Assn2Feedback.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introductory applied machine learning (INFR10069)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "\n",
    "Q1:\t39\t  \n",
    "Q2: \t43\t  \n",
    "Total:\t82\t  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 2: Linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Marking Breakdown\n",
    "\n",
    "**70-100%** results/answer correct plus extra achievement at understanding or analysis of results. Clear explanations, evidence of creative or deeper thought will contribute to a higher grade.\n",
    "\n",
    "**60-69%** results/answer correct or nearly correct and well explained.\n",
    "\n",
    "**50-59%** results/answer in right direction but significant errors.\n",
    "\n",
    "**40-49%** some evidence that the student has gained some understanding, but not answered the questions\n",
    "properly.\n",
    "\n",
    "**0-39%** serious error or slack work."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mechanics\n",
    "\n",
    "You should produce a Jupyter notebook in answer to this assignment.\n",
    "**You need to submit this notebook electronically as described below.**\n",
    "\n",
    "Place your notebook in a directory called `iamlans` and submit this directory using the submit command on a DICE machine. The format is:\n",
    "\n",
    "`submit iaml 2 iamlans`\n",
    "\n",
    "You can check the status of your submissions with the `show_submissions` command.\n",
    "\n",
    "**Late submissions:** The policy stated in the School of Informatics MSc Degree Guide is that normally you will not be allowed to submit coursework late. See http://www.inf.ed.ac.uk/teaching/years/msc/courseguide10.html#exam for exceptions to this, e.g. in case of serious medical illness or serious personal problems.\n",
    "\n",
    "**Collaboration:** You may discuss the assignment with your colleagues, provided that the writing that you submit is entirely your own. That is, you should NOT borrow actual text or code from other students. We ask that you provide a list of the people who you've had discussions with (if any).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Important Instructions\n",
    "\n",
    "1. In the following questions you are asked to run experiments using Python (version 2.7) and the following packages:\n",
    "    * Numpy\n",
    "    * Pandas\n",
    "    * Scikit-learn\n",
    "    * Matplotlib\n",
    "    * Seaborn\n",
    "\n",
    "2. Before you start make sure you have set up a vitual environment (or conda environment if you are working on your own machine) and the required packages installed. Instructions on how to set-up the working enviornment and install the required packages can be found in `01_Lab_1_Introduction`.\n",
    "\n",
    "3. Wherever you are required to produce code you should use code cells, otherwise you should use markdown cells to report results and explain answers.\n",
    "\n",
    "4. The .csv files that you will be using are located at `./datasets/` (the `datasets` directory is adjacent to this file).\n",
    "\n",
    "5. **IMPORTANT:** Keep your answers brief and concise. Most questions can be answered with 2-3 lines of explanation (excluding coding questions)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports\n",
    "\n",
    "Execute the cell below to import all packages you will be using in the rest of the assignemnt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# STUDENTS I DISCUSSED WITH: Sam Ryan\n",
    "\n",
    "from __future__ import print_function, division\n",
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import r2_score, explained_variance_score, mean_absolute_error, mean_squared_error\n",
    "from sklearn.cross_validation import train_test_split, KFold, cross_val_predict\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import OneHotEncoder, LabelEncoder\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Description of the dataset\n",
    "This assignment is based on the automobile pricing dataset. Our goal will be to predict the price of automobiles based on various attributes. This data set consists of three types of entities: (a) the specification of an automobile in terms of various characteristics, (b) its assigned insurance risk rating, (c) its normalized losses in use as compared to other cars. The second rating corresponds to the degree to which the auto is more risky than its price indicates. Cars are initially assigned a risk factor symbol associated with its price. Then, if it is more risky (or less), this symbol is adjusted by moving it up (or down) the scale. Actuaries call this process ”symboling”. A value of +3 indicates that the auto is risky, -3 that it is probably pretty safe. The third factor is the relative average loss payment per insured vehicle year. This value is normalized for all autos within a particular size classification (two door small, station wagons, sports/speciality, etc...), and represents the average loss per car per year. To save you time and to make the problem manageable with limited computational resources, we preprocessed the original dataset. We removed any instances that had one or more missing values and randomized the data set. The resulting representation is much more compact and can be used directly to perform our experiments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Simple Linear Regression [50%]\n",
    "We will begin by studying a simple Linear Regression model. Such a model will consider the relationship between a dependent (response) variable and only one independent (explanatory) variable. When applying machine learning in practice it can be prudent to start out simple in order to get a feeling for the dataset and for any potential difficulties that might warrant a more sophisticated model. In this Section we will consider one independent variable (i.e. feature) `engine-power` against the dependent variable (i.e. target) `price`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.1 ==========\n",
    "Load the dataset `train_auto_numeric.csv` into a pandas DataFrame called `auto_numeric`. Display the number of data points and attributes in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Load the dataset \n",
    "data_path = os.path.join(os.getcwd(), 'datasets', 'train_auto_numeric.csv')\n",
    "auto_numeric = pd.read_csv(data_path, delimiter = ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "You don't report the number of data points and attributes as requested!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.2 ==========\n",
    "Display the first 8 instances of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "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>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>engine-power</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>mean-effective-pressure</th>\n",
       "      <th>torque</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>164.0</td>\n",
       "      <td>99.8</td>\n",
       "      <td>176.6</td>\n",
       "      <td>66.2</td>\n",
       "      <td>54.3</td>\n",
       "      <td>8.85</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>40.52</td>\n",
       "      <td>57.68</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>110.0</td>\n",
       "      <td>99.4</td>\n",
       "      <td>162.4</td>\n",
       "      <td>66.4</td>\n",
       "      <td>54.3</td>\n",
       "      <td>15.18</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>47.39</td>\n",
       "      <td>59.59</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>158.0</td>\n",
       "      <td>105.8</td>\n",
       "      <td>192.7</td>\n",
       "      <td>71.4</td>\n",
       "      <td>51.6</td>\n",
       "      <td>15.18</td>\n",
       "      <td>3.94</td>\n",
       "      <td>2.80</td>\n",
       "      <td>8.5</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>4400.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.85</td>\n",
       "      <td>3344.79</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>106.0</td>\n",
       "      <td>86.6</td>\n",
       "      <td>158.7</td>\n",
       "      <td>67.7</td>\n",
       "      <td>55.9</td>\n",
       "      <td>13.74</td>\n",
       "      <td>3.13</td>\n",
       "      <td>3.50</td>\n",
       "      <td>7.8</td>\n",
       "      <td>140000.0</td>\n",
       "      <td>5600.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>44.74</td>\n",
       "      <td>68.97</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>192.0</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>54.3</td>\n",
       "      <td>8.67</td>\n",
       "      <td>3.50</td>\n",
       "      <td>2.80</td>\n",
       "      <td>8.8</td>\n",
       "      <td>101000.0</td>\n",
       "      <td>5800.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>44.78</td>\n",
       "      <td>53.48</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>194.0</td>\n",
       "      <td>110.0</td>\n",
       "      <td>190.9</td>\n",
       "      <td>71.4</td>\n",
       "      <td>58.7</td>\n",
       "      <td>8.67</td>\n",
       "      <td>3.78</td>\n",
       "      <td>3.90</td>\n",
       "      <td>22.5</td>\n",
       "      <td>101000.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>1.80</td>\n",
       "      <td>1330.28</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>188.0</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>54.3</td>\n",
       "      <td>26.58</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.19</td>\n",
       "      <td>9.0</td>\n",
       "      <td>121000.0</td>\n",
       "      <td>4250.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>7.19</td>\n",
       "      <td>377.06</td>\n",
       "      <td>20970.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>150.0</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>56.1</td>\n",
       "      <td>26.58</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.19</td>\n",
       "      <td>8.0</td>\n",
       "      <td>134000.0</td>\n",
       "      <td>4400.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>57.37</td>\n",
       "      <td>48.20</td>\n",
       "      <td>21105.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   normalized-losses  wheel-base  length  width  height  engine-size  bore  \\\n",
       "0              164.0        99.8   176.6   66.2    54.3         8.85  3.19   \n",
       "1              110.0        99.4   162.4   66.4    54.3        15.18  3.19   \n",
       "2              158.0       105.8   192.7   71.4    51.6        15.18  3.94   \n",
       "3              106.0        86.6   158.7   67.7    55.9        13.74  3.13   \n",
       "4              192.0       101.2   176.8   64.8    54.3         8.67  3.50   \n",
       "5              194.0       110.0   190.9   71.4    58.7         8.67  3.78   \n",
       "6              188.0       101.2   176.8   64.8    54.3        26.58  3.31   \n",
       "7              150.0       101.2   176.8   64.8    56.1        26.58  3.03   \n",
