Salinee_Kingbaisomboon-L07-ParkinsonPCR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 7 - Parkinson PCR\n",
    "## Author - Salinee Kingbaisomboon\n",
    "### UW NetID: 1950831"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Description:\n",
    "\n",
    "Perform Principal Component Regression on a <a href=\"https://archive.ics.uci.edu/ml/datasets/parkinsons+telemonitoring\">dataset that tracked patients with Parkinson's Disease</a>.\n",
    "\n",
    "Citation: A Tsanas, MA Little, PE McSharry, LO Ramig (2009)\n",
    "'Accurate telemonitoring of Parkinson's disease progression by non-invasive speech tests',\n",
    "IEEE Transactions on Biomedical Engineering.\n",
    "\n",
    "About the data:\n",
    "This dataset is composed of a range of biomedical voice measurements from 42 people with early-stage Parkinson's disease recruited to a six-month trial of a telemonitoring device for remote symptom progression monitoring. The recordings were automatically captured in the patient's homes.\n",
    "\n",
    "#### Instructions:\n",
    "\n",
    " 1. Load the dataset.\n",
    " 2. Create the X-matrix (one-hot encoding categorical factors).\n",
    " 3. Scale the X-matrix.\n",
    " 4. Create the principal components and do a simple plot of the explained variance.\n",
    " 5. PCR - Linear regression with the principal components.\n",
    "\n",
    "Report on:\n",
    "\n",
    " 1. Number of components before and after (choose a smaller number of principal components and explain how you chose them).\n",
    " 2. Interpret the adjusted R-squared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = \"https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.formula.api as sm\n",
    "import seaborn as sns\n",
    "\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\") # To suppress warning\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "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>subject#</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>test_time</th>\n",
       "      <th>motor_UPDRS</th>\n",
       "      <th>total_UPDRS</th>\n",
       "      <th>Jitter(%)</th>\n",
       "      <th>Jitter(Abs)</th>\n",
       "      <th>Jitter:RAP</th>\n",
       "      <th>Jitter:PPQ5</th>\n",
       "      <th>...</th>\n",
       "      <th>Shimmer(dB)</th>\n",
       "      <th>Shimmer:APQ3</th>\n",
       "      <th>Shimmer:APQ5</th>\n",
       "      <th>Shimmer:APQ11</th>\n",
       "      <th>Shimmer:DDA</th>\n",
       "      <th>NHR</th>\n",
       "      <th>HNR</th>\n",
       "      <th>RPDE</th>\n",
       "      <th>DFA</th>\n",
       "      <th>PPE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>5.6431</td>\n",
       "      <td>28.199</td>\n",
       "      <td>34.398</td>\n",
       "      <td>0.00662</td>\n",
       "      <td>0.000034</td>\n",
       "      <td>0.00401</td>\n",
       "      <td>0.00317</td>\n",
       "      <td>...</td>\n",
       "      <td>0.230</td>\n",
       "      <td>0.01438</td>\n",
       "      <td>0.01309</td>\n",
       "      <td>0.01662</td>\n",
       "      <td>0.04314</td>\n",
       "      <td>0.014290</td>\n",
       "      <td>21.640</td>\n",
       "      <td>0.41888</td>\n",
       "      <td>0.54842</td>\n",
       "      <td>0.16006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>12.6660</td>\n",
       "      <td>28.447</td>\n",
       "      <td>34.894</td>\n",
       "      <td>0.00300</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>0.00132</td>\n",
       "      <td>0.00150</td>\n",
       "      <td>...</td>\n",
