polynomial_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assignment 2 (Part b):  Polynomial Regression\n",
    "\n",
    "The univariate (one dependent variable) and multivariate (more than one dependent variable) linear regression we have discussed so far always assumes a linear relationship between the independent and dependent variables.  In the real world, it is very common to have data where there is a non-linear relationship between the independent and dependent variables.  In these cases, we can use polynomial regression where we assume the relationship between the independent variable x and the dependent variable(s) y is modelled as an nth degree polynomial in x.\n",
    "\n",
    "For example, we discussed briefly in lecture that the relationship between number of miles walked per day and age can be modeled by a quadratic equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics as s\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "sns.set()\n",
    "sns.set(font_scale=1.5)\n",
    "\n",
    "import statsmodels.formula.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "kms = np.random.normal(5, 2, 50)\n",
    "ages = np.random.normal(40,13,50)\n",
    "ages = [a if a > 0 else -a for a in ages]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "50\n"
     ]
    }
   ],
   "source": [
    "first_kms = sorted(kms[0:int(round(len(kms)/2,0))])\n",
    "second_kms = sorted(kms[int(round(len(kms)/2,0)):len(kms)], reverse=True)\n",
    "\n",
    "ages = sorted(ages)\n",
    "kms = first_kms + second_kms\n",
    "print(len(kms))\n",
    "print(len(ages))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\"age\": ages, \"kilometers\": kms})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>age</th>\n",
       "      <th>kilometers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.325717</td>\n",
       "      <td>0.514630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.794103</td>\n",
       "      <td>0.957490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.204469</td>\n",
       "      <td>1.906189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>21.774347</td>\n",
       "      <td>2.618049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>25.015432</td>\n",
       "      <td>3.558823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>25.145793</td>\n",
       "      <td>3.688061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>26.103146</td>\n",
       "      <td>3.726953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>26.637943</td>\n",
       "      <td>4.331845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>27.334928</td>\n",
       "      <td>4.374696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>27.958694</td>\n",
       "      <td>4.594707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>29.789342</td>\n",
       "      <td>5.004237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>32.398663</td>\n",
       "      <td>5.031393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>32.872848</td>\n",
       "      <td>5.386843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>33.345543</td>\n",
       "      <td>5.578184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>34.408756</td>\n",
       "      <td>5.810907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>34.800460</td>\n",
       "      <td>5.942870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>35.518042</td>\n",
       "      <td>6.106878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>37.289516</td>\n",
       "      <td>6.719177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>38.119946</td>\n",
       "      <td>6.774326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>38.688063</td>\n",
       "      <td>6.906648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>38.934688</td>\n",
       "      <td>6.983892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>39.085517</td>\n",
       "      <td>7.300071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>39.538331</td>\n",
       "      <td>7.636303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>40.513665</td>\n",
       "      <td>7.642316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>41.037950</td>\n",
       "      <td>7.865414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>41.984197</td>\n",
       "      <td>9.781921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>42.138884</td>\n",
       "      <td>7.117938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>42.754484</td>\n",
       "      <td>7.095157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>42.950513</td>\n",
       "      <td>7.091877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>43.520866</td>\n",
       "      <td>6.727435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>44.003595</td>\n",
       "      <td>6.683349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>44.602264</td>\n",
       "      <td>6.510828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>46.006777</td>\n",
       "      <td>6.351108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>46.037100</td>\n",
       "      <td>5.674875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>46.805604</td>\n",
       "      <td>5.495584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>46.867746</td>\n",
       "      <td>5.430537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>47.354598</td>\n",
       "      <td>5.249426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>48.215733</td>\n",
       "      <td>5.152399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>49.154967</td>\n",
       "      <td>5.072284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>49.161368</td>\n",
       "      <td>5.036578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>49.975794</td>\n",
       "      <td>4.755817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>50.615721</td>\n",
       "      <td>4.726410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>50.933114</td>\n",
       "      <td>4.633783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>52.803958</td>\n",
       "      <td>4.354410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>53.439410</td>\n",
       "      <td>4.204320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>57.174373</td>\n",
       "      <td>4.061389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>58.095821</td>\n",
       "      <td>3.867108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>60.093564</td>\n",