       "\n",
       "   stroke  compression-ratio  engine-power  peak-rpm  city-mpg  highway-mpg  \\\n",
       "0    3.40               10.0      102000.0    5500.0      24.0         30.0   \n",
       "1    3.40                8.0      115000.0    5500.0      18.0         22.0   \n",
       "2    2.80                8.5       70000.0    4400.0      28.0         30.0   \n",
       "3    3.50                7.8      140000.0    5600.0      32.0         20.0   \n",
       "4    2.80                8.8      101000.0    5800.0      23.0         29.0   \n",
       "5    3.90               22.5      101000.0    6000.0      47.0         53.0   \n",
       "6    3.19                9.0      121000.0    4250.0      21.0         28.0   \n",
       "7    3.19                8.0      134000.0    4400.0      28.0         37.0   \n",
       "\n",
       "   mean-effective-pressure   torque    price  \n",
       "0                    40.52    57.68  13950.0  \n",
       "1                    47.39    59.59  17450.0  \n",
       "2                     0.85  3344.79  17710.0  \n",
       "3                    44.74    68.97  23875.0  \n",
       "4                    44.78    53.48  16430.0  \n",
       "5                     1.80  1330.28  16925.0  \n",
       "6                     7.19   377.06  20970.0  \n",
       "7                    57.37    48.20  21105.0  "
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto_numeric.head(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.3 ==========\n",
    "Display the summary statistics for the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "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>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>engine-power</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>mean-effective-pressure</th>\n",
       "      <th>torque</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>159.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>121.955975</td>\n",
       "      <td>98.559748</td>\n",
       "      <td>171.698113</td>\n",
       "      <td>65.729560</td>\n",
       "      <td>53.925157</td>\n",
       "      <td>14.056352</td>\n",
       "      <td>3.294528</td>\n",
       "      <td>3.219874</td>\n",
       "      <td>10.446855</td>\n",
       "      <td>98528.301887</td>\n",
       "      <td>5072.012579</td>\n",
       "      <td>27.113208</td>\n",
       "      <td>32.327044</td>\n",
       "      <td>46.180503</td>\n",
       "      <td>200.055031</td>\n",
       "      <td>11684.723270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>39.434186</td>\n",
       "      <td>5.803361</td>\n",
       "      <td>12.656791</td>\n",
       "      <td>2.292021</td>\n",
       "      <td>2.410446</td>\n",
       "      <td>17.143568</td>\n",
       "      <td>0.296959</td>\n",
       "      <td>0.381833</td>\n",
       "      <td>4.414796</td>\n",
       "      <td>34123.715967</td>\n",
       "      <td>549.988239</td>\n",
       "      <td>7.848229</td>\n",
       "      <td>8.231998</td>\n",
       "      <td>28.780966</td>\n",
       "      <td>513.289289</td>\n",
       "      <td>6744.910579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>65.000000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>141.100000</td>\n",
       "      <td>60.300000</td>\n",
       "      <td>49.400000</td>\n",
       "      <td>3.390000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48000.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>0.490000</td>\n",
       "      <td>19.400000</td>\n",
       "      <td>5118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>93.000000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>163.400000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>6.960000</td>\n",
       "      <td>3.050000</td>\n",
       "      <td>3.070000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>69000.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>26.500000</td>\n",
       "      <td>21.775000</td>\n",
       "      <td>34.140000</td>\n",
       "      <td>7372.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>110.000000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>171.700000</td>\n",
       "      <td>65.400000</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>9.030000</td>\n",
       "      <td>3.270000</td>\n",
       "      <td>3.270000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>92000.000000</td>\n",
       "      <td>5100.000000</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>49.800000</td>\n",
       "      <td>55.900000</td>\n",
       "      <td>9233.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>145.000000</td>\n",
       "      <td>101.200000</td>\n",
       "      <td>177.800000</td>\n",
       "      <td>66.500000</td>\n",
       "      <td>55.600000</td>\n",
       "      <td>14.885000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116000.000000</td>\n",
       "      <td>5450.000000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>37.000000</td>\n",
       "      <td>68.495000</td>\n",
       "      <td>119.990000</td>\n",
       "      <td>14719.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>256.000000</td>\n",
       "      <td>115.600000</td>\n",
       "      <td>202.600000</td>\n",
       "      <td>71.700000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>174.160000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>200000.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>99.850000</td>\n",
       "      <td>3912.870000</td>\n",
       "      <td>42056.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       normalized-losses  wheel-base      length       width      height  \\\n",
       "count         159.000000  159.000000  159.000000  159.000000  159.000000   \n",
       "mean          121.955975   98.559748  171.698113   65.729560   53.925157   \n",
       "std            39.434186    5.803361   12.656791    2.292021    2.410446   \n",
       "min            65.000000   86.600000  141.100000   60.300000   49.400000   \n",
       "25%            93.000000   94.500000  163.400000   64.000000   52.000000   \n",
       "50%           110.000000   97.000000  171.700000   65.400000   54.100000   \n",
       "75%           145.000000  101.200000  177.800000   66.500000   55.600000   \n",
       "max           256.000000  115.600000  202.600000   71.700000   59.800000   \n",
       "\n",
       "       engine-size        bore      stroke  compression-ratio   engine-power  \\\n",
       "count   159.000000  159.000000  159.000000         159.000000     159.000000   \n",
       "mean     14.056352    3.294528    3.219874          10.446855   98528.301887   \n",
       "std      17.143568    0.296959    0.381833           4.414796   34123.715967   \n",
       "min       3.390000    2.540000    2.070000           7.000000   48000.000000   \n",
       "25%       6.960000    3.050000    3.070000           8.600000   69000.000000   \n",
       "50%       9.030000    3.270000    3.270000           9.000000   92000.000000   \n",
       "75%      14.885000    3.580000    3.410000           9.400000  116000.000000   \n",
       "max     174.160000    3.940000    4.170000          23.000000  200000.000000   \n",
       "\n",
       "          peak-rpm    city-mpg  highway-mpg  mean-effective-pressure  \\\n",
       "count   159.000000  159.000000   159.000000               159.000000   \n",
       "mean   5072.012579   27.113208    32.327044                46.180503   \n",
       "std     549.988239    7.848229     8.231998                28.780966   \n",
       "min    4150.000000   15.000000    18.000000                 0.490000   \n",
       "25%    4800.000000   22.000000    26.500000                21.775000   \n",
       "50%    5100.000000   26.000000    32.000000                49.800000   \n",
       "75%    5450.000000   31.000000    37.000000                68.495000   \n",
       "max    6600.000000   49.000000    54.000000                99.850000   \n",
       "\n",
       "            torque         price  \n",
       "count   159.000000    159.000000  \n",
       "mean    200.055031  11684.723270  \n",
       "std     513.289289   6744.910579  \n",
       "min      19.400000   5118.000000  \n",
       "25%      34.140000   7372.000000  \n",
       "50%      55.900000   9233.000000  \n",
       "75%     119.990000  14719.500000  \n",
       "max    3912.870000  42056.000000  "
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto_numeric.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.4  ==========\n",
    "Produce a scatter plot of `price` against `engine-power`. Label axes appropriately and include a title in your plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x13b30c710>"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LvQ/I3Xeb2T3A7cD9dPW4A3QAw4FaYFPW8s3AiJzlHVnL2nO2MSKO2EVEJD4VGYbt7p81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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13a8437d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = plt.scatter(auto_numeric[\"engine-power\"], auto_numeric[\"price\"])\n",
    "plt.xlabel('Engine Power')\n",
    "plt.ylabel('Price')\n",
    "plt.title('Price vs. Engine Power')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.5  ==========\n",
    "Do you think that engine-power alone is sufficient for predicting the price? Can you make any other observations on the data from the above plot? Please explain your answer in 2-3 sentences. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Engine-power alone is no sufficient for prediciting price. As shown in the scatter plot above, there seems to be very vague positive correlation between price and Engine Power, but there are too many outliers. The outliers are going to skew any predictor created with just this one attribute. The outliers also show that there's probably multiple additional factors that contribute to the Price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.6  ==========\n",
    "Visualise the distribution of the car prices. Choose a sensible value for the number of bins in the histogram. Again, label axes appropriately and include a title in your plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x13c3e0dd0>"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0LF4HzC2sQZLUotKD3t8ElkXE5fX0a4GrShvJzGMjYj7wU554dtUgcN902w8NDZY21VUj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\nBoYkqYiBIUkqYmBIkor8f6nOcVIUyqdWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x137d1e9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = auto_numeric['price'].copy(deep=True)\n",
    "plt.hist(x, range=[0, int(max(x))])\n",
    "plt.xlabel(\"Price\")\n",
    "plt.ylabel(\"Occurences\")\n",
    "plt.title(\"Histogram of Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.7  ==========\n",