       "      <td>0.179</td>\n",
       "      <td>0.00994</td>\n",
       "      <td>0.01072</td>\n",
       "      <td>0.01689</td>\n",
       "      <td>0.02982</td>\n",
       "      <td>0.011112</td>\n",
       "      <td>27.183</td>\n",
       "      <td>0.43493</td>\n",
       "      <td>0.56477</td>\n",
       "      <td>0.10810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>19.6810</td>\n",
       "      <td>28.695</td>\n",
       "      <td>35.389</td>\n",
       "      <td>0.00481</td>\n",
       "      <td>0.000025</td>\n",
       "      <td>0.00205</td>\n",
       "      <td>0.00208</td>\n",
       "      <td>...</td>\n",
       "      <td>0.181</td>\n",
       "      <td>0.00734</td>\n",
       "      <td>0.00844</td>\n",
       "      <td>0.01458</td>\n",
       "      <td>0.02202</td>\n",
       "      <td>0.020220</td>\n",
       "      <td>23.047</td>\n",
       "      <td>0.46222</td>\n",
       "      <td>0.54405</td>\n",
       "      <td>0.21014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>25.6470</td>\n",
       "      <td>28.905</td>\n",
       "      <td>35.810</td>\n",
       "      <td>0.00528</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.00191</td>\n",
       "      <td>0.00264</td>\n",
       "      <td>...</td>\n",
       "      <td>0.327</td>\n",
       "      <td>0.01106</td>\n",
       "      <td>0.01265</td>\n",
       "      <td>0.01963</td>\n",
       "      <td>0.03317</td>\n",
       "      <td>0.027837</td>\n",
       "      <td>24.445</td>\n",
       "      <td>0.48730</td>\n",
       "      <td>0.57794</td>\n",
       "      <td>0.33277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6420</td>\n",
       "      <td>29.187</td>\n",
       "      <td>36.375</td>\n",
       "      <td>0.00335</td>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.00093</td>\n",
       "      <td>0.00130</td>\n",
       "      <td>...</td>\n",
       "      <td>0.176</td>\n",
       "      <td>0.00679</td>\n",
       "      <td>0.00929</td>\n",
       "      <td>0.01819</td>\n",
       "      <td>0.02036</td>\n",
       "      <td>0.011625</td>\n",
       "      <td>26.126</td>\n",
       "      <td>0.47188</td>\n",
       "      <td>0.56122</td>\n",
       "      <td>0.19361</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   subject#  age  sex  test_time  motor_UPDRS  total_UPDRS  Jitter(%)  \\\n",
       "0         1   72    0     5.6431       28.199       34.398    0.00662   \n",
       "1         1   72    0    12.6660       28.447       34.894    0.00300   \n",
       "2         1   72    0    19.6810       28.695       35.389    0.00481   \n",
       "3         1   72    0    25.6470       28.905       35.810    0.00528   \n",
       "4         1   72    0    33.6420       29.187       36.375    0.00335   \n",
       "\n",
       "   Jitter(Abs)  Jitter:RAP  Jitter:PPQ5  ...  Shimmer(dB)  Shimmer:APQ3  \\\n",
       "0     0.000034     0.00401      0.00317  ...        0.230       0.01438   \n",
       "1     0.000017     0.00132      0.00150  ...        0.179       0.00994   \n",
       "2     0.000025     0.00205      0.00208  ...        0.181       0.00734   \n",
       "3     0.000027     0.00191      0.00264  ...        0.327       0.01106   \n",
       "4     0.000020     0.00093      0.00130  ...        0.176       0.00679   \n",
       "\n",
       "   Shimmer:APQ5  Shimmer:APQ11  Shimmer:DDA       NHR     HNR     RPDE  \\\n",
       "0       0.01309        0.01662      0.04314  0.014290  21.640  0.41888   \n",
