max()], [y_true.min(), y_true.max()], 'k--', lw=4)\n",
    "    ax.set_xlabel('Measured')\n",
    "    ax.set_ylabel('Predicted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WYHe/293jAO7+O4IHBUUkZMkzsl588QWuvvrKsCNJO9PS50g2mNnZwAMExecM4OOspRKR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\nRCQtKiQiIpIWFRIREUmLComIiKTl/wOWbkO2ZI4PDAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a949610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "prediction = lm.predict(X_test)\n",
    "fit_scatter(y_test, prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "If the fit was perfect all the points would be sitting on the straight line going through the origin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.11 ==========\n",
    "Another way of assessing the performance of the model is to inspect the distribution of the errors. Make a histogram plot by using seaborn's `displot` function. This will also show an estimate of the underlying distribution.\n",
    "\n",
    "Does it look like the errors are normally distributed? Would you trust the fit of the distribution on the graph? Explain why."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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grnV1WGU8o6y3UVURiRpyFlKakVAQpmvtDvDe+XYKHHncIxen5YxNKrY1eFR3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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b745290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "g = sns.distplot(y_test-prediction, rug=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "Indeed it seems that the errors follow a Gaussian (normal) distribution, however we should be very careful before making any judgements since the number of samples is relatively small in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.12 ==========\n",
    "Above we deleted the vendor variable. However, we can use nominal attributes in regression by converting them to numeric, exactly in the same way that we did at the first part of this lab. \n",
    "\n",
    "Now, use the original `cpu` dataset and convert the `vendor` attribute to numeric by using a `LabelEncoder`. Then train a linear regression model to the data and compare its performance to the one we had previously. Did adding the *binazired vendor* variable help? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New accuracy on test set: 0.887\n"
     ]
    }
   ],
   "source": [
    "# Your code goes here\n",
    "vendor_le = LabelEncoder()\n",
    "vendor_le.fit(cpu[\"vendor\"])\n",
    "cpu[\"vendor\"] = vendor_le.transform(cpu[\"vendor\"])\n",
    "X = cpu.drop('ERP', axis=1).as_matrix()\n",
    "y = cpu['ERP'].as_matrix()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.9, test_size=0.1, random_state=0)\n",
    "lm = LinearRegression(fit_intercept=True, normalize=True, copy_X=True).fit(X_train,y_train)\n",
    "prediction_new = lm.predict(X_test)\n",
    "print('New accuracy on test set: {:.3f}'.format(lm.score(X_test,y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your answer goes here*\n",
    "\n",
    "Adding the binarized vendor variable only helped a little bit. This was somehow expected, since we made additional use of a discrete variable to predict a continuous one."
   ]
  }
 ],
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