    "How would you preprocess it to improve the performance of linear regression? Don’t do it at this stage, but instead in one sentence explain why you would do what you suggested."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I explained above, the outliers are going to skew any model made only using the Engine Power attribute. These outliers aren't mistakes, they indicate there are other attributes that contribute to the determination of Price. So as a part of preprocessing I would want to either remove the obvious outliers (>\\$25000) or perform a transformation on the dataset to make the outliers less influential. I believe it was mentioned in lecture that a logarithmic transformation would be good at doing such a task."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.8  ==========\n",
    "Now we want to build a simple linear regression model. First we need to define our input and target variables. Store the values of the attribute `engine-power` in a vector `X` and the values of our target variable `price` in a vector `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "auto_numeric_copy = auto_numeric.copy(deep=True)\n",
    "X = auto_numeric['engine-power']\n",
    "y = auto_numeric['price'] # target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.9 ==========\n",
    "For technical reasons, we need to convert `X` into a 2D array, otherwise we will receive an error when trying to use it for building models. Perform this transformation and confirm that the shape of the resulting array is (`n`,1) where `n` is the number of instances in the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New shape of X: (159, 1)\n"
     ]
    }
   ],
   "source": [
    "ninstances = X.shape[0]\n",
    "X = np.array(X).reshape(ninstances,1)\n",
    "print(\"New shape of X: {}\".format(X.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.10  ==========\n",
    "Now we want to use Hold-out validation to split the dataset into training and testing subsets. Use 80% of the data for training and the remaining 20% for testing. Store your data into matrices `X_train`, `X_test`, `y_train`, `y_test`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of instances in X: 159\n",
      "Number of instances in X_train: 127\n",
      "Number of instances in X_test: 32\n",
      "Number of instances in X_train and X_test together: 159\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.8, test_size=0.2, 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": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.11  ==========\n",
    "By using Scikit-learn's [`LinearRegression`](http://scikit-learn.org/0.17/modules/generated/sklearn.linear_model.LinearRegression.html) fit a model to the training data. When initialising the model, set the `normalize` parameter to `True` and use default settings for the other parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.202\n"
     ]
    }
   ],
   "source": [
    "lm = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "lm.fit(X_train, y_train)\n",
    "print('Coefficient of Determination: {:.3f}'.format(lm.score(X_train, y_train)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.12  ==========\n",
    "By looking into the attributes of your model, write down an equation for predicting the price of a car given the engine-power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Price = (0.0899)*(engine-power) + (2823.1219)\n"
     ]
    }
   ],
   "source": [
    "lrc = lm.coef_\n",
    "lri = lm.intercept_\n",
    "\n",
    "print(\"Price = ({:.4f})*(engine-power) + ({:.4f})\".format(lrc[0], lri))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.13  ==========\n",
    "What happens to the price as one more unit of engine-power is added? By examining the magnitude of the regression coefficient is it possible to tell whether or not engine-power is an important influential variable on price? Explain your answer in 1-2 sentences."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As engine-power increases, the price also increases. However the since regression coefficient is tiny(.0899) this means that engine-power is not an influential variable in predicting price. If it was, then the regression coefficient would be greater and the intercept would be less (in this case)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Correct on the first point.\n",
    "\n",
    "The value of the coefficient *can't* tell us how influential the related variable is because the units used for the variable are arbritary. For example, conisder a \"height\" variable - if height is measured in m, the learned coefficient will be 100 times higher than if height was measured in cm. So the magnitude of the coefficient is meaningless.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.14  ==========\n",
    "Produce a scatter plot similar to the one in Question 1.4 but use training data only this time. Add the regression line to the plot and show the predictions on the training set by using a different marker. Label axes appropriately and add a title to the graph. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13a0fec90>"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yc/O45x5/bS+f8eMvrLC2lwi/v3gQpzEl5vOATPW1aXM8Y8eOIjk5mcOHD3PXXUO9DsmE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\nFQIIgAoBBEDFA39ND2DjA4m9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x138c2d990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_train, y_train, label='training data')\n",
    "ax.plot(X_train, lm.predict(X_train), color='black', lw=3, label='regression line', alpha=.75)\n",
    "ax.set_xlabel('Engine Power')\n",
    "ax.set_ylabel('Price')\n",
    "ax.set_title('Training Data: Price vs. Engine Power')\n",
    "ax.legend(loc='upper left')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good, but you missed plotting predicted values for the training set.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.15  ==========\n",
    "So far we have used Hold-out validation. Can you think of a disadvantage of using this method, especially when dealing with small datasets?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have a small dataset, the disadvantage of using Hold-out validation is that you're using less data to train your model, and you could be losing crucial data by putting it in the testing set. The smaller the dataset, the bigger a problem this becomes. For example, is you have a dataset of 10 instances, and there's 1 big outlier. If that outlier ends up in the training set for model1 and the test set for model2, you're going to have 2 very different predictors!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "True, but the even bigger problem is that our testing set would be very small, and so likely not representative of the overall distribution of our data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.16  ==========\n",
    "Now we want to use [`KFold`](http://scikit-learn.org/0.17/modules/generated/sklearn.cross_validation.KFold.html) cross-validation to evaluate the performance of the regression model. Famliriase yourself with the method and make sure you understand the differences between Hold-out and K-fold cross-validation. By using Scikit-learn's `K-fold` class construct a 5-fold cross-validation iterator for the `auto_numeric` dataset. Set the `shuffle` parameter to `True` and `random_state` to `0`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = X.shape[0]\n",
    "kf = KFold(n, n_folds=5, shuffle=True, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.17  ==========\n",
    "By making use of the iterator you constructed in the previous question, loop through the 5 folds and display the mean value of the `price` variable for the training instances only in each fold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "KFold #1\n",
      "Mean Value of Price Variable: 11853.2677165\n",
      "\n",
      "KFold #2\n",
      "Mean Value of Price Variable: 11635.976378\n",
      "\n",
      "KFold #3\n",
      "Mean Value of Price Variable: 11689.8740157\n",
      "\n",
      "KFold #4\n",
      "Mean Value of Price Variable: 11709.8267717\n",
      "\n",
      "KFold #5\n",
      "Mean Value of Price Variable: 11535.84375\n"
     ]
    }
   ],
   "source": [
    "j = 1\n",
    "for train_index, test_index in kf:\n",
    "    X_train, X_test = X[train_index, :], X[test_index, :]\n",
    "    y_train, y_test = y[train_index], y[test_index]\n",
    "    print(\"\\nKFold #{}\".format(j))\n",
    "    #print(\"Number of training instances: {} \\nNumber of testing instances: {}\".format(X_train.shape[0], X_test.shape[0]))\n",
    "    print(\"Mean Value of Price Variable: {}\".format(y_train.mean()))\n",
    "    j+=1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.18  ==========\n",
    "Now initialise a new `LinearRegression` model and fit it by making use of the cross-validation iterator, the `X` and `y` arrays defined above and the [`cross_val_predict`](http://scikit-learn.org/0.17/modules/generated/sklearn.cross_validation.cross_val_predict.html) function. Display the shape of your prediction and confirm it has the same dimensionality as your `y` vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lm2 = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "y_predict = cross_val_predict(lm2, X, y, cv=kf)\n",
    "\n",
    "print(\"Shape of Prediction: {}\".format(y_predict.shape))\n",
    "print(\"Shape of y Vector: {}\".format(y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.19  ==========\n",
    "Report the Coefficient of Determination (R^2), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Correlation Coefficient (CC) from the simple linear regression model you build in Question 1.18. *Hint: RMSE is the square root of the Mean Squared Error (MSE). For CC you might find numpy's [`corrcoef`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.corrcoef.html) function useful.* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.173\n",
      "Root Mean Squared Error (RMSE): 6114.452\n",
      "Mean Absolute Error (MAE): 3987.958\n",
      "Correlation Coefficient: 0.417\n"
     ]
    }
   ],
   "source": [
    "r2 = r2_score(y, y_predict)\n",
    "rmse = mean_squared_error(y, y_predict)**.5\n",
    "mae = mean_absolute_error(y, y_predict)\n",
    "cc = np.corrcoef(y, y_predict)[0,1]\n",
    "\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(rmse))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mae))\n",
    "print('Correlation Coefficient: {:.3f}'.format(cc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.20  ==========\n",
    "What do the above metrics intend to measure? Relate the values of CC, MAE and RMSE to the observations you made in Question 1.5. Explain your answer in 1-2 short paragraphs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike in classification where we want to count how often we are wrong, with linear regression we are always wrong so when measuring error we want to know by <b>how much</b> were we wrong. There are several different ways to measure this error. First the Root Mean Squared error is the average squared deviation from the truth. This error measure is very sensitive to outliers. Our result was roughly \\$6100, which means on average we the price was \\$6100 off the true price. The prices ranged from \\$5000, to \\$45000, so being off by \\$6100 is quite a lot. Mean Absolute Error is much less sensitive to outliers and had a value of roughly \\$4000. This is still a lot, but is much less than the RMSE. \n",