       "1       0.01072        0.01689      0.02982  0.011112  27.183  0.43493   \n",
       "2       0.00844        0.01458      0.02202  0.020220  23.047  0.46222   \n",
       "3       0.01265        0.01963      0.03317  0.027837  24.445  0.48730   \n",
       "4       0.00929        0.01819      0.02036  0.011625  26.126  0.47188   \n",
       "\n",
       "       DFA      PPE  \n",
       "0  0.54842  0.16006  \n",
       "1  0.56477  0.10810  \n",
       "2  0.54405  0.21014  \n",
       "3  0.57794  0.33277  \n",
       "4  0.56122  0.19361  \n",
       "\n",
       "[5 rows x 22 columns]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parkinsons_df = pd.read_csv(filename)\n",
    "parkinsons_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['subject#', 'age', 'sex', 'test_time', 'motor_UPDRS', 'total_UPDRS',\n",
       "       'Jitter(%)', 'Jitter(Abs)', 'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP',\n",
       "       'Shimmer', 'Shimmer(dB)', 'Shimmer:APQ3', 'Shimmer:APQ5',\n",
       "       'Shimmer:APQ11', 'Shimmer:DDA', 'NHR', 'HNR', 'RPDE', 'DFA', 'PPE'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parkinsons_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DataFrame one-hot-expanded shape: (5875, 17)\n"
     ]
    }
   ],
   "source": [
    "# Define the target and features:\n",
    "target_label = 'total_UPDRS'\n",
    "non_features = ['subject#', 'age', 'sex', 'test_time', 'motor_UPDRS']\n",
    "feature_labels = [x for x in parkinsons_df.columns if x not in [target_label] + non_features]\n",
    "\n",
    "# Filter out non-features and non-targets\n",
    "parkinsons_df = parkinsons_df.drop(non_features, axis=1)\n",
    "\n",
    "# One-hot encode inputs\n",
    "parkinsons_expanded = pd.get_dummies(parkinsons_df, drop_first=True)\n",
    "print('DataFrame one-hot-expanded shape: {}'.format(parkinsons_expanded.shape))\n",
    "\n",
    "# Get target and original x-matrix\n",
    "y = parkinsons_df[target_label]\n",
    "X = parkinsons_df.as_matrix(columns=feature_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scale function\n",
    "def scale(col):\n",
    "    mean_col = np.mean(col)\n",
    "    sd_col = np.std(col)\n",
    "    std = (col - mean_col) / sd_col\n",
    "    return std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scale all columns first\n",
    "\n",
    "# Create x-scaled (look into the function np.apply_along_axis to apply 'scale' function\n",
    "#    to each column).\n",
    "x_scaled =  np.apply_along_axis(scale, 1, X)\n",
    "\n",
    "# Create a scaled y-target.\n",
    "y_scaled = scale(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "# PCR!!\n",
    "pca = PCA(n_components=x_scaled.shape[1])\n",
    "pca_result = pca.fit_transform(x_scaled)\n",
    "\n",
    "column_names = ['pc' + str(ix+1) for ix in range(x_scaled.shape[1])]\n",
    "pca_df = pd.DataFrame(data = pca_result, columns=column_names)\n",
    "pca_df[target_label] = y_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pc1</th>\n",
       "      <th>pc2</th>\n",
       "      <th>pc3</th>\n",
       "      <th>pc4</th>\n",
       "      <th>pc5</th>\n",
       "      <th>pc6</th>\n",
       "      <th>pc7</th>\n",
       "      <th>pc8</th>\n",
       "      <th>pc9</th>\n",
       "      <th>pc10</th>\n",
       "      <th>pc11</th>\n",
       "      <th>pc12</th>\n",
       "      <th>pc13</th>\n",
       "      <th>pc14</th>\n",
       "      <th>pc15</th>\n",
       "      <th>pc16</th>\n",
       "      <th>total_UPDRS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.045088</td>\n",
