regression_multiple.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Source Code: Multiple Variables Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Scikit-Learn version 0.18.1\n"
     ]
    }
   ],
   "source": [
    "# Import libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import sklearn\n",
    "\n",
    "# Success\n",
    "print('Using Scikit-Learn version', sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the Data\n",
    "data_train = pd.read_csv('data/reg2_data.csv')\n",
    "data_test = pd.read_csv('data/reg2_check.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting Dataset into Training and Testing Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Split the Data into Training and Testing Sets\n",
    "target_fields = ['TGT0','TGT1','TGT2','TGT3']\n",
    "features_train, targets_train = data_train.drop(target_fields, axis=1), data_train[target_fields]\n",
    "features_test, targets_test = data_test.drop(target_fields, axis=1), data_test[target_fields]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Value00</th>\n",
       "      <th>Value01</th>\n",
       "      <th>Value02</th>\n",
       "      <th>Value03</th>\n",
       "      <th>Value04</th>\n",
       "      <th>Value05</th>\n",
       "      <th>Value06</th>\n",
       "      <th>Value07</th>\n",
       "      <th>Value08</th>\n",
       "      <th>Value09</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.24</td>\n",
       "      <td>-0.87</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.34</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>2.35</td>\n",
       "      <td>1.34</td>\n",
       "      <td>-1.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.34</td>\n",
       "      <td>1.14</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>0.24</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>0.30</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>-0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.06</td>\n",
       "      <td>0.41</td>\n",
       "      <td>2.21</td>\n",
       "      <td>-0.88</td>\n",
       "      <td>-0.35</td>\n",
       "      <td>-0.33</td>\n",
       "      <td>0.01</td>\n",
       "      <td>1.21</td>\n",
       "      <td>-1.43</td>\n",
       "      <td>-0.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.00</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>1.37</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>1.03</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>-1.22</td>\n",
       "      <td>-0.60</td>\n",
       "      <td>1.55</td>\n",
       "      <td>1.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-1.06</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.73</td>\n",
       "      <td>1.11</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.31</td>\n",
       "      <td>-1.18</td>\n",
       "      <td>0.61</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>-1.32</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-0.65</td>\n",
       "      <td>-1.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.48</td>\n",
       "      <td>0.62</td>\n",
       "      <td>-1.01</td>\n",
       "      <td>-0.97</td>\n",
       "      <td>0.41</td>\n",
       "      <td>-1.69</td>\n",
       "      <td>-1.67</td>\n",
       "      <td>-0.69</td>\n",
       "      <td>1.43</td>\n",
       "      <td>0.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.64</td>\n",
       "      <td>-0.69</td>\n",
       "      <td>1.71</td>\n",
       "      <td>0.71</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-0.59</td>\n",
       "      <td>-1.02</td>\n",
       "      <td>0.70</td>\n",
       "      <td>-0.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.14</td>\n",
       "      <td>-1.35</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-1.45</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>0.51</td>\n",
       "      <td>-0.33</td>\n",
       "      <td>-0.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>1.67</td>\n",
       "      <td>-2.12</td>\n",
       "      <td>-0.72</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>1.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.28</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-1.05</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>-0.70</td>\n",
       "      <td>-1.25</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0.34</td>\n",
       "      <td>0.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.36</td>\n",
       "      <td>-1.17</td>\n",
       "      <td>1.30</td>\n",
       "      <td>0.70</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.93</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-1.22</td>\n",
       "      <td>-0.92</td>\n",
       "      <td>0.40</td>\n",
       "      <td>-0.42</td>\n",
       "      <td>0.50</td>\n",
       "      <td>-1.77</td>\n",
       "      <td>0.25</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>-0.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.22</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.10</td>\n",
       "      <td>1.33</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.66</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2.23</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-1.79</td>\n",
       "      <td>0.36</td>\n",
       "      <td>1.12</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>-0.26</td>\n",
       "      <td>0.85</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.91</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.26</td>\n",
       "      <td>-2.03</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.54</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.52</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.59</td>\n",
       "      <td>2.88</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>-0.65</td>\n",
       "      <td>0.24</td>\n",
       "      <td>-1.03</td>\n",
       "      <td>-0.78</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.48</td>\n",
       "      <td>-0.96</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>-1.85</td>\n",
       "      <td>-0.79</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-0.86</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.69</td>\n",
       "      <td>-0.97</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-2.08</td>\n",
       "      <td>1.37</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-1.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-1.04</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.72</td>\n",
       "      <td>-0.78</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.42</td>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>-0.92</td>\n",
       "      <td>1.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.79</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.78</td>\n",
       "      <td>0.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.61</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>-0.60</td>\n",
       "      <td>1.10</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-1.11</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>1.57</td>\n",
       "      <td>2.03</td>\n",
       "      <td>-2.24</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.57</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.46</td>\n",
       "      <td>1.05</td>\n",
       "      <td>-1.17</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>-0.94</td>\n",
       "      <td>1.20</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>-1.64</td>\n",
       "      <td>2.63</td>\n",
       "      <td>-0.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>-1.21</td>\n",
       "      <td>-0.79</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-1.40</td>\n",
       "      <td>2.38</td>\n",
       "      <td>1.14</td>\n",
       "      <td>-0.42</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>0.76</td>\n",
       "      <td>-2.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-1.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.69</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>0.43</td>\n",
       "      <td>-0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.49</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>-1.08</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.38</td>\n",
       "      <td>1.23</td>\n",
       "      <td>0.82</td>\n",