    "\n",
    "This means two things. First, that engine-power is not a very good predictor for the price to begin with. Second, there are some outliers in our dataset that are skewing our model as shown by the large decrease from RMSE to MAE. These results reason well with the Correlation Coefficient, which is insensitive to the mean/scale of the data and indicates how well engine-power and price are correlated. Our result was .4, which supports are results. There is a relationship between engine-power and price, but it is not the only attribute that influences the price and thus does not make a good predictor by itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n",
    "You only miss explaining the R2 metric, which gives the proportion of the variance of the original data 'explained' by the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.21 ==========\n",
    "Show a histogram of the residuals of the linear regression model (i.e. true - predicted values). Label axes appropriately and add a title to your plot. Does the distribution of residuals look like what you expected?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1c02071d0>"
      ]
     },
     "execution_count": 296,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BcU9EfBG4BXh4aGJmeqWUJE0Rm+z0john1y8foBqZ9kVUz8Z4KT45T5KmlM0dYSwA9svM\n4yLi7zPz3FZUSpLUeTZ3WW1fw+tjmlkRSVJn21xgND40qW/MpSRJPa/0xj0Y/Yl7kqQpYnN9GC+I\niCX162c3vPbRrJI0xWwuMPZsSS0kSR1vk4HhI1glSUPG04chSZrCDAxJUhEDQ5JUxMCQJBUpHXxQ\nW2oDLFs28hqClSunsf32T6e/v78NlZKkcgZGq6yGuQuOhhnDpq+CRfMWM3v2Hm2pliSVMjBaaQaw\nU7srIUkTYx+GJKmIgSFJKmJgSJKKGBiSpCIGhiSpiIEhSSpiYEiSihgYkqQi3rjXZQYGBli6dMmY\n82fN2t1hRiQ1hYHRZZYuXcLBF8wZOcQIOMyIpKYyMLqRQ4xIagP7MCRJRQwMSVIRA0OSVMTAkCQV\nMTAkSUXacpVURCwGVtdv783M49tRD0lSuZYHRkRsB5CZL2v1uiVJE9eOI4y9gadGxEKgHzg9M29p\nQz0kSePQjj6Mh4BzMvMI4ETgqxFhX4okdbh2HGHcCdwNkJl3RcQDwDOB+8dTyNbb9E7G7LjjNGbO\nnF607MqV0yatrFbptPpMNtvXvXq5bc3QjsB4O7AXMC8ingVMB3473kLWP75hsuvVNitWrGP58rXF\ny05WWa0wc+b0jqrPZLN93auX2wbNCcN2BMYXgC9FxE3ABuDtmdk7e39J6lEtD4zMfBx4c6vXK0na\nMr3TESBJaioDQ5JUxMCQJBUxMCRJRQwMSVIRA0OSVMRnerfbBli27L5RZ82atTv9/f3tKUuShjEw\n2m01zF1wNMwYNn0VLJq3mNmz92hPWZI0jIHRCWYAO3VgWZLUwD4MSVIRA0OSVMTAkCQVMTAkSUUM\nDElSEQNDklTEwJAkFTEwJElFDAxJUhEDQ5JUxMCQJBUxMCRJRQwMSVIRA0OSVMTAkCQVMTAkSUUM\nDElSEQNDklTEwJAkFfGZ3lPBBli27L5RZ82atTv9/f0bTRsYGGDp0iVjFjeez6xcOY3tt3/6pKxD\nUnsZGFPBapi74GiYMWz6Klg0bzGzZ++x0eSlS5dw8AVzRi4/kc9M4joktZeBMVXMAHZq4vKtWoek\ntrEPQ5JUxMCQJBUxMCRJRQwMSVIRA0OSVMTAkCQVMTAkSUUMDElSEQNDklTEO7071RjjP401JlTL\njLdek9iOscafGhgYAPro7x/5/We8Y1JtaoyrscbQuueeu8Ysr9ljYo23vp1qIr/3Zo9FNpnr6JXt\nZGB0qrHGf1oG7NqOCtXGW69JbMeY408tA7aneByrCa1jjLLuueeeto6JNd76dqpOHItsMtfRK9vJ\nwOhko421tLIdFRlmvPWazHaMVdZkjkvVbWNitXv9k6UTf+/t/LvqQPZhSJKKGBiSpCIGhiSpiIEh\nSSpiYEiSirT8KqmI6AP+FdgbeAR4R2aOfbGzJKkjtOMI4/XAdpn5YuBU4JNtqIMkaZzaERiHAN8D\nyMxbgP3bUAdJ0ji148a97YHVDe/XR8RWmblhtIW3fWRbZq147ojpT3nwj6BvlA+sZXzTJ/KZXlnH\nqk0M27FqktYxkXaMt17jbN+mjLmOMcpavXr52L+rCax/vMZb3/FauXIaK1as2+JyNme87djk32hh\n2zfXtslYx2bLGqv8DtU3ODjY0hVGxLnAosy8vH6/LDPbOdiFJKlAO05J/Rj4HwAR8SLgF22ogyRp\nnNpxSupK4JUR8eP6/XFtqIMkaZxafkpKktSdvHFPklTEwJAkFTEwJElFOvYBSt0+hEhELObJ+03u\nBc4GvgxsAO7IzHn1cn8DnAA8Dnw0M6+OiD8C/g14OrAGeFtmPtDaFowuIg4CPpaZL42I2Wxhm+or\n5T5dL/v9zDyr5Y1qMKx9+wDfAe6sZ1+YmZd1Y/siYmvgi8AsYFvgo8Cv6JHtN0b7/pPe2X5bAfOB\noNpe7wQepcXbr5OPMLp2CJGI2A4gM19W/xxPVf/TMvMwYKuIeF1E7Ay8BzgYeDXwzxGxDXAi8PPM\nPBT438AZbWnIMBFxMtUf7Xb1pMlo04XAX2XmS4CDImLv1rVoY6O0bw5wbsN2vKyL2/dm4A91/V4N\nfJbe2n6N7TuSqn370Tvb77XAYGYeUtftbNqw/To5MLp5CJG9gadGxMKI+EH9rXW/zLypnn8N8Erg\nQOBHmbk+M9cAd9WffaLt9bKvaG31x3Q38IaG93O2oE0vj4jpwLaZubSevpD2tnVE+4CjIuLGiJgf\nEdPo3vZdypM7iX5gPVv2N9nJ7duK6hvzHOA1vbD9MvNbVEcNALtRPZi45duvkwNj1CFE2lWZcXoI\nOCczj6BK9q+y8eAVa6naN52N27gO2GHY9KFl2y4zr6Ta0QzZkjYNTVszrIwdJrfW5UZp3y3AyfU3\nuCXAmYz8u+yK9mXmQ5n5YL2TuAw4nR7afqO078PAfwAf6IXtB5CZGyLiy8B5wNdow/br5B3wGqoG\nDRlzvKkOdCdVSJCZdwEPADs3zJ9ONYrMGjYOg+lU3xwa2z60bCdq3B4TadPwMOy0tl6VmbcNvQb2\nofpP15Xti4jnANcBX8nMb9Bj22+U9vXU9gPIzGOBPYGLgac0zGrJ9uvkwOjmIUTeDpwLEBHPotoo\n10bEYfX8I4GbgJ8Ch0TEthGxA/B84A7gZuq21//eRGe6NSIOrV+Pu02ZuRZ4NCKeW1/kcASd1daF\nETF0KvTlwGK6tH31ue2FwAcz8yv15Nt6ZfuN0b5e2n5vjogP1W8fAQaAn23JPmUi7evYq6To7iFE\nvgB8KSJuovoWdyzVUcbFdQfUr4HLM3MwIs4DfkR1eHlaZj4WERcCX6k//yjw1+1oRIEPAPO3sE3v\npDq83gq4NjN/2vJWjO1E4PyIeAz4HXBCZq7r0vadCswAzoiIfwAGgfdRta8Xtt9o7TsJ+HSPbL8r\nqPYpN1Ltt98L/IYt36eMq30ODSJJKtLJp6QkSR3EwJAkFTEwJElFDAxJUhEDQ5JUxMCQJBXp5Psw\npEkREbtR3X3/S6pr07eiuqv1ksz8x3GWdRHwucy8ddj0LwHXZ+YlE6jfvcBhmblsvJ+VWsnA0FRx\nf2buN/QmIp4J3BURX8/MLC0kM0/Y/FLj5s1Q6goGhqaqZ9X/ro2IU4C/pDryWJiZH6oHsfs6T44B\n9k+Z+Z2IuB44MzN/GBGfBI4C/h/VCLDX10czN2TmcwEi4kyqYanPioh3Uw3D/cdUIwDMrcOqr152\nL+CiuqxHgOMy854m/x6kYvZhaKp4dkTcGhG/jojlwFlUQ5nvRTUM9v5Uz0/YJSKOqefdm5kHAG8B\nXtJYWET8BdWw0X8KvAl4XsPsEUcMdQD9OdWppxcC3wLeNWyxk4BPZOaBwPnAi7asydLkMjA0Vdyf\nmftl5p8Cl1A9le06qvH/D6QamO5WqvD4b1SDX74+Iq6kepbAR4aVdzhwRWZuyMw/AN/d1Mrrgd6O\nAf5nRJxN9UCcacMWuxq4ICIupnqew9cm2FapKQwMTUUfpDrVdDLV/4FP12GyL3AQ1WMt76Ea6fPf\nqI4uhg/KNsjG/3/WjzF9G4CI2AVYRPW8ge9SPVqz8XkGZOY3gX2pnsPxfuDzW9JIabIZGJoqntg5\nZ+YAVVicBtwGvDUinhrVc6G/BbwxIuYBZ9U78XnAzIhofHbAD4A31cNI/wnV4zChep7AjIh4WlSP\n6h2afgBwV2Z+hip8jqTqq3hCRHwDOCgz51M9PW7fSWy/tMUMDE0VG/UrZOZCqm/8hwKXU32r/zlw\na31p7CVARMTPgRuoOrrXDJWTmd8GbqR61sBVVJfsUi/zCeBnwLV1uVA9q6E/In5J9WyCe4HnDqvb\n2cBpEbEYOIeqT0PqGA5vLkkq4hGGJKmIgSFJKmJgSJKKGBiSpCIGhiSpiIEhSSpiYEiSihgYkqQi\n/x+AUP/UHfJF1gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14f0cae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get residuals\n",
    "residuals = np.absolute(y - y_predict)\n",
    "\n",
    "# Plot Histogram\n",
    "plt.hist(residuals, 50, facecolor='green')\n",
    "plt.title(\"Residuals Histogram\")\n",
    "plt.xlabel(\"Residuals\")\n",
    "plt.ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the large RMSE and MAE values, but the decrease from RMSE to MAE, the plot should show a couple very large outliers that skew our predictor. Most of the residuals fall in a normal/acceptable range of <\\$5000, but there are a couple residuals with values >\\$20000. These residuals are unreasonably large and are the source of our large RMSE and MAE values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good, but you missed the most important observation - the errors appear approximately normally distributed. This is a good sign, since normality of errors is a fundamental assumption of the linear regression model.\n",
    "\n",
    "You also shouldn't take the absolute value here - we are often interested in which side of 0 our residuals fall.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.22 ==========\n",
    "Load the new dataset `train_auto_base.csv` into a pandas DataFrame `auto_base`. Again by using the `engine-power` attribute as predictor and `price` as target variable build a LinearRegression model on this dataset. Report the R^2, RMSE, MAE and CC metrics for this model by making use of the K-fold CV iterator constructed in Question 1.16."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: -0.002\n",
      "Root Mean Squared Error (RMSE): 6730.844\n",
      "Mean Absolute Error (MAE): 4901.861\n",
      "Correlation Coefficient: -0.062\n"
     ]
    }
   ],
   "source": [
    "# Load the dataset \n",
    "data_path2 = os.path.join(os.getcwd(), 'datasets', 'train_auto_base.csv')\n",
    "auto_base = pd.read_csv(data_path2, delimiter = ',')\n",
    "\n",
    "# Get predictor and Target variables\n",
    "X2 = auto_base['engine-power']\n",
    "y2 = auto_base['price']\n",
    "\n",
    "# Convert to 2D array\n",
    "ninstances = X2.shape[0]\n",
    "X2 = np.array(X2).reshape(ninstances,1)\n",
    "\n",
    "# Hold-out validation to split the dataset into training and testing subsets\n",
    "X2_train, X2_test, y2_train, y2_test = train_test_split(X2, y2, train_size=0.8, test_size=0.2, random_state=0)\n",
    "\n",
    "# KFold\n",
    "n = X2.shape[0]\n",
    "kf2 = KFold(n, n_folds=5, shuffle=True, random_state=0)\n",
    "\n",
    "# fit a model to the training data\n",
    "lm3 = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "y2_predict = cross_val_predict(lm3, X2, y2, cv=kf2)\n",
    "\n",
    "# Report Errors\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2_score(y2, y2_predict)))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(mean_squared_error(y2, y2_predict)**.5))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mean_absolute_error(y2, y2_predict)))\n",
    "print('Correlation Coefficient: {:.3f}'.format(np.corrcoef(y2, y2_predict)[0,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.23 ==========\n",
    "Show a scatter plot of predicted vs. true price and another one of predicted price vs. engine-power. Use a single plot with two subplots. Label axes appropriately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7ALuAl2Xmtoh4PPA2YBy4KjMvbHcdJElqB9tISVKnausdyYg4H/h7oL+c3hQR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\nJWmjpKUkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153c4f910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(221)\n",
    "ax1.scatter(y2, y2_predict, c='blue', marker=\"s\", alpha=.5)\n",
    "ax1.set_title('Predicted vs. True Price')\n",
    "ax1.set_ylabel('Predicted Price')\n",
    "ax1.set_xlabel('True Price')\n",
    "\n",
    "ax2 = fig.add_subplot(222)\n",
    "ax2.scatter(X2, y2_predict, c='red', marker=\"o\", alpha=.5)\n",
    "ax2.set_title('Predicted Price vs. Engine Power')\n",
    "ax2.set_xlabel('Engine Power')\n",
    "\n",
    "fig.suptitle('Sharing Y Axis', fontsize=14)\n",
    "fig.set_figheight(15)\n",
    "fig.set_figwidth(15)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.24 ==========\n",
    "What is the simplest baseline model for the purposes of regression? Relate your answer to the regression model you have just built as part of this question. Can the predictions of this model be justified given the procedure you followed to train it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I find this question difficult becuase I think my train_auto_base.csv is incorrect because the model I built given this database only predicts the same value for each kfold. This makes sense because all of the engine powers in the database had a value of 1. There is not way to make a prediction other than picking a single value from the dataset. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "The dataset is \"supposed\" to be like that, and you correctly identify what your model does in this strange situation!\n",
    "\n",
    "It essentially acts like the baseline model, which is to always predict the mean of the target variable.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 1.25 ==========\n",
    "Why do you think this model performs so poorly? (*Hint: Justify your answer by displaying some statistics of the `auto_base` dataset.*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "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>engine-power</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>159.0</td>\n",