       "      <td>0.021846</td>\n",
       "      <td>-0.011965</td>\n",
       "      <td>0.002224</td>\n",
       "      <td>-0.003324</td>\n",
       "      <td>-0.000952</td>\n",
       "      <td>-0.001371</td>\n",
       "      <td>0.000894</td>\n",
       "      <td>0.000743</td>\n",
       "      <td>-0.000064</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>-0.000069</td>\n",
       "      <td>-0.000018</td>\n",
       "      <td>-9.254165e-08</td>\n",
       "      <td>-4.101552e-07</td>\n",
       "      <td>1.480556e-15</td>\n",
       "      <td>0.502745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.064457</td>\n",
       "      <td>0.036847</td>\n",
       "      <td>-0.017445</td>\n",
       "      <td>-0.003462</td>\n",
       "      <td>-0.006028</td>\n",
       "      <td>-0.001887</td>\n",
       "      <td>0.000433</td>\n",
       "      <td>0.000536</td>\n",
       "      <td>0.000411</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000113</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>-8.425380e-08</td>\n",
       "      <td>3.734431e-07</td>\n",
       "      <td>2.175479e-15</td>\n",
       "      <td>0.549103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.052680</td>\n",
       "      <td>0.020125</td>\n",
       "      <td>-0.004610</td>\n",
       "      <td>0.001911</td>\n",
       "      <td>-0.014712</td>\n",
       "      <td>-0.000134</td>\n",
       "      <td>-0.000101</td>\n",
       "      <td>0.000922</td>\n",
       "      <td>-0.000104</td>\n",
       "      <td>0.000088</td>\n",
       "      <td>-0.000167</td>\n",
       "      <td>-0.000078</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>1.518409e-07</td>\n",
       "      <td>-3.843817e-07</td>\n",
       "      <td>2.306288e-15</td>\n",
       "      <td>0.595367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.033055</td>\n",
       "      <td>0.017032</td>\n",
       "      <td>-0.013254</td>\n",
       "      <td>0.013447</td>\n",
       "      <td>-0.025724</td>\n",
       "      <td>0.002620</td>\n",
       "      <td>-0.001050</td>\n",
       "      <td>0.001790</td>\n",
       "      <td>-0.001052</td>\n",
       "      <td>-0.000038</td>\n",
       "      <td>-0.001359</td>\n",
       "      <td>-0.000215</td>\n",
       "      <td>-0.000030</td>\n",
       "      <td>1.039336e-06</td>\n",
       "      <td>-3.562540e-07</td>\n",
       "      <td>2.302477e-15</td>\n",
       "      <td>0.634716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.060086</td>\n",
       "      <td>0.027857</td>\n",
       "      <td>-0.010304</td>\n",
       "      <td>0.000267</td>\n",
       "      <td>-0.014814</td>\n",
       "      <td>0.000494</td>\n",
       "      <td>0.000529</td>\n",
       "      <td>0.000657</td>\n",
       "      <td>-0.000013</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>-0.000077</td>\n",
       "      <td>-0.000039</td>\n",
       "      <td>0.000048</td>\n",
       "      <td>2.201413e-07</td>\n",
       "      <td>2.117552e-08</td>\n",
       "      <td>2.434191e-15</td>\n",
       "      <td>0.687522</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        pc1       pc2       pc3       pc4       pc5       pc6       pc7  \\\n",
       "0 -0.045088  0.021846 -0.011965  0.002224 -0.003324 -0.000952 -0.001371   \n",
       "1 -0.064457  0.036847 -0.017445 -0.003462 -0.006028 -0.001887  0.000433   \n",
       "2 -0.052680  0.020125 -0.004610  0.001911 -0.014712 -0.000134 -0.000101   \n",
       "3 -0.033055  0.017032 -0.013254  0.013447 -0.025724  0.002620 -0.001050   \n",