       "      <td>-0.70</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1.33</td>\n",
       "      <td>-1.53</td>\n",
       "      <td>-1.28</td>\n",
       "      <td>-0.79</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-1.39</td>\n",
       "      <td>1.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-1.46</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.84</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.37</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-3.02</td>\n",
       "      <td>-2.30</td>\n",
       "      <td>-0.42</td>\n",
       "      <td>1.13</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.17</td>\n",
       "      <td>1.99</td>\n",
       "      <td>0.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>970</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1.12</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>-1.42</td>\n",
       "      <td>-0.85</td>\n",
       "      <td>-1.52</td>\n",
       "      <td>-0.98</td>\n",
       "      <td>-1.36</td>\n",
       "      <td>-0.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>971</th>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>0.51</td>\n",
       "      <td>-1.41</td>\n",
       "      <td>-2.16</td>\n",
       "      <td>-0.86</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>-1.17</td>\n",
       "      <td>-1.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>972</th>\n",
       "      <td>-1.02</td>\n",
       "      <td>-1.66</td>\n",
       "      <td>0.39</td>\n",
       "      <td>-1.70</td>\n",
       "      <td>-2.26</td>\n",
       "      <td>-1.47</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.65</td>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>973</th>\n",
       "      <td>-0.37</td>\n",
       "      <td>-1.71</td>\n",
       "      <td>-1.35</td>\n",
       "      <td>-1.14</td>\n",
       "      <td>1.05</td>\n",
       "      <td>-1.69</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>-1.66</td>\n",
       "      <td>-1.34</td>\n",
       "      <td>-0.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>974</th>\n",
       "      <td>0.57</td>\n",
       "      <td>-1.54</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>0.54</td>\n",
       "      <td>1.63</td>\n",
       "      <td>-2.37</td>\n",
       "      <td>-0.79</td>\n",
       "      <td>-0.26</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>975</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>1.82</td>\n",
       "      <td>0.57</td>\n",
       "      <td>-1.51</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.83</td>\n",
       "      <td>0.31</td>\n",
       "      <td>1.64</td>\n",
       "      <td>-1.33</td>\n",
       "      <td>-0.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>976</th>\n",
       "      <td>1.80</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.09</td>\n",
       "      <td>1.31</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.19</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.18</td>\n",
       "      <td>1.04</td>\n",
       "      <td>-0.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>977</th>\n",
       "      <td>0.27</td>\n",
       "      <td>1.40</td>\n",
       "      <td>0.88</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.37</td>\n",
       "      <td>2.12</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.76</td>\n",
       "      <td>-0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>978</th>\n",
       "      <td>0.42</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>0.50</td>\n",
       "      <td>-1.20</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.69</td>\n",
       "      <td>2.68</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>1.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>979</th>\n",
       "      <td>-0.61</td>\n",
       "      <td>1.93</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>-0.73</td>\n",
       "      <td>0.63</td>\n",
       "      <td>1.24</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.94</td>\n",
       "      <td>-1.02</td>\n",
       "      <td>1.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>980</th>\n",
       "      <td>-0.84</td>\n",
       "      <td>-0.40</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>-1.30</td>\n",
       "      <td>-2.31</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>-1.54</td>\n",
       "      <td>0.80</td>\n",
       "      <td>-0.89</td>\n",
       "      <td>-0.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>981</th>\n",
       "      <td>0.53</td>\n",
       "      <td>-1.35</td>\n",
       "      <td>1.32</td>\n",
       "      <td>-2.37</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.87</td>\n",
       "      <td>0.83</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-1.68</td>\n",
       "      <td>-1.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>982</th>\n",
       "      <td>-1.38</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>-1.00</td>\n",
       "      <td>-2.64</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>-1.17</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.43</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>1.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>983</th>\n",
       "      <td>-1.22</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>-1.10</td>\n",
       "      <td>-2.72</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.65</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>1.40</td>\n",
       "      <td>0.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>984</th>\n",
       "      <td>-0.78</td>\n",
       "      <td>-1.04</td>\n",
       "      <td>0.57</td>\n",
       "      <td>-1.62</td>\n",
       "      <td>1.90</td>\n",
       "      <td>-2.31</td>\n",
       "      <td>-0.19</td>\n",
       "      <td>-2.26</td>\n",
       "      <td>0.38</td>\n",
       "      <td>1.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>985</th>\n",
       "      <td>-0.44</td>\n",
       "      <td>1.33</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-0.59</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>0.02</td>\n",
       "      <td>2.34</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>1.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>986</th>\n",
       "      <td>0.24</td>\n",
       "      <td>-1.32</td>\n",
       "      <td>-0.42</td>\n",
       "      <td>1.04</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>0.73</td>\n",
       "      <td>2.03</td>\n",
       "      <td>1.23</td>\n",
       "      <td>1.37</td>\n",
       "      <td>1.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>987</th>\n",
       "      <td>1.70</td>\n",
       "      <td>1.83</td>\n",
       "      <td>1.43</td>\n",
       "      <td>-0.97</td>\n",
       "      <td>2.49</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.47</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>988</th>\n",
       "      <td>1.48</td>\n",
       "      <td>-0.78</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.93</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>-1.88</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-1.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>989</th>\n",
       "      <td>1.09</td>\n",
       "      <td>2.13</td>\n",
       "      <td>-1.21</td>\n",
       "      <td>-1.44</td>\n",
       "      <td>-0.79</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.23</td>\n",
       "      <td>1.27</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>990</th>\n",
       "      <td>0.82</td>\n",
       "      <td>-1.55</td>\n",
       "      <td>1.14</td>\n",
       "      <td>1.68</td>\n",
       "      <td>-1.53</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>-1.20</td>\n",
       "      <td>-1.07</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>-0.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>0.28</td>\n",
       "      <td>1.73</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.50</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>0.94</td>\n",
       "      <td>2.33</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.07</td>\n",
       "      <td>-0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>992</th>\n",
       "      <td>-0.79</td>\n",
       "      <td>-1.66</td>\n",
       "      <td>1.20</td>\n",
       "      <td>-0.66</td>\n",
       "      <td>-1.59</td>\n",
