{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Learning Practice 2 for the University of Tulsa's QM-7063 Data Mining Course\n",
    "# Dimension Reduction\n",
    "# Professor: Dr. Abdulrashid, Spring 2023\n",
    "# Noah L. Schrick - 1492657\n",
    "\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>min</th>\n",
       "      <th>max</th>\n",
       "      <th>median</th>\n",
       "      <th>length</th>\n",
       "      <th>miss.val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>3.613524</td>\n",
       "      <td>8.601545</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>88.9762</td>\n",
       "      <td>0.25651</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>11.363636</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>100.0000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>11.136779</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.46000</td>\n",
       "      <td>27.7400</td>\n",
       "      <td>9.69000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>0.554695</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.38500</td>\n",
       "      <td>0.8710</td>\n",
       "      <td>0.53800</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>6.284634</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>3.56100</td>\n",
       "      <td>8.7800</td>\n",
       "      <td>6.20850</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>68.574901</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.90000</td>\n",
       "      <td>100.0000</td>\n",
       "      <td>77.50000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>3.795043</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>1.12960</td>\n",
       "      <td>12.1265</td>\n",
       "      <td>3.20745</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>9.549407</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>24.0000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>408.237154</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>187.00000</td>\n",
       "      <td>711.0000</td>\n",
       "      <td>330.00000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>18.455534</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>12.60000</td>\n",
       "      <td>22.0000</td>\n",
       "      <td>19.05000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>12.653063</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>1.73000</td>\n",
       "      <td>37.9700</td>\n",
       "      <td>11.36000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MEDV</th>\n",
       "      <td>22.532806</td>\n",
       "      <td>9.197104</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>50.0000</td>\n",
       "      <td>21.20000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT. MEDV</th>\n",
       "      <td>0.166008</td>\n",
       "      <td>0.372456</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>506</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean          sd        min       max     median  length  \\\n",
       "CRIM         3.613524    8.601545    0.00632   88.9762    0.25651     506   \n",
       "ZN          11.363636   23.322453    0.00000  100.0000    0.00000     506   \n",
       "INDUS       11.136779    6.860353    0.46000   27.7400    9.69000     506   \n",
       "CHAS         0.069170    0.253994    0.00000    1.0000    0.00000     506   \n",
       "NOX          0.554695    0.115878    0.38500    0.8710    0.53800     506   \n",
       "RM           6.284634    0.702617    3.56100    8.7800    6.20850     506   \n",
       "AGE         68.574901   28.148861    2.90000  100.0000   77.50000     506   \n",
       "DIS          3.795043    2.105710    1.12960   12.1265    3.20745     506   \n",
       "RAD          9.549407    8.707259    1.00000   24.0000    5.00000     506   \n",
       "TAX        408.237154  168.537116  187.00000  711.0000  330.00000     506   \n",
       "PTRATIO     18.455534    2.164946   12.60000   22.0000   19.05000     506   \n",
       "LSTAT       12.653063    7.141062    1.73000   37.9700   11.36000     506   \n",
       "MEDV        22.532806    9.197104    5.00000   50.0000   21.20000     506   \n",
       "CAT. MEDV    0.166008    0.372456    0.00000    1.0000    0.00000     506   \n",
       "\n",
       "           miss.val  \n",
       "CRIM              0  \n",
       "ZN                0  \n",
       "INDUS             0  \n",
       "CHAS              0  \n",
       "NOX               0  \n",
       "RM                0  \n",
       "AGE               0  \n",
       "DIS               0  \n",
       "RAD               0  \n",
       "TAX               0  \n",
       "PTRATIO           0  \n",
       "LSTAT             0  \n",
       "MEDV              0  \n",
       "CAT. MEDV         0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bostonHousing_df = pd.read_csv('BostonHousing.csv')\n",
    "bostonHousing_df = bostonHousing_df.rename(columns={'CAT.MEDV': 'CAT_MEDV'})\n",
    "\n",