       "4 -0.060086  0.027857 -0.010304  0.000267 -0.014814  0.000494  0.000529   \n",
       "\n",
       "        pc8       pc9      pc10      pc11      pc12      pc13          pc14  \\\n",
       "0  0.000894  0.000743 -0.000064  0.000037 -0.000069 -0.000018 -9.254165e-08   \n",
       "1  0.000536  0.000411  0.000058  0.000113  0.000058  0.000017 -8.425380e-08   \n",
       "2  0.000922 -0.000104  0.000088 -0.000167 -0.000078  0.000031  1.518409e-07   \n",
       "3  0.001790 -0.001052 -0.000038 -0.001359 -0.000215 -0.000030  1.039336e-06   \n",
       "4  0.000657 -0.000013  0.000212 -0.000077 -0.000039  0.000048  2.201413e-07   \n",
       "\n",
       "           pc15          pc16  total_UPDRS  \n",
       "0 -4.101552e-07  1.480556e-15     0.502745  \n",
       "1  3.734431e-07  2.175479e-15     0.549103  \n",
       "2 -3.843817e-07  2.306288e-15     0.595367  \n",
       "3 -3.562540e-07  2.302477e-15     0.634716  \n",
       "4  2.117552e-08  2.434191e-15     0.687522  "
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[4mExplained Variance: \u001b[0m\n",
      "[3.47834662e-02 1.20302807e-03 6.70121366e-04 2.72446869e-04\n",
      " 1.97675170e-04 8.11822128e-05 1.68296588e-05 1.51410636e-05\n",
      " 4.70752702e-06 1.80571521e-06 7.76025353e-07 1.71546249e-07\n",
      " 5.86072793e-08 1.51846603e-11 3.30694608e-13 5.04738438e-30]\n",
      "\u001b[1m\u001b[4mComponent Direction: \u001b[0m\n",
      "[[-1.49934592e-01 -1.76979481e-01 -1.62974924e-01 -1.57366235e-01\n",
      "  -1.34695129e-01 -6.50672166e-02  8.05487599e-01 -1.24307118e-01\n",
      "  -1.03124992e-01 -9.89139645e-02 -1.86927844e-02  1.49524933e-01\n",
      "  -2.68162078e-01  2.37910936e-01  1.54530227e-01  1.12764819e-01]\n",
      " [ 1.12833541e-01  9.49335666e-02  1.04609509e-01  1.12217478e-01\n",
      "   1.24040474e-01  1.04531311e-01  9.89510503e-02  9.66205723e-02\n",
      "   1.02387286e-01  8.25721521e-02  1.00068377e-01  4.46739808e-01\n",
      "  -5.80938115e-01 -4.05603530e-01 -3.41644592e-01 -2.52318888e-01]\n",
      " [ 1.16463305e-02 -2.05280345e-02 -3.01164530e-03  1.16094277e-03\n",
      "   3.23961731e-02 -7.32350708e-02 -4.86987488e-01 -4.96920472e-02\n",
      "  -5.57620306e-02 -6.21677933e-02 -1.07649432e-01  3.05723493e-01\n",
      "  -5.17347692e-01  4.31130890e-01  3.72099735e-01  2.22223671e-01]\n",
      " [ 9.18107055e-03 -2.80496972e-02 -1.07790112e-02 -5.39256001e-03\n",
      "   2.39094381e-02 -2.17170260e-02  1.74860835e-02 -3.52991260e-02\n",
      "  -3.49625388e-02  3.28892986e-03 -4.96590231e-02 -7.56835825e-02\n",
      "  -8.21887490e-02 -6.89921680e-01  3.79842170e-01  5.99945302e-01]\n",
      " [ 1.65656244e-02  2.18625128e-02  2.50764770e-02  1.77738009e-02\n",
      "   3.14462714e-02  4.26608703e-02  4.68974595e-02  4.88212178e-02\n",
      "   3.74089855e-02  1.85890650e-02  1.02687264e-01 -2.02055693e-01\n",
      "  -1.05054521e-01 -1.54600542e-01  6.97343253e-01 -6.45422046e-01]\n",
      " [ 5.69004336e-02  1.04793931e-01  6.96830453e-02  7.53069103e-02\n",
      "  -1.10905271e-03  1.34919415e-01  6.49112006e-02  1.01239707e-01\n",
      "   8.61375235e-02  2.61033657e-01  9.35412305e-02 -7.35765793e-01\n",
      "  -4.88101216e-01  1.70505125e-01 -1.54468641e-01  1.60472524e-01]\n",
      " [-4.52444422e-02  4.14932169e-02 -2.83508090e-02  3.81757533e-03\n",
      "  -1.69327481e-01 -5.03148094e-03  3.02441184e-02 -1.66084316e-01\n",
      "   4.52672915e-02  7.56734226e-01 -5.82584831e-01  1.12820897e-01\n",
      "   5.37613900e-02 -1.60505027e-02  4.64958301e-02 -7.79606814e-02]\n",