       "      <td>-2.57</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>993</th>\n",
       "      <td>-0.80</td>\n",
       "      <td>-1.04</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>-1.76</td>\n",
       "      <td>0.53</td>\n",
       "      <td>-0.34</td>\n",
       "      <td>1.17</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>-0.88</td>\n",
       "      <td>-1.46</td>\n",
       "      <td>-0.69</td>\n",
       "      <td>0.75</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>-1.14</td>\n",
       "      <td>1.38</td>\n",
       "      <td>-1.82</td>\n",
       "      <td>-2.06</td>\n",
       "      <td>-1.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>1.95</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.88</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-1.37</td>\n",
       "      <td>0.71</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>2.45</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>-1.50</td>\n",
       "      <td>1.77</td>\n",
       "      <td>1.26</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.38</td>\n",
       "      <td>2.53</td>\n",
       "      <td>1.32</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>-0.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>-0.28</td>\n",
       "      <td>-2.58</td>\n",
       "      <td>0.23</td>\n",
       "      <td>2.10</td>\n",
       "      <td>-1.13</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>-1.24</td>\n",
       "      <td>0.68</td>\n",
       "      <td>-1.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>1.66</td>\n",
       "      <td>0.42</td>\n",
       "      <td>1.45</td>\n",
       "      <td>0.34</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>-0.85</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.88</td>\n",
       "      <td>2.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.18</td>\n",
       "      <td>2.06</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>-0.76</td>\n",
       "      <td>0.48</td>\n",
       "      <td>1.44</td>\n",
       "      <td>1.20</td>\n",
       "      <td>0.90</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Value00  Value01  Value02  Value03  Value04  Value05  Value06  Value07  \\\n",
       "0       1.24    -0.87    -0.53    -0.34    -0.25    -0.58    -0.62     2.35   \n",
       "1      -0.34     1.14    -0.53     0.24    -0.47     0.97    -1.46     0.30   \n",
       "2       0.06     0.41     2.21    -0.88    -0.35    -0.33     0.01     1.21   \n",
       "3      -1.00    -0.30     1.37    -0.09     1.03    -0.07    -1.22    -0.60   \n",
       "4      -0.30     0.91     0.01    -1.06     0.79     0.73     1.11    -0.13   \n",
       "5      -0.31    -1.18     0.61    -0.06    -0.15    -1.32     0.00     0.15   \n",
       "6       0.48     0.62    -1.01    -0.97     0.41    -1.69    -1.67    -0.69   \n",
       "7      -0.02    -0.64    -0.69     1.71     0.71    -0.45    -0.59    -1.02   \n",
       "8      -0.14    -1.35    -0.45    -1.45     0.32    -0.47    -0.96     0.51   \n",
       "9      -0.53    -0.24     1.67    -2.12    -0.72     0.20     0.36    -1.46   \n",
       "10     -0.28     0.13     0.17    -1.05    -0.48    -0.70    -1.25     0.17   \n",
       "11     -0.36    -1.17     1.30     0.70    -0.22     0.35     0.93     0.53   \n",
       "12     -1.22    -0.92     0.40    -0.42     0.50    -1.77     0.25    -0.47   \n",
       "13      0.22     0.47     0.50     0.10     1.33    -0.04    -0.66    -0.04   \n",
       "14      2.23     0.42    -1.79     0.36     1.12    -0.50    -0.26     0.85   \n",
       "15      0.12    -0.91    -0.30     0.26    -2.03     0.26     0.21    -0.54   \n",
       "16      1.52     0.11    -0.59     2.88    -0.76    -0.65     0.24    -1.03   \n",
       "17     -0.18     0.48    -0.96    -0.24    -0.36    -0.22    -1.85    -0.79   \n",
       "18     -0.86    -1.15     0.56     0.69    -0.97     0.04    -2.08     1.37   \n",
       "19     -1.04     0.25     0.72    -0.78     0.66    -0.42     0.35    -0.52   \n",
       "20      0.55    -0.76     0.64     0.86     0.65     0.79    -0.32     0.76   \n",
       "21     -0.14     0.61    -1.15    -0.60     1.10     0.98     0.03    -1.11   \n",
       "22     -0.06     0.97    -0.20     1.57     2.03    -2.24     0.53     0.57   \n",
       "23     -0.46     1.05    -1.17    -0.55    -0.94     1.20    -0.12    -1.64   \n",
       "24     -1.21    -0.79     0.46    -1.40     2.38     1.14    -0.42    -0.95   \n",
       "25     -1.80     0.00     0.67     0.69    -0.49     1.06    -0.20    -1.46   \n",
       "26      0.49    -0.36    -1.08     0.41     0.38     1.23     0.82    -0.70   \n",
       "27      1.33    -1.53    -1.28    -0.79    -0.71    -0.51    -0.76    -0.45   \n",
       "28     -1.46    -0.49    -0.18    -0.06    -0.67     0.66    -0.84     0.63   \n",
       "29      0.37     0.37    -3.02    -2.30    -0.42     1.13    -0.38     0.17   \n",
       "..       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "970     0.30     1.12    -0.77    -0.05    -1.42    -0.85    -1.52    -0.98   \n",
       "971     0.31    -0.25     0.51    -1.41    -2.16    -0.86     0.19    -0.81   \n",
       "972    -1.02    -1.66     0.39    -1.70    -2.26    -1.47     0.04     1.65   \n",
       "973    -0.37    -1.71    -1.35    -1.14     1.05    -1.69    -0.07    -1.66   \n",
       "974     0.57    -1.54    -0.29     0.54     1.63    -2.37    -0.79    -0.26   \n",
       "975    -0.06     1.82     0.57    -1.51     1.00     1.83     0.31     1.64   \n",
       "976     1.80    -0.03     0.09     1.31     0.01    -0.19     0.95     1.18   \n",
       "977     0.27     1.40     0.88    -0.10    -0.09     0.37     2.12     0.49   \n",
       "978     0.42     0.05    -0.74     0.50    -1.20     0.91     0.69     2.68   \n",
       "979    -0.61     1.93    -0.17    -0.73     0.63     1.24    -0.23     0.94   \n",
       "980    -0.84    -0.40    -0.09    -1.30    -2.31    -0.67    -1.54     0.80   \n",
       "981     0.53    -1.35     1.32    -2.37    -0.51    -0.87     0.83    -0.10   \n",
       "982    -1.38    -0.50    -1.00    -2.64    -0.68    -1.17    -0.12     0.43   \n",
       "983    -1.22    -1.46    -1.10    -2.72     0.02     0.09    -0.65    -0.48   \n",
       "984    -0.78    -1.04     0.57    -1.62     1.90    -2.31    -0.19    -2.26   \n",
       "985    -0.44     1.33    -0.18     0.06    -0.59    -0.32     0.02     2.34   \n",
       "986     0.24    -1.32    -0.42     1.04    -0.62     0.73     2.03     1.23   \n",
       "987     1.70     1.83     1.43    -0.97     2.49    -0.48     0.14     0.47   \n",
       "988     1.48    -0.78     0.26     1.00     0.93    -1.46    -1.88    -1.15   \n",
       "989     1.09     2.13    -1.21    -1.44    -0.79    -0.04     0.23     1.27   \n",
       "990     0.82    -1.55     1.14     1.68    -1.53    -0.61    -1.20    -1.07   \n",
       "991     0.28     1.73     0.72     0.50    -0.51     0.94     2.33     1.78   \n",
       "992    -0.79    -1.66     1.20    -0.66    -1.59    -2.57    -0.62    -0.62   \n",
       "993    -0.80    -1.04    -1.46    -1.76     0.53    -0.34     1.17    -1.15   \n",
       "994    -0.88    -1.46    -0.69     0.75    -0.62    -1.14     1.38    -1.82   \n",
       "995     1.95    -0.52     0.88    -0.47    -1.37     0.71    -0.48     2.45   \n",
       "996    -1.50     1.77     1.26    -0.06     0.70     0.38     2.53     1.32   \n",
       "997    -0.28    -2.58     0.23     2.10    -1.13     0.97    -0.74    -1.24   \n",
       "998     1.66     0.42     1.45     0.34    -0.21    -0.49    -0.85     0.25   \n",
       "999    -0.03     0.82     0.18     2.06    -0.07    -0.76     0.48     1.44   \n",
       "\n",
       "     Value08  Value09  \n",
       "0       1.34    -1.14  \n",
       "1      -0.81    -0.01  \n",
       "2      -1.43    -0.58  \n",
       "3       1.55     1.03  \n",
       "4       0.09    -0.37  \n",
       "5      -0.65    -1.84  \n",
       "6       1.43     0.86  \n",
       "7       0.70    -0.59  \n",
       "8      -0.33    -0.40  \n",
       "9      -0.51     1.99  \n",
       "10     -0.34     0.45  \n",
       "11      0.58     0.87  \n",
       "12     -0.20    -0.65  \n",
       "13      0.26     0.73  \n",
       "14      0.67     0.36  \n",
       "15     -0.12     0.35  \n",
       "16     -0.78     0.39  \n",