    "# Compute mean, standard dev., min, max, median, length, and missing values for all variables\n",
    "pd.DataFrame({'mean': bostonHousing_df.mean(),\n",
    "'sd': bostonHousing_df.std(),\n",
    "'min': bostonHousing_df.min(),\n",
    "'max': bostonHousing_df.max(),\n",
    "'median': bostonHousing_df.median(),\n",
    "'length': len(bostonHousing_df),\n",
    "'miss.val': bostonHousing_df.isnull().sum(),\n",
    "})\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "      <th>CAT. MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>-0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>-0.20</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.57</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.76</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.64</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>-0.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.09</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.73</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.59</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>-0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.57</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.73</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>-0.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>0.63</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.61</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.49</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>-0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>0.58</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>0.72</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.67</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>0.51</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>0.91</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.54</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-0.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.38</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.26</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.46</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.59</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.37</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>-0.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MEDV</th>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>0.70</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.25</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT. MEDV</th>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.64</td>\n",
       "      <td>-0.19</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>0.79</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           CRIM    ZN  INDUS  CHAS   NOX    RM   AGE   DIS   RAD   TAX  \\\n",
       "CRIM       1.00 -0.20   0.41 -0.06  0.42 -0.22  0.35 -0.38  0.63  0.58   \n",
       "ZN        -0.20  1.00  -0.53 -0.04 -0.52  0.31 -0.57  0.66 -0.31 -0.31   \n",
       "INDUS      0.41 -0.53   1.00  0.06  0.76 -0.39  0.64 -0.71  0.60  0.72   \n",
       "CHAS      -0.06 -0.04   0.06  1.00  0.09  0.09  0.09 -0.10 -0.01 -0.04   \n",
       "NOX        0.42 -0.52   0.76  0.09  1.00 -0.30  0.73 -0.77  0.61  0.67   \n",
       "RM        -0.22  0.31  -0.39  0.09 -0.30  1.00 -0.24  0.21 -0.21 -0.29   \n",
       "AGE        0.35 -0.57   0.64  0.09  0.73 -0.24  1.00 -0.75  0.46  0.51   \n",
       "DIS       -0.38  0.66  -0.71 -0.10 -0.77  0.21 -0.75  1.00 -0.49 -0.53   \n",
       "RAD        0.63 -0.31   0.60 -0.01  0.61 -0.21  0.46 -0.49  1.00  0.91   \n",
       "TAX        0.58 -0.31   0.72 -0.04  0.67 -0.29  0.51 -0.53  0.91  1.00   \n",
       "PTRATIO    0.29 -0.39   0.38 -0.12  0.19 -0.36  0.26 -0.23  0.46  0.46   \n",
       "LSTAT      0.46 -0.41   0.60 -0.05  0.59 -0.61  0.60 -0.50  0.49  0.54   \n",
       "MEDV      -0.39  0.36  -0.48  0.18 -0.43  0.70 -0.38  0.25 -0.38 -0.47   \n",
       "CAT. MEDV -0.15  0.37  -0.37  0.11 -0.23  0.64 -0.19  0.12 -0.20 -0.27   \n",
       "\n",
       "           PTRATIO  LSTAT  MEDV  CAT. MEDV  \n",
       "CRIM          0.29   0.46 -0.39      -0.15  \n",
       "ZN           -0.39  -0.41  0.36       0.37  \n",
       "INDUS         0.38   0.60 -0.48      -0.37  \n",
       "CHAS         -0.12  -0.05  0.18       0.11  \n",
       "NOX           0.19   0.59 -0.43      -0.23  \n",
       "RM           -0.36  -0.61  0.70       0.64  \n",
       "AGE           0.26   0.60 -0.38      -0.19  \n",
       "DIS          -0.23  -0.50  0.25       0.12  \n",
       "RAD           0.46   0.49 -0.38      -0.20  \n",
       "TAX           0.46   0.54 -0.47      -0.27  \n",
       "PTRATIO       1.00   0.37 -0.51      -0.44  \n",
       "LSTAT         0.37   1.00 -0.74      -0.47  \n",
       "MEDV         -0.51  -0.74  1.00       0.79  \n",
       "CAT. MEDV    -0.44  -0.47  0.79       1.00  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation Matrix\n",
    "bostonHousing_df.corr().round(2)"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
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