      " [ 3.09624217e-01 -1.04484773e-02  1.98042267e-01  1.76609658e-01\n",
      "   6.15988896e-01 -9.17658725e-02  1.53590523e-01 -1.75962182e-01\n",
      "  -2.31272913e-01 -2.39676776e-01 -5.06006359e-01 -1.37279919e-01\n",
      "  -9.07075504e-03  3.45810046e-02 -3.08862391e-02 -5.60670735e-02]\n",
      " [ 5.44583106e-03 -3.94600054e-01 -1.07009331e-01 -2.02044574e-01\n",
      "   4.71117554e-01 -2.28220523e-01 -6.52453892e-02 -1.14710147e-01\n",
      "  -2.95153466e-01  4.58904735e-01  4.47931961e-01  2.15914599e-02\n",
      "   2.90656917e-02  6.26010104e-03 -2.84666069e-02 -4.86724180e-03]\n",
      " [ 2.23718699e-02 -3.13723013e-01 -1.45250448e-01 -9.33966826e-03\n",
      "   1.91999796e-01 -2.08475859e-01 -1.15224737e-02 -2.23500269e-01\n",
      "   8.60602382e-01 -6.91246377e-02 -4.24188867e-02 -4.40512941e-02\n",
      "  -1.21330542e-02  6.44290042e-03 -9.18992817e-03  7.31258357e-03]\n",
      " [-2.99543385e-02 -2.94343885e-01 -1.55538321e-01 -1.48233398e-01\n",
      "   1.22387782e-01  8.89556074e-01 -7.81525967e-02 -2.16664953e-01\n",
      "  -9.69379038e-03 -5.13794419e-02 -6.09693101e-02  1.45104885e-02\n",
      "   1.70814573e-02  1.67287172e-03 -1.26964585e-03  9.91007442e-04]\n",
      " [ 4.23409012e-01 -3.08148816e-01 -3.09727455e-01  6.86382938e-01\n",
      "  -3.10546092e-01 -1.78035652e-02 -3.87727914e-03 -1.65870914e-01\n",
      "  -1.38506590e-01  2.03001601e-02  1.20517824e-01 -3.89736075e-04\n",
      "   1.26708800e-02  2.81047332e-03  7.20968348e-04 -1.19418091e-02]\n",
      " [ 7.87362093e-01  3.90231149e-02 -4.50599990e-02 -5.73512084e-01\n",
      "  -2.13079378e-01 -2.93452202e-02  2.37881069e-03  2.32262840e-02\n",
      "   2.57814647e-02 -4.76753312e-03 -7.40019688e-03  1.18856303e-03\n",
      "  -4.61590007e-04  4.54299054e-04  4.05102678e-04 -6.19373186e-03]\n",
      " [ 5.44700101e-04 -6.67302916e-01  5.10908175e-01  1.89940229e-04\n",
      "  -1.69894506e-01 -2.42230256e-04 -3.71763078e-05  4.88331582e-01\n",
      "  -3.72302694e-04 -3.37516705e-05 -1.62318283e-01  1.26658311e-04\n",
      "  -5.81767527e-07  2.91760476e-05  2.77041663e-05  4.38114565e-05]\n",
      " [-1.08612887e-04  1.12146225e-02  6.62293123e-01  1.77058583e-04\n",
      "  -2.20783869e-01  1.49251129e-05 -3.70125007e-07 -6.79148256e-01\n",
      "  -8.14146646e-05  2.93754381e-05  2.26393750e-01  9.72134771e-07\n",
      "   1.97281412e-07 -1.23484124e-06 -6.34213898e-07  3.68077751e-07]\n",
      " [-2.50000000e-01 -2.50000000e-01 -2.50000000e-01 -2.50000000e-01\n",
      "  -2.50000000e-01 -2.50000000e-01 -2.50000000e-01 -2.50000000e-01\n",
      "  -2.50000000e-01 -2.50000000e-01 -2.50000000e-01 -2.50000000e-01\n",
      "  -2.50000000e-01 -2.50000000e-01 -2.50000000e-01 -2.50000000e-01]]\n"
     ]
    }
   ],
   "source": [
    "# Plot the explained variance for all principal components.\n",
    "# Note: If the first value is too large, it may dwarf how the rest look.\n",
    "# You may consider plotting starting with the 2nd value (python index at 1).\n",
    "plt.title('Explained variance by Principal Component Num = 16')\n",
    "plt.plot(pca_df.loc[1:, 'pc1'], pca_df.loc[1:, 'pc2'], pca_df.loc[1:, 'pc3'], pca_df.loc[1:, 'pc4'], pca_df.loc[1:, 'pc5'], pca_df.loc[1:, 'pc6'], pca_df.loc[1:, 'pc7'], pca_df.loc[1:, 'pc8'], pca_df.loc[1:, 'pc9'], pca_df.loc[1:, 'pc10'], pca_df.loc[1:, 'pc11'], pca_df.loc[1:, 'pc12'], pca_df.loc[1:, 'pc13'], pca_df.loc[1:, 'pc14'], pca_df.loc[1:, 'pc15'], pca_df.loc[1:, 'pc16'])\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Explained Variance')\n",