       "17     -0.01    -0.24  \n",
       "18     -0.03    -1.48  \n",
       "19     -0.92     1.75  \n",
       "20      0.78     0.59  \n",
       "21     -0.55     0.29  \n",
       "22     -0.04    -0.36  \n",
       "23      2.63    -0.58  \n",
       "24      0.76    -2.16  \n",
       "25      0.43    -0.01  \n",
       "26     -0.04     0.09  \n",
       "27     -1.39     1.16  \n",
       "28      0.20    -0.11  \n",
       "29      1.99     0.77  \n",
       "..       ...      ...  \n",
       "970    -1.36    -0.95  \n",
       "971    -1.17    -1.36  \n",
       "972     0.16    -0.99  \n",
       "973    -1.34    -0.16  \n",
       "974     0.13    -0.77  \n",
       "975    -1.33    -0.61  \n",
       "976     1.04    -0.29  \n",
       "977     0.76    -0.43  \n",
       "978    -0.20     1.35  \n",
       "979    -1.02     1.95  \n",
       "980    -0.89    -0.42  \n",
       "981    -1.68    -1.56  \n",
       "982    -0.49     1.30  \n",
       "983     1.40     0.17  \n",
       "984     0.38     1.18  \n",
       "985    -0.61     1.58  \n",
       "986     1.37     1.40  \n",
       "987    -0.09     0.36  \n",
       "988     0.10    -1.40  \n",
       "989     0.21     0.94  \n",
       "990    -0.12    -0.60  \n",
       "991     2.07    -0.14  \n",
       "992     0.34     0.44  \n",
       "993     0.14     0.06  \n",
       "994    -2.06    -1.29  \n",
       "995    -0.21     1.02  \n",
       "996    -0.17    -0.17  \n",
       "997     0.68    -1.18  \n",
       "998     0.88     2.01  \n",
       "999     1.20     0.90  \n",
       "\n",
       "[1000 rows x 10 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The training dataset dataset has 1000 data points with 14 variables each.\n",
      "The testing dataset dataset has 105 data points with 14 variables each.\n",
      "The dataset has 10 number of feature variables.\n",
      "The dataset has 4 number of target variables.\n"
     ]
    }
   ],
   "source": [
    "# Number of Features and Targets\n",
    "num_features = features_train.shape[1]\n",
    "num_targets = targets_train.shape[1]\n",
    "\n",
    "print(\"The training dataset dataset has {} data points with {} variables each.\".format(*data_train.shape))\n",
    "print(\"The testing dataset dataset has {} data points with {} variables each.\".format(*data_test.shape))\n",
    "print(\"The dataset has {} number of feature variables.\".format(num_features))\n",
    "print(\"The dataset has {} number of target variables.\".format(num_targets))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1000 entries, 0 to 999\n",
      "Data columns (total 14 columns):\n",
      "Value00    1000 non-null float64\n",
      "Value01    1000 non-null float64\n",
      "Value02    1000 non-null float64\n",
      "Value03    1000 non-null float64\n",
      "Value04    1000 non-null float64\n",
      "Value05    1000 non-null float64\n",
      "Value06    1000 non-null float64\n",
      "Value07    1000 non-null float64\n",
      "Value08    1000 non-null float64\n",
      "Value09    1000 non-null float64\n",
      "TGT0       1000 non-null float64\n",
      "TGT1       1000 non-null float64\n",
      "TGT2       1000 non-null float64\n",
      "TGT3       1000 non-null float64\n",
      "dtypes: float64(14)\n",
      "memory usage: 109.5 KB\n"
     ]
    }
   ],
   "source": [
    "# Row and column sizes: Training Data\n",
    "data_train.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Value00</th>\n",
       "      <th>Value01</th>\n",
       "      <th>Value02</th>\n",
       "      <th>Value03</th>\n",
       "      <th>Value04</th>\n",
       "      <th>Value05</th>\n",
       "      <th>Value06</th>\n",
       "      <th>Value07</th>\n",
       "      <th>Value08</th>\n",
       "      <th>Value09</th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.00000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.053770</td>\n",
       "      <td>-0.047270</td>\n",
       "      <td>0.021190</td>\n",
       "      <td>-0.019120</td>\n",
       "      <td>-0.038300</td>\n",
       "      <td>-0.046830</td>\n",
       "      <td>-0.033790</td>\n",
       "      <td>-0.016430</td>\n",
       "      <td>0.058730</td>\n",
       "      <td>-0.009080</td>\n",
       "      <td>87.47173</td>\n",
       "      <td>91.664730</td>\n",
       "      <td>94.518420</td>\n",
       "      <td>90.352870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.974953</td>\n",
       "      <td>0.990043</td>\n",
       "      <td>0.982625</td>\n",
       "      <td>1.016896</td>\n",
       "      <td>0.999852</td>\n",
       "      <td>1.008939</td>\n",
       "      <td>0.991402</td>\n",
       "      <td>1.005754</td>\n",
       "      <td>0.954923</td>\n",
       "      <td>0.946831</td>\n",
       "      <td>169.21764</td>\n",
       "      <td>143.648337</td>\n",
       "      <td>168.817263</td>\n",
       "      <td>196.360771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.760000</td>\n",
       "      <td>-2.840000</td>\n",
       "      <td>-3.020000</td>\n",
       "      <td>-2.810000</td>\n",
       "      <td>-3.740000</td>\n",
       "      <td>-3.070000</td>\n",
       "      <td>-2.840000</td>\n",
       "      <td>-3.120000</td>\n",
       "      <td>-3.390000</td>\n",
       "      <td>-2.990000</td>\n",
       "      <td>-355.86000</td>\n",
       "      <td>-368.270000</td>\n",
       "      <td>-436.150000</td>\n",
       "      <td>-564.110000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.730000</td>\n",
       "      <td>-0.710000</td>\n",
       "      <td>-0.622500</td>\n",
       "      <td>-0.760000</td>\n",
       "      <td>-0.680000</td>\n",
       "      <td>-0.720000</td>\n",
       "      <td>-0.712500</td>\n",
       "      <td>-0.762500</td>\n",
       "      <td>-0.552500</td>\n",
       "      <td>-0.652500</td>\n",
       "      <td>-27.26750</td>\n",
       "      <td>-9.247500</td>\n",
       "      <td>-16.052500</td>\n",
       "      <td>-33.852500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.060000</td>\n",
       "      <td>-0.080000</td>\n",
       "      <td>-0.005000</td>\n",
       "      <td>-0.020000</td>\n",
       "      <td>-0.030000</td>\n",
       "      <td>-0.030000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.050000</td>\n",
       "      <td>0.050000</td>\n",
       "      <td>-0.010000</td>\n",
       "      <td>86.16500</td>\n",
       "      <td>92.915000</td>\n",
       "      <td>86.595000</td>\n",
       "      <td>91.370000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.640000</td>\n",
       "      <td>0.690000</td>\n",
       "      <td>0.672500</td>\n",
       "      <td>0.630000</td>\n",
       "      <td>0.637500</td>\n",
       "      <td>0.620000</td>\n",
       "      <td>0.652500</td>\n",
       "      <td>0.670000</td>\n",
       "      <td>0.640000</td>\n",
       "      <td>198.67000</td>\n",
       "      <td>189.027500</td>\n",
       "      <td>213.725000</td>\n",
       "      <td>222.695000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.930000</td>\n",
       "      <td>2.660000</td>\n",
       "      <td>2.870000</td>\n",
       "      <td>3.210000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.430000</td>\n",
       "      <td>3.170000</td>\n",
       "      <td>3.800000</td>\n",
       "      <td>2.980000</td>\n",
       "      <td>3.090000</td>\n",
       "      <td>723.19000</td>\n",
       "      <td>585.310000</td>\n",
       "      <td>650.520000</td>\n",
       "      <td>705.460000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Value00      Value01      Value02      Value03      Value04  \\\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000  1000.000000   \n",
       "mean     -0.053770    -0.047270     0.021190    -0.019120    -0.038300   \n",
       "std       0.974953     0.990043     0.982625     1.016896     0.999852   \n",
       "min      -2.760000    -2.840000    -3.020000    -2.810000    -3.740000   \n",
       "25%      -0.730000    -0.710000    -0.622500    -0.760000    -0.680000   \n",
       "50%      -0.060000    -0.080000    -0.005000    -0.020000    -0.030000   \n",
       "75%       0.600000     0.640000     0.690000     0.672500     0.630000   \n",
       "max       2.930000     2.660000     2.870000     3.210000     3.310000   \n",
       "\n",