       "      <td>159.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>11684.723270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>6744.910579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>7372.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>9233.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>14719.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.0</td>\n",
       "      <td>42056.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       engine-power         price\n",
       "count         159.0    159.000000\n",
       "mean            1.0  11684.723270\n",
       "std             0.0   6744.910579\n",
       "min             1.0   5118.000000\n",
       "25%             1.0   7372.000000\n",
       "50%             1.0   9233.000000\n",
       "75%             1.0  14719.500000\n",
       "max             1.0  42056.000000"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto_base.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model performed poorly because the auto_base dataset is horrible; all of the engine-power's had a value of 1, but the prices ranged from \\$5118 to \\$42056 as shown in the summary statistics above. I honestly think this might be a mistake in the auto_base dataset we were given, but I'm not sure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Correct! There's no variance in this attribute, so we can't make a prediction based on it.\n",
    "\n",
    "(In real life you will often get datasets that have information-less attributes!)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Multivariate Linear Regression [50%]\n",
    "In this Section we will fit a Multivariate Linear Regression model (LinearRegression) to the dataset. In contrast to Part 1, we will now train a model with multiple explanatory variables and ascertain how they affect our ability to predict the retail price of a car. One of our foremost concerns will be to determine exactly which attributes to include in the model and which may be left out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.1 ==========\n",
    "Use the original dataset (`auto_numeric`) and a visualisation tool of your choice to examine whether or not any of the other attributes are particularly good at predicting the price. Can you find any? Do any attributes appear useless at predicting the price? Do any attributes exhibit significant correlations? As you answer these questions, list two attributes for each question but do not modify the dataset at this stage. Of the attributes you listed, which ones could you safely remove? Explain in 4-5 sentences. *Hint: you might find seaborn's [`pairplot`](https://seaborn.github.io/generated/seaborn.pairplot.html?highlight=pairplot#seaborn.pairplot) function useful for this question.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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N+wdC+32mY0diHDuYrA41Nb5kh6REbc1sFd54t8cwL2z7AxvYtLbBlutapZCuu1D3mg3s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\nPzqDhJY9Vv70AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bd88bc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BncDXlsrL2bNjKypLTY1nRfdI9/XpysN73UOm467eEVrrlz+rmCnvMRWsNJ/RSMR7SPcz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\nsGo72JCWewq9FpKukLRdjOUpwDGE9lWYHdVoh/zWxjd1VCg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9CVvz/gYQZ6VnSfrczB4h\nxPJxwM6ShsVVwx2Iq31mtn6irMqYbknoS2KbfyvQYmaDgFHx+xPAWUndzOxoQofqUuBuYAPa+iRJ\n5YRxZZty5n8qY7YHKfdtM1sZuJ8wgfAX4HVgo4RsWf40s5GEFfZW4NB4TrIdpNX9efycpa05Cy5l\nuTs+l7hElXMvJ0xwrErcbREnQCCsXA+Mn/Pm955RjzmU58Fa+XKBw1cUFxwGm9nKZtYDOAA4B9g8\n8ZazYaS/POR+YA8zW87MWgjb/o7rCIWdBYP4nML+kv4EHA0MJCTutM7qZGCzGnH7GGEr1cWxc3Qf\nYVthLzNbkjCD6Ksl3YeJwJ7x+i5OWBFpLW0XNbPNCduZptcpJ9kx2MnMepvZooQtT+NTzr+PuGXP\nzFYkzECvambXAZtJGgmcBgyIbza9StJfgGOB9wnPwJS4H9jVzJaO34dS40VOkqZIGiBpoKRhKfrv\nAFwaVxZbCAOBnlRvU/cSBwFm9hXCVtlHqtXvzJdsHd9k2wPYn3CPTrtvbwK8EJ/Tfpzw/oGeiXKS\n+XMxSUMTsfZklbq/BxCfJ39O0rt1dPVOuANtc/d4wjPV0DZX3UTYZbGCpMcBYlwOSAwSs/JdmPts\n96aELf13A/vE4/0J22H95U4RHyguOEwnzMo8BbwKnEfoZI81s2mEZweOiOfObSCSniZsY7kPmEZI\n8ud0nNrOAsAIYK84Q3gzcDhhu90lsaOfjMeZ1IlbSRMJ8foL4GLgBcIzC48Bo+PvTjcgrhQ/BDxJ\nmET4HWGgc6yZPU18NipuI61140/+NpOw2jIVuFXS3SnnnwksFmPwHuCEuEXqbOAUM5tCeInSjwjb\noT42s2cI2zpvis/eluJ1GvArYKKZPUvYmndail61SJ43nLAq9ATh+d2HgDUI27peNbN7K2SPBbaP\n/rqZ8Gxwmy1gznzNa4TnA6cT7u8XkX7fvgvoGWPxYcKLO9aIZVTmz1+m1JMWj1vF3H08YZBa7bxa\nZTgLGCm5ezjwfPy5LFdJ+oSQO6+tUWTWuFo85sbbgaGS3ibsyljbzP5GeJnO67RdOV9gaWlt9Tbr\nOI7jOPGtp0MkHdzZujhOFuJbT0+XtH3dk4uvewahvfjbIZ12I76V9CHg63GyuNFy5r5puuL4D4CX\nJD1iZqsQ3gi9ZlNKdyP8OQTHcRzHcRwnL77S4LQrZrYJYVfG6c0MEiPV4vXvhB1MpS36w6qct0Di\nK4qO4ziO4ziO4zhOGf6MouM4juM4juM4jlOGDxQdx3Ecx3Ecx3GcMnyg6DiO4ziO4ziO45ThA0XH\ncRzHcRzHcRynDB8oOo7jOI7jOI7jOGX8P1bPAb6BwGmYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bbd30610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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P1FerF0qJowYK/k6ld2CYzu4hrlpbH/n8sI4w6vlBscB5c4vjomfBSbZzy2wH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\neWVjouq6HpvZzpyCEf7okmU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XdSjO+NkjwCeNMT9wdm8TkXXO31cDT4aenPj8ZPJ/l9hJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bc247dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code goes here\n",
    "g1 = sns.pairplot(data=auto_numeric, x_vars=['normalized-losses', 'wheel-base', 'length', 'width', 'height', 'engine-size'], y_vars = 'price')\n",
    "g2 = sns.pairplot(data=auto_numeric, x_vars=['bore','stroke','compression-ratio','peak-rpm','city-mpg'], y_vars = 'price')\n",
    "g3 = sns.pairplot(data=auto_numeric, x_vars=['highway-mpg','mean-effective-pressure','torque'], y_vars = 'price')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "None of these attribute seem exceptionally good at predicting price. The attributes wheel-base, length, width, and bore seem to be the most positively correlated. Engine-size seems to have a very steep positive corrlation. Even the slighest increase in size seems to increase the size. However the attributes torque, mean-effective-pressure, highway-mpg, city-mpg, peak-rpm, comprssion-ratio, stroke, height, and normalized-losses all seem useless at predicting the price because the there's no obvious correlation. I think most of those attributes can be safely removed, but especially compression-ratio, torque, and mean-effectiveness-pressure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Mostly good, although the mpg attributes definitely have a (negative) correlation with price.\n",
    "\n",
    "You were also asked to report on correlations *between* attributes, which you didn't do. For example, length and width are highly correlated, so keeping *both* of these is unlikely to help improve predictive power.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.2 ==========\n",
    "We will now make a first attempt at building a Multivariate Linear Regression model using all numeric attributes. Initialise a `LinearRegression` model and predict the output by using 5-fold cross-validation and the `cross_val_predict` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get predictor and Target variables\n",
    "X3 = auto_numeric.copy(deep=True)\n",
    "X3 = X3[['wheel-base','length','width','engine-size','bore','city-mpg','highway-mpg']]\n",
    "y3 = auto_numeric['price'].copy(deep=True)\n",
    "\n",
    "# Hold-out validation to split the dataset into training and testing subsets\n",
    "# DONT NEED\n",
    "X3_train, X3_test, y3_train, y3_test = train_test_split(X3, y3, train_size=0.8, test_size=0.2, random_state=0)\n",
    "\n",
    "# KFold\n",
    "n = X3.shape[0]\n",
    "kf3 = KFold(n, n_folds=5, shuffle=True, random_state=0)\n",
    "\n",
    "# fit a model to the training data\n",
    "lm4 = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "y3_predict = cross_val_predict(lm4, X3, y3, cv=kf3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good, although you weren't suppsed to drop any attributes!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.3 ==========\n",
    "Display the Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Correlation Coefficient (CC)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.491\n",
      "Root Mean Squared Error (RMSE): 4798.281\n",
      "Mean Absolute Error (MAE): 2990.603\n",
      "Correlation Coefficient: 0.742\n"
     ]
    }
   ],
   "source": [
    "# Report Errors\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2_score(y3, y3_predict)))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(mean_squared_error(y3, y3_predict)**.5))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mean_absolute_error(y3, y3_predict)))\n",
    "print('Correlation Coefficient: {:.3f}'.format(np.corrcoef(y3, y3_predict)[0,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.4 ==========\n",
    " Comment on each metric display above in comparison to what you have obtained for the Simple Linear Regression model in Question 1.19."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Coefficient of Determination greatly improved from 0.173 to 0.491. This is a pretty large jump for the CoD, and means that model is much more likely to predict an accurate price given the attributes 7 attributes I used to train the model.\n",
    "\n",
    "The Root Mean Squared Error also decreased from \\$6114 to \\$4798, a roughly \\$1300 difference. This means that on average we were \\$1300 closer to the true price than the Simple Linear Regression Model.\n",
    "\n",
    "The Mean Absolute Error also decreased from \\$3987.958 to \\$2990.60, a roughly \\$1000 difference. This is also still pretty far from our new RMSE value, which means that outliers are still having a strong influence on the accuracy of our model!\n",
    "\n",
    "Finally, the Correlation Coefficient increased from 0.417 to 0.742. This confirms that our new model is more positively correlated with the true price than the Simple Linear Regression Model, and that the correlation is pretty strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.5 ==========\n",
    "Examine the histogram for the `engine-size` attribute. Choose a sensible value for the number of bins in the histogram. Label axes appropriately and include a title in your plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x15f2f7e90>"
      ]
     },
     "execution_count": 414,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x156252a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get engine-size data\n",
    "engine_size = X3['engine-size']\n",
    "\n",
    "# Plot Histogram\n",
    "plt.hist(engine_size, 50)\n",
    "plt.title(\"Engine Size Histogram\")\n",
    "plt.xlabel(\"Engine Size\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "\n",
    "# Isolate Outliers\n",
    "#outliers = engine_size[engine_size > 100]\n",
    "#print(outliers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.6 ==========\n",