       "      <td>3.205686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>66.101958</td>\n",
       "      <td>1.365946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>66.397847</td>\n",
       "      <td>0.850045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          age  kilometers\n",
       "0    6.325717    0.514630\n",
       "1    8.794103    0.957490\n",
       "2   21.204469    1.906189\n",
       "3   21.774347    2.618049\n",
       "4   25.015432    3.558823\n",
       "5   25.145793    3.688061\n",
       "6   26.103146    3.726953\n",
       "7   26.637943    4.331845\n",
       "8   27.334928    4.374696\n",
       "9   27.958694    4.594707\n",
       "10  29.789342    5.004237\n",
       "11  32.398663    5.031393\n",
       "12  32.872848    5.386843\n",
       "13  33.345543    5.578184\n",
       "14  34.408756    5.810907\n",
       "15  34.800460    5.942870\n",
       "16  35.518042    6.106878\n",
       "17  37.289516    6.719177\n",
       "18  38.119946    6.774326\n",
       "19  38.688063    6.906648\n",
       "20  38.934688    6.983892\n",
       "21  39.085517    7.300071\n",
       "22  39.538331    7.636303\n",
       "23  40.513665    7.642316\n",
       "24  41.037950    7.865414\n",
       "25  41.984197    9.781921\n",
       "26  42.138884    7.117938\n",
       "27  42.754484    7.095157\n",
       "28  42.950513    7.091877\n",
       "29  43.520866    6.727435\n",
       "30  44.003595    6.683349\n",
       "31  44.602264    6.510828\n",
       "32  46.006777    6.351108\n",
       "33  46.037100    5.674875\n",
       "34  46.805604    5.495584\n",
       "35  46.867746    5.430537\n",
       "36  47.354598    5.249426\n",
       "37  48.215733    5.152399\n",
       "38  49.154967    5.072284\n",
       "39  49.161368    5.036578\n",
       "40  49.975794    4.755817\n",
       "41  50.615721    4.726410\n",
       "42  50.933114    4.633783\n",
       "43  52.803958    4.354410\n",
       "44  53.439410    4.204320\n",
       "45  57.174373    4.061389\n",
       "46  58.095821    3.867108\n",
       "47  60.093564    3.205686\n",
       "48  66.101958    1.365946\n",
       "49  66.397847    0.850045"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df\n",
    "#below is a dataframe I made to experiment with polynomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1. Plot histogram of age and kilometers and age vs. kilometers (sample output shown in the graphs below) (2 points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your code here\n",
    "#sample output shown below\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "num_bins = 5\n",
    "plt.hist(df['age'], num_bins, facecolor='blue', alpha=0.5)\n",
    "plt.title('Age Histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your code here\n",
    "#sample output shown here\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "num_bins = 5\n",
    "plt.hist(df['kilometers'], num_bins, facecolor='blue', alpha=0.5, rwidth = 0.9)\n",
    "plt.title('Kilometers Histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot kilometers vs. age\n",
    "#your code goes here\n",
    "#sample output shown below\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "#plt.hist(df['age'], num_bins, facecolor='blue', alpha=0.5)\n",
    "Age = df['age']\n",
    "Kms = df['kilometers']\n",
    "plt.scatter(Age, Kms, edgecolors='r')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Kilometers')\n",
    "plt.title('Scatter plot of kilometers walked in a day vs age')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2. Does the above relationship look linear to you?  If no, what kind of relationship do you think it is? (1 point)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does the above relationship look linear to you?  If no, what kind of relationship do you think it is?\n",
    "The relationship betweenage and kilomerters walked is positive initially because as the age increases, kilometers walked also increases but after 40 years of age, we see negative correlation between the 2 variables, which means that with the increase in age, number of kilometers walked decreases. \n",
    "\n",
    "</br>\n",
    "</br>\n",
    "</br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3. Fit a parabola (a 2-degree polynomial) to the data (3 points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.options.mode.chained_assignment = None  # default='warn'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Square the age column\n",
    "#A = np.power(df['age'], 2)\n",
    "df['age_square']  = np.square(df['age'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>age</th>\n",
       "      <th>kilometers</th>\n",
       "      <th>age_square</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.325717</td>\n",
       "      <td>0.514630</td>\n",
       "      <td>40.014690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.794103</td>\n",
       "      <td>0.957490</td>\n",
       "      <td>77.336243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.204469</td>\n",
       "      <td>1.906189</td>\n",
       "      <td>449.629506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>21.774347</td>\n",
       "      <td>2.618049</td>\n",
       "      <td>474.122202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>25.015432</td>\n",
       "      <td>3.558823</td>\n",
       "      <td>625.771817</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age  kilometers  age_square\n",
       "0   6.325717    0.514630   40.014690\n",
       "1   8.794103    0.957490   77.336243\n",
       "2  21.204469    1.906189  449.629506\n",
       "3  21.774347    2.618049  474.122202\n",
       "4  25.015432    3.558823  625.771817"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#concatenating new col ageSq with existing dataset\n",
    "#df = pd.concat([df, A], axis=1) \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define our dependent variable\n",
    "y_column = 'kilometers'\n",
    "y = df[y_column]\n",
    "# Define our independent variables\n",
    "x_columns = ['age', 'age_square']\n",
    "X = df[x_columns]\n",
    "\n",
    "# Add an intercept term to the independent variables. This is needed in order to include the constant term from\n",
    "# linear regression equation.\n",