       "           Value05      Value06      Value07      Value08      Value09  \\\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000  1000.000000   \n",
       "mean     -0.046830    -0.033790    -0.016430     0.058730    -0.009080   \n",
       "std       1.008939     0.991402     1.005754     0.954923     0.946831   \n",
       "min      -3.070000    -2.840000    -3.120000    -3.390000    -2.990000   \n",
       "25%      -0.720000    -0.712500    -0.762500    -0.552500    -0.652500   \n",
       "50%      -0.030000     0.000000    -0.050000     0.050000    -0.010000   \n",
       "75%       0.637500     0.620000     0.652500     0.670000     0.640000   \n",
       "max       3.430000     3.170000     3.800000     2.980000     3.090000   \n",
       "\n",
       "             TGT0         TGT1         TGT2         TGT3  \n",
       "count  1000.00000  1000.000000  1000.000000  1000.000000  \n",
       "mean     87.47173    91.664730    94.518420    90.352870  \n",
       "std     169.21764   143.648337   168.817263   196.360771  \n",
       "min    -355.86000  -368.270000  -436.150000  -564.110000  \n",
       "25%     -27.26750    -9.247500   -16.052500   -33.852500  \n",
       "50%      86.16500    92.915000    86.595000    91.370000  \n",
       "75%     198.67000   189.027500   213.725000   222.695000  \n",
       "max     723.19000   585.310000   650.520000   705.460000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Mean, Stddev, Min, Max Values: Training Data\n",
    "datatrain_describe = data_train.describe()\n",
    "datatest_describe = data_test.describe()\n",
    "\n",
    "datatrain_describe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building Machine Learning Model\n",
    "\n",
    "## Analytical Linear Regression (Ordinary Least Squares)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Analytical Solution using Normal Equation\n",
    "def analytic_normal(features_train, features_test, targets_train):\n",
    "    \n",
    "    # Append Bias Term to Features Matrix\n",
    "    n_training_samples = features_train.shape[0]\n",
    "    n_dimensions = features_train.shape[1]\n",
    "    n_targets = targets_train.shape[1]\n",
    "    \n",
    "    # Features + Bias Matrix\n",
    "    X = np.reshape(np.c_[np.ones(n_training_samples),features_train],[n_training_samples,n_dimensions + 1])\n",
    "    \n",
    "    # Targets Matrix\n",
    "    Y = targets_train\n",
    "    \n",
    "    # Solve for Theta = (X(T).X)^(-1).X(T).Y\n",
    "    # Theta will include Bias + Weights Matrix\n",
    "    theta = np.dot(np.linalg.inv(np.matrix(np.dot(X.T, X))), np.dot(X.T, Y))\n",
    "    theta = np.array(np.reshape(theta,(-1,n_targets)))\n",
    "    \n",
    "    # Split Theta into Bias and Weights\n",
    "    bias = theta[0]\n",
    "    weights = theta[1:]\n",
    "    \n",
    "    # Predictions on Training and Testing Sets\n",
    "    pred_trn = np.dot(features_train, weights) + bias\n",
    "    pred_tst = np.dot(features_test, weights) + bias\n",
    "    \n",
    "    return bias, weights, pred_trn, pred_tst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Returning Solution to the Analytical Function\n",
    "bias, weights, pred_trn, pred_tst = analytic_normal(features_train, features_test, targets_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Value00</th>\n",
       "      <td>20.905332</td>\n",
       "      <td>41.552513</td>\n",
       "      <td>50.182144</td>\n",
       "      <td>82.005159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value01</th>\n",
       "      <td>88.158113</td>\n",
       "      <td>45.449590</td>\n",
       "      <td>62.034891</td>\n",
       "      <td>69.434200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value02</th>\n",
       "      <td>13.217732</td>\n",
       "      <td>43.906325</td>\n",
       "      <td>69.673260</td>\n",
       "      <td>63.395746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value03</th>\n",
       "      <td>9.643977</td>\n",
       "      <td>40.141460</td>\n",
       "      <td>52.256499</td>\n",
       "      <td>73.243410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value04</th>\n",
       "      <td>8.246295</td>\n",
       "      <td>33.614186</td>\n",
       "      <td>5.062020</td>\n",
       "      <td>14.806817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value05</th>\n",
       "      <td>75.144577</td>\n",
       "      <td>36.345816</td>\n",
       "      <td>5.585402</td>\n",
       "      <td>81.583236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value06</th>\n",
       "      <td>77.771108</td>\n",
       "      <td>50.226606</td>\n",
       "      <td>31.071148</td>\n",
       "      <td>13.283668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value07</th>\n",
       "      <td>65.365560</td>\n",
       "      <td>46.032369</td>\n",
       "      <td>98.183041</td>\n",
       "      <td>67.698966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value08</th>\n",
       "      <td>13.210945</td>\n",
       "      <td>35.044600</td>\n",
       "      <td>53.477449</td>\n",
       "      <td>79.023733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value09</th>\n",
       "      <td>74.468893</td>\n",
       "      <td>82.573827</td>\n",
       "      <td>49.184078</td>\n",
       "      <td>43.227789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bias</th>\n",
       "      <td>100.104347</td>\n",
       "      <td>100.019108</td>\n",
       "      <td>100.096213</td>\n",
       "      <td>99.801738</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TGT0        TGT1        TGT2       TGT3\n",
       "Value00   20.905332   41.552513   50.182144  82.005159\n",
       "Value01   88.158113   45.449590   62.034891  69.434200\n",
       "Value02   13.217732   43.906325   69.673260  63.395746\n",
       "Value03    9.643977   40.141460   52.256499  73.243410\n",
       "Value04    8.246295   33.614186    5.062020  14.806817\n",
       "Value05   75.144577   36.345816    5.585402  81.583236\n",
       "Value06   77.771108   50.226606   31.071148  13.283668\n",
       "Value07   65.365560   46.032369   98.183041  67.698966\n",
       "Value08   13.210945   35.044600   53.477449  79.023733\n",
       "Value09   74.468893   82.573827   49.184078  43.227789\n",
       "Bias     100.104347  100.019108  100.096213  99.801738"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for Linear Coefficients\n",
    "inhouse_lc = pd.DataFrame(weights)\n",
    "inhouse_lc.columns = ['TGT0', 'TGT1', 'TGT2', 'TGT3']\n",
    "inhouse_lc = inhouse_lc.set_index(features_train.columns)\n",
    "\n",
    "# Create Dataframe for Bias Value\n",
    "inhouse_bias = pd.DataFrame(bias)\n",
    "inhouse_bias.columns = ['Bias']\n",
    "inhouse_bias = inhouse_bias.set_index(targets_train.columns)\n",
    "\n",
    "# Merge Dataframe\n",
    "inhouse_result = pd.concat([inhouse_lc.T, inhouse_bias], axis=1, join_axes=[inhouse_lc.T.index])\n",
    "\n",
    "inhouse_result.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/andridsasmita/anaconda3/envs/tf3/lib/python3.5/site-packages/sklearn/metrics/regression.py:482: DeprecationWarning: Default 'multioutput' behavior now corresponds to 'variance_weighted' value which is deprecated since 0.17, it will be changed to 'uniform_average' starting from 0.19.\n",
      "  DeprecationWarning)\n",
      "/home/andridsasmita/anaconda3/envs/tf3/lib/python3.5/site-packages/sklearn/metrics/regression.py:482: DeprecationWarning: Default 'multioutput' behavior now corresponds to 'variance_weighted' value which is deprecated since 0.17, it will be changed to 'uniform_average' starting from 0.19.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R-Squared Accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               R-Squared Accuracy\n",
       "Training Data            0.999450\n",
       "Testing Data             0.999839"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for R-Squared Values\n",
    "from sklearn.metrics import r2_score\n",
    "rsquared = np.array([r2_score(targets_train, pred_trn),r2_score(targets_test, pred_tst)])\n",
    "rs_rows = np.array(['Training Data', 'Testing Data'])\n",
    "\n",
    "inhouse_rs = pd.DataFrame(rsquared)\n",
    "inhouse_rs.columns = ['R-Squared Accuracy']\n",
    "inhouse_rs = inhouse_rs.set_index(rs_rows)\n",
    "\n",