    "Is the distribution expected to cause a problem for regression? Explain your answer in 2-3 sentences."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, this distribution will most certainly cause a problem. As the histogram shows there is a heavy concentration of engine sizes less than or equal to 45. Out of the 159 total datapoints there are only 2 engine sizes in the dataset that are larger, 107.77 and 174.16. These outliers differ from the maximum of the cluster(45) but 62 and 129! These are very large difference, and these two datapoints could be considered extreme outliers, greatly skewing the results. As you can also see by looking at the graph, there is a heavy concentration of point on the left, and on 2 onthe right, similar to the graph of log. A log transformation of this attribute could help remove the strong effects of the two outliers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.7 ==========\n",
    "Transform this attribute using an appropriate simple technique from the lectures. Plot the histogram of the transformed attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x16c63ab50>"
      ]
     },
     "execution_count": 415,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UJEmV/w9o4KUZ9+pjfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1591bdcd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# transform engine-size data\n",
    "X3['engine-size'] = np.log(X3['engine-size'])\n",
    "\n",
    "# Plot Histogram\n",
    "plt.hist(X3['engine-size'], 50)\n",
    "plt.title(\"Engine Size Histogram\")\n",
    "plt.xlabel(\"Engine Size\")\n",
    "plt.ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.8 ==========\n",
    "Now re-build a Linear Regression model on the transformed dataset and report the R^2, RMSE, MAE and CC metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.685\n",
      "Root Mean Squared Error (RMSE): 3771.588\n",
      "Mean Absolute Error (MAE): 2663.191\n",
      "Correlation Coefficient: 0.828\n"
     ]
    }
   ],
   "source": [
    "# KFold\n",
    "n = X3.shape[0]\n",
    "kf4 = KFold(n, n_folds=5, shuffle=True, random_state=0)\n",
    "\n",
    "# fit a model to the training data\n",
    "lm5 = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "y4_predict = cross_val_predict(lm5, X3, y3, cv=kf4)\n",
    "\n",
    "# Report Errors\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2_score(y3, y4_predict)))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(mean_squared_error(y3, y4_predict)**.5))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mean_absolute_error(y3, y4_predict)))\n",
    "print('Correlation Coefficient: {:.3f}'.format(np.corrcoef(y3, y4_predict)[0,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.9 ==========\n",
    "How has the performance of your model changed? Explain your answer in 1-2 sentences."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performace of the model increased after performing the attribute log transformation. The R^2 value increased from 0.491 to .685, and the CC increased from 0.742 to .828. Since linear regression is so sensitive to outliers, using a log transformation is useful of an attribute can help make those outliers less influential on your predictor, as these results demonstrate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.10 ==========\n",
    "So far we have performed regression with numeric attributes. We will now attempt to integrate nominal (categorical) attributes into our regression model. \n",
    "Load the dataset `train_auto_full.csv` into a pandas DataFrame called `auto_full`. Display the number of samples and attributes in the dataset. Also, display the first 20 instances of the dataset. *Hint: Execute the cell below to change the default for `max_columns` display option in pandas.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pd.set_option('max_columns', 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of attributes: 27\n",
      "Number of samples: 159\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>fuel-type</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>engine-power</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>symboling</th>\n",
       "      <th>mean-effective-pressure</th>\n",
       "      <th>torque</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>164.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>176.6</td>\n",
       "      <td>66.2</td>\n",
       "      <td>54.3</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>8.85</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.00</td>\n",
       "      <td>102000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>2</td>\n",
       "      <td>40.52</td>\n",
       "      <td>57.68</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>110.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>162.4</td>\n",
       "      <td>66.4</td>\n",
       "      <td>54.3</td>\n",
       "      <td>ohc</td>\n",
       "      <td>5</td>\n",
       "      <td>15.18</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.00</td>\n",
       "      <td>115000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>2</td>\n",
       "      <td>47.39</td>\n",
       "      <td>59.59</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>158.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>105.8</td>\n",
       "      <td>192.7</td>\n",
       "      <td>71.4</td>\n",
       "      <td>51.6</td>\n",
       "      <td>ohc</td>\n",
       "      <td>5</td>\n",
       "      <td>15.18</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.94</td>\n",
       "      <td>2.80</td>\n",
       "      <td>8.50</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>4400.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>3344.79</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>106.0</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>turbo</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>86.6</td>\n",
       "      <td>158.7</td>\n",
       "      <td>67.7</td>\n",
       "      <td>55.9</td>\n",
       "      <td>ohc</td>\n",
       "      <td>5</td>\n",
       "      <td>13.74</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.13</td>\n",
       "      <td>3.50</td>\n",
       "      <td>7.80</td>\n",
       "      <td>140000.0</td>\n",
       "      <td>5600.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1</td>\n",
       "      <td>44.74</td>\n",
       "      <td>68.97</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>192.0</td>\n",
       "      <td>bmw</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>54.3</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>8.67</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.50</td>\n",
       "      <td>2.80</td>\n",
       "      <td>8.80</td>\n",
       "      <td>101000.0</td>\n",
       "      <td>5800.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>2</td>\n",
       "      <td>44.78</td>\n",
       "      <td>53.48</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>194.0</td>\n",
       "      <td>bmw</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>110.0</td>\n",
       "      <td>190.9</td>\n",
       "      <td>71.4</td>\n",
       "      <td>58.7</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>8.67</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.78</td>\n",
       "      <td>3.90</td>\n",
       "      <td>22.50</td>\n",
       "      <td>101000.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.80</td>\n",
       "      <td>1330.28</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>188.0</td>\n",
       "      <td>bmw</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>54.3</td>\n",
       "      <td>ohc</td>\n",
       "      <td>6</td>\n",
       "      <td>26.58</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.19</td>\n",
       "      <td>9.00</td>\n",
       "      <td>121000.0</td>\n",
       "      <td>4250.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.19</td>\n",
       "      <td>377.06</td>\n",
       "      <td>20970.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>150.0</td>\n",
       "      <td>bmw</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>101.2</td>\n",
       "      <td>176.8</td>\n",
       "      <td>64.8</td>\n",
       "      <td>56.1</td>\n",
       "      <td>ohc</td>\n",
       "      <td>6</td>\n",
       "      <td>26.58</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.19</td>\n",
       "      <td>8.00</td>\n",
       "      <td>134000.0</td>\n",
       "      <td>4400.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>0</td>\n",
       "      <td>57.37</td>\n",
       "      <td>48.20</td>\n",
       "      <td>21105.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>121.0</td>\n",
       "      <td>chevrolet</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.4</td>\n",
       "      <td>141.1</td>\n",
       "      <td>60.3</td>\n",
       "      <td>53.2</td>\n",
       "      <td>l</td>\n",
       "      <td>3</td>\n",
       "      <td>3.39</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.03</td>\n",
       "      <td>9.50</td>\n",
       "      <td>48000.0</td>\n",
       "      <td>5300.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>2</td>\n",
       "      <td>59.33</td>\n",
       "      <td>25.08</td>\n",
       "      <td>5151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>98.0</td>\n",
       "      <td>chevrolet</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>104.3</td>\n",
       "      <td>155.9</td>\n",
       "      <td>68.3</td>\n",
       "      <td>52.0</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.47</td>\n",
       "      <td>7.80</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>1</td>\n",
       "      <td>51.55</td>\n",
       "      <td>36.35</td>\n",
       "      <td>6295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>93.0</td>\n",
       "      <td>chevrolet</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>158.8</td>\n",
       "      <td>63.6</td>\n",
       "      <td>52.0</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.11</td>\n",
       "      <td>9.60</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>0</td>\n",
       "      <td>65.57</td>\n",
       "      <td>29.11</td>\n",
       "      <td>6575.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>231.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>113.0</td>\n",
       "      <td>199.6</td>\n",
       "      <td>71.4</td>\n",
       "      <td>59.1</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.78</td>\n",
       "      <td>4.17</td>\n",
       "      <td>9.41</td>\n",
       "      <td>176000.0</td>\n",
       "      <td>6600.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>1</td>\n",
       "      <td>93.12</td>\n",
       "      <td>20.15</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>118.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>93.7</td>\n",
       "      <td>174.6</td>\n",
       "      <td>63.8</td>\n",