    "plt.show()\n",
    "\n",
    "print(f'\\033[1m\\033[4mExplained Variance: \\033[0m')\n",
    "print(pca.explained_variance_)\n",
    "print(f'\\033[1m\\033[4mComponent Direction: \\033[0m')\n",
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            total_UPDRS   R-squared:                       0.002\n",
      "Model:                            OLS   Adj. R-squared:                  0.002\n",
      "Method:                 Least Squares   F-statistic:                     11.68\n",
      "Date:                Sun, 12 Jan 2020   Prob (F-statistic):           0.000636\n",
      "Time:                        20:15:56   Log-Likelihood:                -8330.4\n",
      "No. Observations:                5875   AIC:                         1.666e+04\n",
      "Df Residuals:                    5873   BIC:                         1.668e+04\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept  -4.847e-15      0.013  -3.72e-13      1.000      -0.026       0.026\n",
      "pc1            0.2389      0.070      3.417      0.001       0.102       0.376\n",
      "==============================================================================\n",
      "Omnibus:                      123.476   Durbin-Watson:                   0.041\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              111.307\n",
      "Skew:                           0.286   Prob(JB):                     6.76e-25\n",
      "Kurtosis:                       2.644   Cond. No.                         5.36\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Histogram')"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform linear regression with the first N columns.\n",
    "n = 6\n",
    "formula_start = target_label + ' ~ '\n",
    "formula_terms = ['pc' + str(x+1) for x in range(n)]\n",
    "formula_end = ' + '.join(formula_terms)\n",
    "formula_final = formula_start + formula_end\n",
    "\n",
    "pcr_model = sm.ols(formula = formula_final, data=pca_df)\n",
    "\n",
    "results = pcr_model.fit()\n",
    "\n",
    "# Get most of the linear regression statistics we are interested in:\n",
    "print(results.summary())\n",
    "\n",
    "# Plot a histogram of the residuals\n",
    "sns.distplot(results.resid, hist=True)\n",
    "plt.xlabel('Residual')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Residual Histogram')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary of your results!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "***\n",
    "#### Examine the results:\n",
    "1. **Number of components before and after:**\n",
    "    - Before = 16\n",
    "    - After = 6\n",
    "    \n",
    "    Based on the p-value for each principal components when we perform linear regression with the all 16 columns, we can see that the first 6 principal components **(pc1-pc6)** yield pretty small p-value **(except pc3)**. The overall adjusted R-squared won't go above 0.44 eventhough we keep adding more principal components after 6.\n",
    "2. **Adjusted R-squared = 0.044:** 4.4% of the variation in the output variable is explained by the input variables. However, as I already try with **n=16**, adding more variables won't improve our existing model. \n",
    "3. Based on the **Parkinson dataframe's columns**, the first five columns are **Jitter's related**, we can conclude that for  **Accurate Telemonitoring of Parkinson's Disease Progression by Noninvasive Speech Tests**, **Jitter** has more explanatory power compared with **Shimmer**.\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}