    "inhouse_rs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analytical Linear Regression (Ordinary Least Squares) Using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ML Linear Regression using Scikit-Learn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "LinReg = LinearRegression()\n",
    "LinReg.fit(features_train, targets_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Value00</th>\n",
       "      <td>20.905332</td>\n",
       "      <td>41.552513</td>\n",
       "      <td>50.182144</td>\n",
       "      <td>82.005159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value01</th>\n",
       "      <td>88.158113</td>\n",
       "      <td>45.449590</td>\n",
       "      <td>62.034891</td>\n",
       "      <td>69.434200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value02</th>\n",
       "      <td>13.217732</td>\n",
       "      <td>43.906325</td>\n",
       "      <td>69.673260</td>\n",
       "      <td>63.395746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value03</th>\n",
       "      <td>9.643977</td>\n",
       "      <td>40.141460</td>\n",
       "      <td>52.256499</td>\n",
       "      <td>73.243410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value04</th>\n",
       "      <td>8.246295</td>\n",
       "      <td>33.614186</td>\n",
       "      <td>5.062020</td>\n",
       "      <td>14.806817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value05</th>\n",
       "      <td>75.144577</td>\n",
       "      <td>36.345816</td>\n",
       "      <td>5.585402</td>\n",
       "      <td>81.583236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value06</th>\n",
       "      <td>77.771108</td>\n",
       "      <td>50.226606</td>\n",
       "      <td>31.071148</td>\n",
       "      <td>13.283668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value07</th>\n",
       "      <td>65.365560</td>\n",
       "      <td>46.032369</td>\n",
       "      <td>98.183041</td>\n",
       "      <td>67.698966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value08</th>\n",
       "      <td>13.210945</td>\n",
       "      <td>35.044600</td>\n",
       "      <td>53.477449</td>\n",
       "      <td>79.023733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value09</th>\n",
       "      <td>74.468893</td>\n",
       "      <td>82.573827</td>\n",
       "      <td>49.184078</td>\n",
       "      <td>43.227789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bias</th>\n",
       "      <td>100.104347</td>\n",
       "      <td>100.019108</td>\n",
       "      <td>100.096213</td>\n",
       "      <td>99.801738</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TGT0        TGT1        TGT2       TGT3\n",
       "Value00   20.905332   41.552513   50.182144  82.005159\n",
       "Value01   88.158113   45.449590   62.034891  69.434200\n",
       "Value02   13.217732   43.906325   69.673260  63.395746\n",
       "Value03    9.643977   40.141460   52.256499  73.243410\n",
       "Value04    8.246295   33.614186    5.062020  14.806817\n",
       "Value05   75.144577   36.345816    5.585402  81.583236\n",
       "Value06   77.771108   50.226606   31.071148  13.283668\n",
       "Value07   65.365560   46.032369   98.183041  67.698966\n",
       "Value08   13.210945   35.044600   53.477449  79.023733\n",
       "Value09   74.468893   82.573827   49.184078  43.227789\n",
       "Bias     100.104347  100.019108  100.096213  99.801738"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for Linear Coefficients\n",
    "sklearn_lc = pd.DataFrame(LinReg.coef_.T)\n",
    "sklearn_lc.columns = ['TGT0', 'TGT1', 'TGT2', 'TGT3']\n",
    "sklearn_lc = sklearn_lc.set_index(features_train.columns)\n",
    "\n",
    "# Create Dataframe for Bias Value\n",
    "sklearn_bias = pd.DataFrame(LinReg.intercept_)\n",
    "sklearn_bias.columns = ['Bias']\n",
    "sklearn_bias = sklearn_bias.set_index(targets_train.columns)\n",
    "\n",
    "# Merge Dataframe\n",
    "sklearn_result = pd.concat([sklearn_lc.T, sklearn_bias], axis=1, join_axes=[sklearn_lc.T.index])\n",
    "\n",
    "sklearn_result.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R-Squared Accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               R-Squared Accuracy\n",
       "Training Data            0.999450\n",
       "Testing Data             0.999839"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for R-Squared Values\n",
    "rsquared = np.array([LinReg.score(features_train,targets_train), LinReg.score(features_test,targets_test)])\n",
    "rs_rows = np.array(['Training Data', 'Testing Data'])\n",
    "\n",
    "sklearn_rs = pd.DataFrame(rsquared)\n",
    "sklearn_rs.columns = ['R-Squared Accuracy']\n",
    "sklearn_rs = sklearn_rs.set_index(rs_rows)\n",
    "\n",
    "sklearn_rs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Building Neural Network Model\n",
    "\n",
    "## Single-Layer Neural Network Using Google TensorFlow\n",
    "\n",
    "- Optimized Using Gradient Descent\n",
    "- No Hidden Layer\n",
    "- No Activation Function\n",
    "- Predictions is therefore Y = W.X + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Google TensorFlow version 1.0.0\n"
     ]
    }
   ],
   "source": [
    "# Import TF Library\n",
    "import tensorflow as tf\n",
    "print(\"Using Google TensorFlow version\", tf.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Build successful!\n"
     ]
    }
   ],
   "source": [
    "# Build NN Architecture\n",
    "def neural_network(learning_rate, epochs, features_train, targets_train, \\\n",
    "                   features_test, targets_test, size_in, size_out):\n",
    "\n",
    "    # Start TensorFlow Graph\n",
    "    tf.reset_default_graph()\n",
    "    sess = tf.Session()\n",
    "       \n",
    "    # Inputs\n",
    "    with tf.name_scope(\"Inputs\"):\n",
    "        x = tf.placeholder(tf.float32, shape=[None, size_in], name=\"features\")\n",
    "    \n",
    "    # Targets    \n",
    "    with tf.name_scope(\"Targets\"):\n",
    "        y = tf.placeholder(tf.float32, shape=[None, size_out], name=\"targets\")\n",
    "\n",
    "    # Single-Layer Dense Neural Network\n",
    "    with tf.name_scope(\"Dense\"):\n",
    "        w = tf.Variable(tf.ones([size_in, size_out]), name=\"weights\")\n",
    "        b = tf.Variable(tf.constant(1.0, shape=[size_out]), name=\"biases\")\n",
    "        y_ = tf.add(tf.matmul(x, w), b)\n",
    "        tf.summary.histogram(\"Weights\", w)\n",
    "        tf.summary.histogram(\"Biases\", b)\n",
    "        tf.summary.histogram(\"Predictions\", y_)\n",
    "\n",
    "    # Mean Squared Error (MSE) Cost Function\n",
    "    with tf.name_scope(\"MSE-Cost\"):\n",
    "        mse = tf.reduce_mean(tf.square(y_ - y), name=\"MSE\")\n",
    "        tf.summary.scalar(\"Mean_Squared_Error\", mse)\n",
    "\n",
    "    # Gradient Descent Optimizer\n",
    "    with tf.name_scope(\"Training\"):\n",
    "        train_step = tf.train.GradientDescentOptimizer(learning_rate).minimize(mse)\n",
    "\n",
    "    # R-Squared Accuracy Score\n",
    "    with tf.name_scope(\"R-Squared\"):\n",
    "        model_error = tf.reduce_sum(tf.square(tf.subtract(y, y_)))\n",
    "        average_error = tf.reduce_sum(tf.square(tf.subtract(y, tf.reduce_mean(y))))\n",
    "        # R-Squared Value\n",
    "        accuracy = tf.subtract(1.0, (tf.div(model_error, average_error)))\n",
    "        tf.summary.scalar(\"R_Squared_Value\", accuracy)\n",
    "\n",
    "    # Initialization\n",
    "    summ = tf.summary.merge_all()  \n",
    "    saver = tf.train.Saver()\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    writer = tf.summary.FileWriter('./logs/1/train')\n",
    "    writer.add_graph(sess.graph)\n",
    "    \n",
    "    # Training Set\n",
    "    for i in range(epochs):\n",
    "        if i % 10 == 0:\n",
    "            [train_accuracy, s] = sess.run([accuracy, summ], \\\n",
    "                        feed_dict={x: features_train, y: targets_train})\n",
    "            writer.add_summary(s, i)\n",
    "        sess.run(train_step, feed_dict={x: features_train, y: targets_train})\n",
    "    \n",
    "    # Results\n",
    "    slope = sess.run(w)\n",
    "    intercept = sess.run(b)\n",
    "    pred_train = sess.run(y_, feed_dict={x: features_train, y: targets_train})\n",
    "    pred_test = sess.run(y_, feed_dict={x: features_test, y: targets_test})\n",
    "\n",
    "    \n",