       "      <td>49.4</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>2.97</td>\n",
       "      <td>3.23</td>\n",
       "      <td>21.50</td>\n",
       "      <td>68000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>12.28</td>\n",
       "      <td>152.80</td>\n",
       "      <td>6377.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>118.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>turbo</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>93.7</td>\n",
       "      <td>157.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>50.8</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>7.10</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.39</td>\n",
       "      <td>7.60</td>\n",
       "      <td>102000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1</td>\n",
       "      <td>28.80</td>\n",
       "      <td>73.88</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>197.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>110.0</td>\n",
       "      <td>192.7</td>\n",
       "      <td>71.4</td>\n",
       "      <td>58.7</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.78</td>\n",
       "      <td>3.90</td>\n",
       "      <td>22.50</td>\n",
       "      <td>162000.0</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>1</td>\n",
       "      <td>47.53</td>\n",
       "      <td>41.38</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>148.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>93.7</td>\n",
       "      <td>157.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>50.6</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>2.97</td>\n",
       "      <td>3.23</td>\n",
       "      <td>9.40</td>\n",
       "      <td>68000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>14.59</td>\n",
       "      <td>136.33</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>148.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>93.7</td>\n",
       "      <td>157.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>50.6</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.05</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>2.97</td>\n",
       "      <td>3.23</td>\n",
       "      <td>9.40</td>\n",
       "      <td>68000.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>4.07</td>\n",
       "      <td>488.77</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>110.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>4</td>\n",
       "      <td>wagon</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>103.3</td>\n",
       "      <td>174.6</td>\n",
       "      <td>64.6</td>\n",
       "      <td>59.8</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>11.47</td>\n",
       "      <td>2bbl</td>\n",
       "      <td>3.34</td>\n",
       "      <td>3.46</td>\n",
       "      <td>8.50</td>\n",
       "      <td>88000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>-1</td>\n",
       "      <td>76.69</td>\n",
       "      <td>33.05</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>118.0</td>\n",
       "      <td>dodge</td>\n",
       "      <td>gas</td>\n",
       "      <td>turbo</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>95.9</td>\n",
       "      <td>173.2</td>\n",
       "      <td>66.3</td>\n",
       "      <td>50.2</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>22.65</td>\n",
       "      <td>mfi</td>\n",
       "      <td>3.60</td>\n",
       "      <td>3.90</td>\n",
       "      <td>7.00</td>\n",
       "      <td>145000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>3</td>\n",
       "      <td>24.17</td>\n",
       "      <td>116.32</td>\n",
       "      <td>12964.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>137.0</td>\n",
       "      <td>honda</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>86.6</td>\n",
       "      <td>144.6</td>\n",
       "      <td>63.9</td>\n",
       "      <td>50.8</td>\n",
       "      <td>ohc</td>\n",
       "      <td>4</td>\n",
       "      <td>6.30</td>\n",
       "      <td>1bbl</td>\n",
       "      <td>2.91</td>\n",
       "      <td>3.41</td>\n",
       "      <td>9.60</td>\n",
       "      <td>58000.0</td>\n",
       "      <td>4800.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>2</td>\n",
       "      <td>51.27</td>\n",
       "      <td>33.41</td>\n",
       "      <td>6479.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    normalized-losses       make fuel-type aspiration  num-of-doors  \\\n",
       "0               164.0       audi       gas        std             4   \n",
       "1               110.0       audi       gas        std             4   \n",
       "2               158.0       audi       gas        std             4   \n",
       "3               106.0       audi       gas      turbo             4   \n",
       "4               192.0        bmw       gas        std             2   \n",
       "5               194.0        bmw       gas        std             4   \n",
       "6               188.0        bmw       gas        std             2   \n",
       "7               150.0        bmw       gas        std             4   \n",
       "8               121.0  chevrolet       gas        std             2   \n",
       "9                98.0  chevrolet       gas        std             2   \n",
       "10               93.0  chevrolet       gas        std             4   \n",
       "11              231.0      dodge       gas        std             2   \n",
       "12              118.0      dodge       gas        std             2   \n",
       "13              118.0      dodge       gas      turbo             2   \n",
       "14              197.0      dodge       gas        std             4   \n",
       "15              148.0      dodge       gas        std             4   \n",
       "16              148.0      dodge       gas        std             4   \n",
       "17              110.0      dodge       gas        std             4   \n",
       "18              118.0      dodge       gas      turbo             2   \n",
       "19              137.0      honda       gas        std             2   \n",
       "\n",
       "   body-style drive-wheels engine-location  wheel-base  length  width  height  \\\n",
       "0       sedan          fwd           front        99.8   176.6   66.2    54.3   \n",
       "1       sedan          4wd           front        99.4   162.4   66.4    54.3   \n",
       "2       sedan          fwd           front       105.8   192.7   71.4    51.6   \n",
       "3       sedan          fwd           front        86.6   158.7   67.7    55.9   \n",
       "4       sedan          rwd           front       101.2   176.8   64.8    54.3   \n",
       "5       sedan          rwd           front       110.0   190.9   71.4    58.7   \n",
       "6       sedan          rwd           front       101.2   176.8   64.8    54.3   \n",
       "7       sedan          rwd           front       101.2   176.8   64.8    56.1   \n",
       "8   hatchback          fwd           front        88.4   141.1   60.3    53.2   \n",
       "9   hatchback          fwd           front       104.3   155.9   68.3    52.0   \n",
       "10      sedan          fwd           front        94.5   158.8   63.6    52.0   \n",
       "11  hatchback          fwd           front       113.0   199.6   71.4    59.1   \n",
       "12  hatchback          fwd           front        93.7   174.6   63.8    49.4   \n",
       "13  hatchback          fwd           front        93.7   157.3   63.8    50.8   \n",
       "14  hatchback          fwd           front       110.0   192.7   71.4    58.7   \n",
       "15      sedan          fwd           front        93.7   157.3   63.8    50.6   \n",
       "16      sedan          fwd           front        93.7   157.3   63.8    50.6   \n",
       "17      wagon          fwd           front       103.3   174.6   64.6    59.8   \n",
       "18  hatchback          fwd           front        95.9   173.2   66.3    50.2   \n",
       "19  hatchback          fwd           front        86.6   144.6   63.9    50.8   \n",
       "\n",
       "   engine-type  num-of-cylinders  engine-size fuel-system  bore  stroke  \\\n",
       "0          ohc                 4         8.85        mpfi  3.19    3.40   \n",
       "1          ohc                 5        15.18        mpfi  3.19    3.40   \n",
       "2          ohc                 5        15.18        mpfi  3.94    2.80   \n",
       "3          ohc                 5        13.74        mpfi  3.13    3.50   \n",
       "4          ohc                 4         8.67        mpfi  3.50    2.80   \n",
       "5          ohc                 4         8.67        mpfi  3.78    3.90   \n",
       "6          ohc                 6        26.58        mpfi  3.31    3.19   \n",
       "7          ohc                 6        26.58        mpfi  3.03    3.19   \n",
       "8            l                 3         3.39        2bbl  3.03    3.03   \n",
       "9          ohc                 4         6.05        2bbl  3.31    3.47   \n",
       "10         ohc                 4         6.05        2bbl  3.03    3.11   \n",
       "11         ohc                 4         6.05        2bbl  3.78    4.17   \n",
       "12         ohc                 4         6.05        2bbl  2.97    3.23   \n",
       "13         ohc                 4         7.10        mpfi  3.03    3.39   \n",
       "14         ohc                 4         6.05        2bbl  3.78    3.90   \n",
       "15         ohc                 4         6.05        2bbl  2.97    3.23   \n",
       "16         ohc                 4         6.05        2bbl  2.97    3.23   \n",
       "17         ohc                 4        11.47        2bbl  3.34    3.46   \n",
       "18         ohc                 4        22.65         mfi  3.60    3.90   \n",
       "19         ohc                 4         6.30        1bbl  2.91    3.41   \n",
       "\n",
       "    compression-ratio  engine-power  peak-rpm  city-mpg  highway-mpg  \\\n",
       "0               10.00      102000.0    5500.0      24.0         30.0   \n",
       "1                8.00      115000.0    5500.0      18.0         22.0   \n",
       "2                8.50       70000.0    4400.0      28.0         30.0   \n",
       "3                7.80      140000.0    5600.0      32.0         20.0   \n",
       "4                8.80      101000.0    5800.0      23.0         29.0   \n",
       "5               22.50      101000.0    6000.0      47.0         53.0   \n",
       "6                9.00      121000.0    4250.0      21.0         28.0   \n",
       "7                8.00      134000.0    4400.0      28.0         37.0   \n",
       "8                9.50       48000.0    5300.0      47.0         53.0   \n",
       "9                7.80       70000.0    5000.0      34.0         34.0   \n",
       "10               9.60       70000.0    5400.0      38.0         43.0   \n",
       "11               9.41      176000.0    6600.0      49.0         54.0   \n",