    "X['intercept'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import the library\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split our data into training and test data sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=41)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             kilometers   R-squared:                       0.715\n",
      "Model:                            OLS   Adj. R-squared:                  0.700\n",
      "Method:                 Least Squares   F-statistic:                     46.50\n",
      "Date:                Wed, 20 Feb 2019   Prob (F-statistic):           8.02e-11\n",
      "Time:                        23:17:07   Log-Likelihood:                -59.372\n",
      "No. Observations:                  40   AIC:                             124.7\n",
      "Df Residuals:                      37   BIC:                             129.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "age            0.5432      0.056      9.614      0.000       0.429       0.658\n",
      "age_square    -0.0069      0.001     -9.135      0.000      -0.008      -0.005\n",
      "intercept     -4.3455      1.039     -4.180      0.000      -6.452      -2.239\n",
      "==============================================================================\n",
      "Omnibus:                        6.997   Durbin-Watson:                   1.542\n",
      "Prob(Omnibus):                  0.030   Jarque-Bera (JB):                5.803\n",
      "Skew:                           0.730   Prob(JB):                       0.0549\n",
      "Kurtosis:                       4.162   Cond. No.                     1.22e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.22e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#your code goes here\n",
    "#sm.OLS refers to simple ordinary least square model\n",
    "#endog - endogenous response variable. The dependent variable.\n",
    "#exog - A nobs x k array where nobs is the number of observations and k is the number of regressors.\n",
    "model = sm.OLS(endog=y_train, exog=X_train)\n",
    "model_fit = model.fit()\n",
    "print(model_fit.summary())\n",
    "\n",
    "#sample output shown below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.34552794437377"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_fit.params.intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4. Predit on training data and plot the results (1 point)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get predictions for the training data and plot\n",
    "\n",
    "#your code goes here\n",
    "#sample output shown below\n",
    "y_pred_train = model_fit.predict(X_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#store 40 age values from train dataset to age_train variable\n",
    "age_train = X_train.iloc[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Kilometers')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,7))\n",
    "\n",
    "#the below scatter plots compares train predicted and actual kilometer values\n",
    "#plot age_train values Vs predicted values in green\n",
    "plt.scatter(age_train,y_pred_train, alpha=0.5, c='g', label= \"preds\")\n",
    "\n",
    "#plot actual age values Vs actual Kms values of training data in red\n",
    "plt.scatter(age_train,y_train, alpha=0.5, c='r', label = \"kilometers\")\n",
    "\n",
    "#for adding labels and title\n",
    "plt.legend()\n",
    "plt.legend()\n",
    "plt.title('predicted and true kilometers by age for training data')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Kilometers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5.  Finish this notebook to fit the model to the test data.  How is the fit? (4 points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_test = model_fit.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#stores 10 age data values of test data in test_age variable\n",
    "test_age = X_test.iloc[:,0:1]\n",
    "#test_age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e7d47fc630>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,7))\n",
    "#the below scatter plots compares predicted and actual kilometer values\n",
    "#plot test_age values Vs predicted values in green\n",
    "plt.scatter(test_age,y_pred_test, alpha=0.5, c='g',label= \"preds\")\n",
    "\n",
    "#plot actual age values Vs actual Kms values in red\n",
    "plt.scatter(test_age,y_test, alpha=0.5, c='r',label= \"kilometers\")\n",
    "\n",
    "#for adding labels and title\n",
    "plt.title('predicted and true kilometers by age for test data')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Kilometers')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3976475134564331\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "#to Print MSE for test data\n",
    "#source: https://towardsdatascience.com/linear-regression-in-python-9a1f5f000606\n",
    "print(metrics.mean_squared_error(y_test,y_pred_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1396754424975004\n"
     ]
    }
   ],
   "source": [
    "#to Print MSE for train data\n",
    "print(metrics.mean_squared_error(y_train,y_pred_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6305929855750325\n"
     ]
    }
   ],
   "source": [
    "#to print RMSE for test data\n",
    "print(np.sqrt(metrics.mean_squared_error(y_test,y_pred_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0675558264079217\n"
     ]
    }
   ],
   "source": [
    "#to print RMSE for train data\n",
    "print(np.sqrt(metrics.mean_squared_error(y_train,y_pred_train)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8390175458041148\n"
     ]
    }
   ],
   "source": [
    "r2 = r2_score(y_test,y_pred_test)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.715377959967922\n"
     ]
    }
   ],
   "source": [
    "r2_train = r2_score(y_train,y_pred_train)\n",
    "print(r2_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training data set has 40 values and the predicted values in green shows parabola shape. The test data has 10 rows and it also shows parabola shape as opposed to the original data set values, which initially show positive correlation between kms and age but then after the age of 40, there exist negative correlation between age and Kms. \n",
    "The r-square value for train data was 71.5% but for test data is 83.9%.\n",
    "Also the RMSE and MSE values for are more for train data than for test data. so we can say that the scatter plot \n",
    "from test data (as shown in Q5) is better fit."
   ]
  }
 ],
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