    "    return (slope, intercept, pred_train, pred_test)\n",
    "\n",
    "print('Build successful!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 0.01 learning rate on 5000 training epochs\n"
     ]
    }
   ],
   "source": [
    "# Setting up Hyperparameters\n",
    "learning_rate = 0.01\n",
    "epochs = 5000\n",
    "\n",
    "print('Using {} learning rate on {} training epochs'.format(learning_rate, epochs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Run Training\n",
    "(slope, intercept, pred_train, pred_test) = neural_network(learning_rate, epochs, \\\n",
    "        features_train, targets_train, features_test, targets_test, num_features, num_targets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": 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>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Value00</th>\n",
       "      <td>20.904984</td>\n",
       "      <td>41.551949</td>\n",
       "      <td>50.181709</td>\n",
       "      <td>82.004158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value01</th>\n",
       "      <td>88.157341</td>\n",
       "      <td>45.449181</td>\n",
       "      <td>62.034386</td>\n",
       "      <td>69.433388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value02</th>\n",
       "      <td>13.217596</td>\n",
       "      <td>43.905907</td>\n",
       "      <td>69.672462</td>\n",
       "      <td>63.395287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value03</th>\n",
       "      <td>9.644102</td>\n",
       "      <td>40.141880</td>\n",
       "      <td>52.256523</td>\n",
       "      <td>73.244209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value04</th>\n",
       "      <td>8.246093</td>\n",
       "      <td>33.613712</td>\n",
       "      <td>5.061895</td>\n",
       "      <td>14.806627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value05</th>\n",
       "      <td>75.143692</td>\n",
       "      <td>36.345295</td>\n",
       "      <td>5.585310</td>\n",
       "      <td>81.582352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value06</th>\n",
       "      <td>77.770287</td>\n",
       "      <td>50.226204</td>\n",
       "      <td>31.070923</td>\n",
       "      <td>13.283564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value07</th>\n",
       "      <td>65.365891</td>\n",
       "      <td>46.032795</td>\n",
       "      <td>98.182350</td>\n",
       "      <td>67.699799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value08</th>\n",
       "      <td>13.211051</td>\n",
       "      <td>35.044247</td>\n",
       "      <td>53.477032</td>\n",
       "      <td>79.022911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value09</th>\n",
       "      <td>74.467979</td>\n",
       "      <td>82.572884</td>\n",
       "      <td>49.183640</td>\n",
       "      <td>43.227200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bias</th>\n",
       "      <td>100.103455</td>\n",
       "      <td>100.018280</td>\n",
       "      <td>100.095413</td>\n",
       "      <td>99.800919</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TGT0        TGT1        TGT2       TGT3\n",
       "Value00   20.904984   41.551949   50.181709  82.004158\n",
       "Value01   88.157341   45.449181   62.034386  69.433388\n",
       "Value02   13.217596   43.905907   69.672462  63.395287\n",
       "Value03    9.644102   40.141880   52.256523  73.244209\n",
       "Value04    8.246093   33.613712    5.061895  14.806627\n",
       "Value05   75.143692   36.345295    5.585310  81.582352\n",
       "Value06   77.770287   50.226204   31.070923  13.283564\n",
       "Value07   65.365891   46.032795   98.182350  67.699799\n",
       "Value08   13.211051   35.044247   53.477032  79.022911\n",
       "Value09   74.467979   82.572884   49.183640  43.227200\n",
       "Bias     100.103455  100.018280  100.095413  99.800919"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for Linear Coefficients\n",
    "tensorflow_lc = pd.DataFrame(slope)\n",
    "tensorflow_lc.columns = ['TGT0', 'TGT1', 'TGT2', 'TGT3']\n",
    "tensorflow_lc = tensorflow_lc.set_index(features_train.columns)\n",
    "\n",
    "# Create Dataframe for Bias Value\n",
    "tensorflow_bias = pd.DataFrame(intercept)\n",
    "tensorflow_bias.columns = ['Bias']\n",
    "tensorflow_bias = tensorflow_bias.set_index(targets_train.columns)\n",
    "\n",
    "# Merge Dataframe\n",
    "tensorflow_result = pd.concat([tensorflow_lc.T, tensorflow_bias], axis=1, join_axes=[tensorflow_lc.T.index])\n",
    "\n",
    "tensorflow_result.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/andridsasmita/anaconda3/envs/tf3/lib/python3.5/site-packages/sklearn/metrics/regression.py:482: DeprecationWarning: Default 'multioutput' behavior now corresponds to 'variance_weighted' value which is deprecated since 0.17, it will be changed to 'uniform_average' starting from 0.19.\n",
      "  DeprecationWarning)\n",
      "/home/andridsasmita/anaconda3/envs/tf3/lib/python3.5/site-packages/sklearn/metrics/regression.py:482: DeprecationWarning: Default 'multioutput' behavior now corresponds to 'variance_weighted' value which is deprecated since 0.17, it will be changed to 'uniform_average' starting from 0.19.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R-Squared Accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               R-Squared Accuracy\n",
       "Training Data            0.999450\n",
       "Testing Data             0.999839"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Dataframe for R-Squared Values\n",
    "tf_rsquared = np.array([r2_score(targets_train, pred_train), r2_score(targets_test, pred_test)])\n",
    "tf_rs_rows = np.array(['Training Data', 'Testing Data'])\n",
    "\n",
    "tensorflow_rs = pd.DataFrame(tf_rsquared)\n",
    "tensorflow_rs.columns = ['R-Squared Accuracy']\n",
    "tensorflow_rs = tensorflow_rs.set_index(tf_rs_rows)\n",
    "\n",
    "tensorflow_rs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Conclusion\n",
    "\n",
    "## Merging Dataframes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"4\" halign=\"left\">In-House</th>\n",
       "      <th colspan=\"4\" halign=\"left\">Scikit-Learn</th>\n",
       "      <th colspan=\"4\" halign=\"left\">TensorFlow</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "      <th>TGT0</th>\n",
       "      <th>TGT1</th>\n",
       "      <th>TGT2</th>\n",
       "      <th>TGT3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Value00</th>\n",
       "      <td>20.905332</td>\n",
       "      <td>41.552513</td>\n",
       "      <td>50.182144</td>\n",
       "      <td>82.005159</td>\n",
       "      <td>20.905332</td>\n",
       "      <td>41.552513</td>\n",
       "      <td>50.182144</td>\n",
       "      <td>82.005159</td>\n",
       "      <td>20.904984</td>\n",
       "      <td>41.551949</td>\n",
       "      <td>50.181709</td>\n",
       "      <td>82.004158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value01</th>\n",
       "      <td>88.158113</td>\n",
       "      <td>45.449590</td>\n",
       "      <td>62.034891</td>\n",
       "      <td>69.434200</td>\n",
       "      <td>88.158113</td>\n",
       "      <td>45.449590</td>\n",
       "      <td>62.034891</td>\n",
       "      <td>69.434200</td>\n",
       "      <td>88.157341</td>\n",
       "      <td>45.449181</td>\n",
       "      <td>62.034386</td>\n",
       "      <td>69.433388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value02</th>\n",
       "      <td>13.217732</td>\n",
       "      <td>43.906325</td>\n",
       "      <td>69.673260</td>\n",
       "      <td>63.395746</td>\n",
       "      <td>13.217732</td>\n",
       "      <td>43.906325</td>\n",
       "      <td>69.673260</td>\n",
       "      <td>63.395746</td>\n",
       "      <td>13.217596</td>\n",
       "      <td>43.905907</td>\n",
       "      <td>69.672462</td>\n",
       "      <td>63.395287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value03</th>\n",
       "      <td>9.643977</td>\n",
       "      <td>40.141460</td>\n",
       "      <td>52.256499</td>\n",
       "      <td>73.243410</td>\n",
       "      <td>9.643977</td>\n",
       "      <td>40.141460</td>\n",
       "      <td>52.256499</td>\n",
       "      <td>73.243410</td>\n",
       "      <td>9.644102</td>\n",
       "      <td>40.141880</td>\n",
       "      <td>52.256523</td>\n",