       "12              21.50       68000.0    5500.0      31.0         38.0   \n",
       "13               7.60      102000.0    5500.0      24.0         30.0   \n",
       "14              22.50      162000.0    6000.0      47.0         53.0   \n",
       "15               9.40       68000.0    5500.0      31.0         38.0   \n",
       "16               9.40       68000.0    5500.0      31.0         38.0   \n",
       "17               8.50       88000.0    5000.0      24.0         30.0   \n",
       "18               7.00      145000.0    5000.0      19.0         24.0   \n",
       "19               9.60       58000.0    4800.0      49.0         54.0   \n",
       "\n",
       "    symboling  mean-effective-pressure   torque    price  \n",
       "0           2                    40.52    57.68  13950.0  \n",
       "1           2                    47.39    59.59  17450.0  \n",
       "2           1                     0.85  3344.79  17710.0  \n",
       "3           1                    44.74    68.97  23875.0  \n",
       "4           2                    44.78    53.48  16430.0  \n",
       "5           0                     1.80  1330.28  16925.0  \n",
       "6           0                     7.19   377.06  20970.0  \n",
       "7           0                    57.37    48.20  21105.0  \n",
       "8           2                    59.33    25.08   5151.0  \n",
       "9           1                    51.55    36.35   6295.0  \n",
       "10          0                    65.57    29.11   6575.0  \n",
       "11          1                    93.12    20.15   5572.0  \n",
       "12          1                    12.28   152.80   6377.0  \n",
       "13          1                    28.80    73.88   7957.0  \n",
       "14          1                    47.53    41.38   6229.0  \n",
       "15          1                    14.59   136.33   6692.0  \n",
       "16          1                     4.07   488.77   7609.0  \n",
       "17         -1                    76.69    33.05   8921.0  \n",
       "18          3                    24.17   116.32  12964.0  \n",
       "19          2                    51.27    33.41   6479.0  "
      ]
     },
     "execution_count": 346,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the dataset \n",
    "data_path3 = os.path.join(os.getcwd(), 'datasets', 'train_auto_full.csv')\n",
    "auto_full = pd.read_csv(data_path3, delimiter = ',')\n",
    "\n",
    "print(\"Number of attributes: {}\".format(auto_full.shape[1]))\n",
    "print(\"Number of samples: {}\".format(auto_full.shape[0]))\n",
    "auto_full.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.11 ==========\n",
    "This dataset contains a mixture of numeric and nominal attributes. Name the variables that you think are categorical. Why can we not use the nominal attributes in their current form for the purposes of regression? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The attributes: make, fuel-type, aspiration, num-of-doors, body-style, drive-wheels, engine-location, engine-type, num-of-cylinders, and fuel-system are all categorical.\n",
    "\n",
    "In order to perform linear regression, you need to have numbers in order to see how much an attribute contributes to the output. So with categorical attributes, you could assign each category a number but that doesn't help us because the number has to mean something in order to contribute to the output. For example, if you're prediciting CPU Performance and you have the categorical attribute of manufacturer, where {1:Intel, 4:Motorola}. Let's say the weight vecotr for this attribute is .5, Intel would contribute .5 to the prediction and Motorola would contribute 2. This is saying that Motorola is 4 times faster than Intel. This is not what we want!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.12 ==========\n",
    "Now we want to convert the categorical variables by using [One-Hot-Encoding](http://scikit-learn.org/0.17/modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder). Familiriase yourself with the class. One limitation with this module is that it can deal only with categorical attributes in integer format (remember that in our example we have attributes in string format). \n",
    "\n",
    "Copy the `auto_full` dataframe into a new dataframe `auto_full_edit` and transform the categorical variables by using [Label Encoding](http://scikit-learn.org/0.17/modules/generated/sklearn.preprocessing.LabelEncoder.html). Then transform again the categorical variables by using One-Hot-Encoding. Make sure you don't transform the continuous variables. *Hint: make appropriate use of the `categorical_features` parameter in [`OneHotEncoder`](http://scikit-learn.org/0.17/modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder).*\n",
    "\n",
    "Store the transformed attributes into a numpy array `X_enc` and display its dimensionality.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(159, 51)"
      ]
     },
     "execution_count": 392,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto_full_edit = auto_full.copy(deep=True)\n",
    "target = auto_full_edit['price']\n",
    "auto_full_edit = auto_full_edit.drop(['price'], axis=1) # DROP TARGET\n",
    "\n",
    "# Transform Variables using Label Encoding\n",
    "le_dict = dict() # Initialise an empty dictionary to keep all LabelEncoders\n",
    "\n",
    "# Loop over attributes by excluding the ones that are continuous and the target variable\n",
    "auto_full_droppped = auto_full_edit.drop(['normalized-losses','num-of-doors','wheel-base','length','width','height'], axis=1)\n",
    "auto_full_droppped = auto_full_droppped.drop(['num-of-cylinders','engine-size','bore','stroke','compression-ratio','engine-power'], axis=1)\n",
    "auto_full_droppped = auto_full_droppped.drop(['peak-rpm','city-mpg','highway-mpg','mean-effective-pressure','torque'], axis=1)\n",
    "\n",
    "for column in auto_full_droppped:  \n",
    "    le = LabelEncoder().fit(auto_full_edit[column]) # Initialise the LabelEncoder and fit\n",
    "    auto_full_edit[column] = le.transform(auto_full_edit[column]) # Transform data and save in credit_clean DataFrame\n",
    "    le_dict[column] = le # Store the LabelEncdoer in dictionary\n",
    "\n",
    "# Transform the categorical variables using One Hot Encoding\n",
    "feature_indices = [1,2,3,5,6,7]\n",
    "enc = OneHotEncoder(categorical_features=feature_indices)\n",
    "enc.fit(auto_full_edit)\n",
    "X_enc = enc.transform(auto_full_edit).toarray()\n",
    "X_enc.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.13 ==========\n",
    "By using the transformed data train a multivariate linear regression model and by using 5-fold cross-validation report the R^2, RMSE, MAE and CC metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.842\n",
      "Root Mean Squared Error (RMSE): 2670.201\n",
      "Mean Absolute Error (MAE): 1862.359\n",
      "Correlation Coefficient: 0.922\n"
     ]
    }
   ],
   "source": [
    "# KFold\n",
    "n = X_enc.shape[0]\n",
    "kf5 = KFold(n, n_folds=5, shuffle=True, random_state=0)\n",
    "\n",
    "# fit a model to the training data\n",
    "lm6 = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "y5_predict = cross_val_predict(lm6, X_enc, target, cv=kf5)\n",
    "\n",
    "# Report Errors\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2_score(target, y5_predict)))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(mean_squared_error(target, y5_predict)**.5))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mean_absolute_error(target, y5_predict)))\n",
    "print('Correlation Coefficient: {:.3f}'.format(np.corrcoef(target, y5_predict)[0,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.14 ==========\n",
    "How does this more complex model perform with respect to your best performing model from either question 2.3 or 2.8? List one advantage and one disadvantage of using the more complex model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This more complex model performs much better than my best performing in 2.8 by a lot. The R^2 value increased from 0.588 to 0.842 the CC increased from .769 to .922, the RMSE decreased from 3848.436 to 2670.201, and the MAE decreased from 2706.512 to 1862.359.\n",
    "\n",
    "An advantage of using the more complex model is obviously the higher accuracy of the resulting predictor, but one disadvantage is that it would be very hard to add new features to the dataset, or play with the accuracy with and without certain labels because creating the predictor is very catered to the layout of the dataset. For example, adding a new attribute in column 0 would throw off the categorical indices in the One Hot Encoder and you'd have to determine if it needs to be dropped from the Label Encoding dataframe and added to the categorical indices. This is a lot of work, especially if you have a large, changing dataset!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ========== Question 2.15 ==========\n",
    "Finally, experiment with tree-based regressors (e.g. [`DecisionTreeRegressor`](http://scikit-learn.org/0.17/modules/generated/sklearn.tree.DecisionTreeRegressor.html), [`RandomForestRegressor`](http://scikit-learn.org/0.17/modules/generated/sklearn.ensemble.RandomForestRegressor.html)) and report 5-fold cross-validation scores for R^2, RMSE, MAE and CC. Has your performance improved? Explain your answer in 1-2 sentences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of Determination: 0.782\n",
      "Root Mean Squared Error (RMSE): 3142.866\n",
      "Mean Absolute Error (MAE): 2128.484\n",
      "Correlation Coefficient: 0.892\n"
     ]
    }
   ],
   "source": [
    "dt = DecisionTreeRegressor()\n",
    "y6_predict = cross_val_predict(dt, X_enc, target, cv=kf5)\n",
    "\n",
    "# Report Errors\n",
    "print('Coefficient of Determination: {:.3f}'.format(r2_score(target, y6_predict)))\n",
    "print('Root Mean Squared Error (RMSE): {:.3f}'.format(mean_squared_error(target, y6_predict)**.5))\n",
    "print('Mean Absolute Error (MAE): {:.3f}'.format(mean_absolute_error(target, y6_predict)))\n",
    "print('Correlation Coefficient: {:.3f}'.format(np.corrcoef(target, y6_predict)[0,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance did not improve compared to the Linear Regression Model in 2.13 as seen by a lower R^2 & CC, and a higher RMSE & MAE. However, the Decision Tree Regressor did perform better than the Linear Regression Model in 2.8, which was the data without the categorical values. This is as expected because Linear Regression (when done correctly) is often times a better predictor than a Decision Tree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>\n",
    "Good, although I'm not sure I agree with your unsupported statement that \"Linear Regression (when done correctly) is often times a better predictor than a Decision Tree\". This will very much depend on the nature of the dataset!\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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