       "      <td>73.244209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value04</th>\n",
       "      <td>8.246295</td>\n",
       "      <td>33.614186</td>\n",
       "      <td>5.062020</td>\n",
       "      <td>14.806817</td>\n",
       "      <td>8.246295</td>\n",
       "      <td>33.614186</td>\n",
       "      <td>5.062020</td>\n",
       "      <td>14.806817</td>\n",
       "      <td>8.246093</td>\n",
       "      <td>33.613712</td>\n",
       "      <td>5.061895</td>\n",
       "      <td>14.806627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value05</th>\n",
       "      <td>75.144577</td>\n",
       "      <td>36.345816</td>\n",
       "      <td>5.585402</td>\n",
       "      <td>81.583236</td>\n",
       "      <td>75.144577</td>\n",
       "      <td>36.345816</td>\n",
       "      <td>5.585402</td>\n",
       "      <td>81.583236</td>\n",
       "      <td>75.143692</td>\n",
       "      <td>36.345295</td>\n",
       "      <td>5.585310</td>\n",
       "      <td>81.582352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value06</th>\n",
       "      <td>77.771108</td>\n",
       "      <td>50.226606</td>\n",
       "      <td>31.071148</td>\n",
       "      <td>13.283668</td>\n",
       "      <td>77.771108</td>\n",
       "      <td>50.226606</td>\n",
       "      <td>31.071148</td>\n",
       "      <td>13.283668</td>\n",
       "      <td>77.770287</td>\n",
       "      <td>50.226204</td>\n",
       "      <td>31.070923</td>\n",
       "      <td>13.283564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value07</th>\n",
       "      <td>65.365560</td>\n",
       "      <td>46.032369</td>\n",
       "      <td>98.183041</td>\n",
       "      <td>67.698966</td>\n",
       "      <td>65.365560</td>\n",
       "      <td>46.032369</td>\n",
       "      <td>98.183041</td>\n",
       "      <td>67.698966</td>\n",
       "      <td>65.365891</td>\n",
       "      <td>46.032795</td>\n",
       "      <td>98.182350</td>\n",
       "      <td>67.699799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value08</th>\n",
       "      <td>13.210945</td>\n",
       "      <td>35.044600</td>\n",
       "      <td>53.477449</td>\n",
       "      <td>79.023733</td>\n",
       "      <td>13.210945</td>\n",
       "      <td>35.044600</td>\n",
       "      <td>53.477449</td>\n",
       "      <td>79.023733</td>\n",
       "      <td>13.211051</td>\n",
       "      <td>35.044247</td>\n",
       "      <td>53.477032</td>\n",
       "      <td>79.022911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Value09</th>\n",
       "      <td>74.468893</td>\n",
       "      <td>82.573827</td>\n",
       "      <td>49.184078</td>\n",
       "      <td>43.227789</td>\n",
       "      <td>74.468893</td>\n",
       "      <td>82.573827</td>\n",
       "      <td>49.184078</td>\n",
       "      <td>43.227789</td>\n",
       "      <td>74.467979</td>\n",
       "      <td>82.572884</td>\n",
       "      <td>49.183640</td>\n",
       "      <td>43.227200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bias</th>\n",
       "      <td>100.104347</td>\n",
       "      <td>100.019108</td>\n",
       "      <td>100.096213</td>\n",
       "      <td>99.801738</td>\n",
       "      <td>100.104347</td>\n",
       "      <td>100.019108</td>\n",
       "      <td>100.096213</td>\n",
       "      <td>99.801738</td>\n",
       "      <td>100.103455</td>\n",
       "      <td>100.018280</td>\n",
       "      <td>100.095413</td>\n",
       "      <td>99.800919</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           In-House                                    Scikit-Learn  \\\n",
       "               TGT0        TGT1        TGT2       TGT3         TGT0   \n",
       "Value00   20.905332   41.552513   50.182144  82.005159    20.905332   \n",
       "Value01   88.158113   45.449590   62.034891  69.434200    88.158113   \n",
       "Value02   13.217732   43.906325   69.673260  63.395746    13.217732   \n",
       "Value03    9.643977   40.141460   52.256499  73.243410     9.643977   \n",
       "Value04    8.246295   33.614186    5.062020  14.806817     8.246295   \n",
       "Value05   75.144577   36.345816    5.585402  81.583236    75.144577   \n",
       "Value06   77.771108   50.226606   31.071148  13.283668    77.771108   \n",
       "Value07   65.365560   46.032369   98.183041  67.698966    65.365560   \n",
       "Value08   13.210945   35.044600   53.477449  79.023733    13.210945   \n",
       "Value09   74.468893   82.573827   49.184078  43.227789    74.468893   \n",
       "Bias     100.104347  100.019108  100.096213  99.801738   100.104347   \n",
       "\n",
       "                                            TensorFlow              \\\n",
       "               TGT1        TGT2       TGT3        TGT0        TGT1   \n",
       "Value00   41.552513   50.182144  82.005159   20.904984   41.551949   \n",
       "Value01   45.449590   62.034891  69.434200   88.157341   45.449181   \n",
       "Value02   43.906325   69.673260  63.395746   13.217596   43.905907   \n",
       "Value03   40.141460   52.256499  73.243410    9.644102   40.141880   \n",
       "Value04   33.614186    5.062020  14.806817    8.246093   33.613712   \n",
       "Value05   36.345816    5.585402  81.583236   75.143692   36.345295   \n",
       "Value06   50.226606   31.071148  13.283668   77.770287   50.226204   \n",
       "Value07   46.032369   98.183041  67.698966   65.365891   46.032795   \n",
       "Value08   35.044600   53.477449  79.023733   13.211051   35.044247   \n",
       "Value09   82.573827   49.184078  43.227789   74.467979   82.572884   \n",
       "Bias     100.019108  100.096213  99.801738  100.103455  100.018280   \n",
       "\n",
       "                                \n",
       "               TGT2       TGT3  \n",
       "Value00   50.181709  82.004158  \n",
       "Value01   62.034386  69.433388  \n",
       "Value02   69.672462  63.395287  \n",
       "Value03   52.256523  73.244209  \n",
       "Value04    5.061895  14.806627  \n",
       "Value05    5.585310  81.582352  \n",
       "Value06   31.070923  13.283564  \n",
       "Value07   98.182350  67.699799  \n",
       "Value08   53.477032  79.022911  \n",
       "Value09   49.183640  43.227200  \n",
       "Bias     100.095413  99.800919  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Merge Result Dataframes: Linear Coefficients & Biases\n",
    "combined_result = pd.concat([inhouse_result, sklearn_result, tensorflow_result], \\\n",
    "                            keys=['In-House', 'Scikit-Learn', 'TensorFlow'])\n",
    "\n",
    "combined_result.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>R-Squared Accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">In-House</th>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Scikit-Learn</th>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">TensorFlow</th>\n",
       "      <th>Training Data</th>\n",
       "      <td>0.999450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Testing Data</th>\n",
       "      <td>0.999839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            R-Squared Accuracy\n",
       "In-House     Training Data            0.999450\n",
       "             Testing Data             0.999839\n",
       "Scikit-Learn Training Data            0.999450\n",
       "             Testing Data             0.999839\n",
       "TensorFlow   Training Data            0.999450\n",
       "             Testing Data             0.999839"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Merge Result Dataframes: R-Squared Values\n",
    "combined_accuracy = pd.concat([inhouse_rs, sklearn_rs, tensorflow_rs], \\\n",
    "                            keys=['In-House', 'Scikit-Learn', 'TensorFlow'])\n",
    "\n",
    "combined_accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exporting Dataframes to CSV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Export Data Statistics\n",
    "datatrain_describe.to_csv('result/reg2_train_describe.csv')\n",
    "datatest_describe.to_csv('result/reg2_test_describe.csv')\n",
    "\n",
    "# Export Combined Result\n",
    "combined_result.T.to_csv('result/reg2_results.csv')\n",
    "\n",
    "# Export Accuracy Result\n",
    "combined_accuracy.to_csv('result/reg2_accuracy.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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