03-05-Polynomial Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression: extending linear models with basis functions\n",
    "\n",
    "[link](http://scikit-learn.org/stable/modules/linear_model.html#polynomial-regression-extending-linear-models-with-basis-functions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One common pattern within machine learning is to use linear models trained on nonlinear functions of the data. This approach maintains the generally fast performance of linear methods, while allowing them to fit a much wider range of data.\n",
    "\n",
    "For example, a simple linear regression can be extended by constructing polynomial features from the coefficients. In the standard linear regression case, you might have a model that looks like this for two-dimensional data:\n",
    "\n",
    "$$\\hat{y}(w, x) = w_0 + w_1 x_1 + w_2 x_2$$\n",
    "\n",
    "If we want to fit a paraboloid to the data instead of a plane, we can combine the features in second-order polynomials, so that the model looks like this:\n",
    "\n",
    "$$\\hat{y}(w, x) = w_0 + w_1 x_1 + w_2 x_2 + w_3 x_1 x_2 + w_4 x_1^2 + w_5 x_2^2$$\n",
    "\n",
    "The (sometimes surprising) observation is that this is still a linear model: to see this, imagine creating a new variable\n",
    "\n",
    "$$z = [x_1, x_2, x_1 x_2, x_1^2, x_2^2]$$\n",
    "\n",
    "With this re-labeling of the data, our problem can be written\n",
    "\n",
    "$$\\hat{y}(w, x) = w_0 + w_1 z_1 + w_2 z_2 + w_3 z_3 + w_4 z_4 + w_5 z_5$$\n",
    "\n",
    "We see that the resulting polynomial regression is in the same class of linear models we’d considered above (i.e. the model is linear in w) and can be solved by the same techniques. By considering linear fits within a higher-dimensional space built with these basis functions, the model has the flexibility to fit a much broader range of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "%matplotlib inline\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.16.5\n",
      "0.25.1\n",
      "3.7.4 (default, Aug 13 2019, 15:17:50) \n",
      "[Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "0.21.3\n"
     ]
    }
   ],
   "source": [
    "print(np.__version__)\n",
    "print(pd.__version__)\n",
    "import sys\n",
    "print(sys.version)\n",
    "import sklearn\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y = X^3 + 100 + \\epsilon$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "n_samples = 100\n",
    "\n",
    "X = np.linspace(0, 10, 100)\n",
    "rng = np.random.randn(n_samples) * 100\n",
    "\n",
    "y = X ** 3 + 100 + rng\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(X, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7643394574930141\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(X.reshape(-1, 1), y)\n",
    "model_pred = lr.predict(X.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(X, y);\n",
    "plt.plot(X, model_pred);\n",
    "print(r2_score(y, model_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_reg = PolynomialFeatures(degree=2)\n",
    "X_poly = poly_reg.fit_transform(X.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.       , 0.1010101, 0.2020202, 0.3030303, 0.4040404])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.        , 0.        ],\n",
       "       [1.        , 0.1010101 , 0.01020304],\n",
       "       [1.        , 0.2020202 , 0.04081216],\n",
       "       [1.        , 0.3030303 , 0.09182736],\n",
       "       [1.        , 0.4040404 , 0.16324865]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "degree_three = PolynomialFeatures(degree=3)\n",
    "example = degree_three.fit_transform(X.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.        , 0.        , 0.        ],\n",
       "       [1.        , 0.1010101 , 0.01020304, 0.00103061],\n",
       "       [1.        , 0.2020202 , 0.04081216, 0.00824488],\n",
       "       [1.        , 0.3030303 , 0.09182736, 0.02782647],\n",
       "       [1.        , 0.4040404 , 0.16324865, 0.06595905]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = np.array([0, 1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 1.,  1.,  1.],\n",
       "       [ 1.,  2.,  4.],\n",
       "       [ 1.,  3.,  9.],\n",
       "       [ 1.,  4., 16.],\n",
       "       [ 1.,  5., 25.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_two = poly_reg.fit_transform(res.reshape(-1, 1))\n",
    "res_two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   0.,   0.,   0.],\n",
       "       [  1.,   1.,   1.,   1.],\n",
       "       [  1.,   2.,   4.,   8.],\n",
       "       [  1.,   3.,   9.,  27.],\n",
       "       [  1.,   4.,  16.,  64.],\n",
       "       [  1.,   5.,  25., 125.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_three = degree_three.fit_transform(res.reshape(-1, 1))\n",
    "res_three"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "lin_reg_2 = LinearRegression()\n",
    "lin_reg_2.fit(X_poly, y.reshape(-1, 1))\n",
    "y_pred = lin_reg_2.predict(X_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9173858308909386\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(X, y);\n",
    "plt.plot(X, y_pred);\n",
    "print(r2_score(y, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boston Housing Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_boston = pd.read_csv('data//housing.data', delim_whitespace=True, header=None)\n",
    "df_boston.columns = ['CRIM', 'ZN' , 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \n",
    "              'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']\n",
    "#sns.pairplot(df_boston, size=1.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>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>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>CRIM</td>\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>-0.39</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>ZN</td>\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>0.18</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>INDUS</td>\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>-0.36</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>CHAS</td>\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>-0.05</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>NOX</td>\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>-0.38</td>\n",
       "      <td>0.59</td>\n",
       "      <td>-0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>RM</td>\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>0.13</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>AGE</td>\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>-0.27</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>DIS</td>\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>0.29</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>RAD</td>\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>-0.44</td>\n",
       "      <td>0.49</td>\n",
       "      <td>-0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TAX</td>\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>-0.44</td>\n",
       "      <td>0.54</td>\n",
       "      <td>-0.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>PTRATIO</td>\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>-0.18</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-0.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>B</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>LSTAT</td>\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>-0.37</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>MEDV</td>\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>0.33</td>\n",
       "      <td>-0.74</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  PTRATIO  \\\n",
       "CRIM     1.00 -0.20   0.41 -0.06  0.42 -0.22  0.35 -0.38  0.63  0.58     0.29   \n",
       "ZN      -0.20  1.00  -0.53 -0.04 -0.52  0.31 -0.57  0.66 -0.31 -0.31    -0.39   \n",
       "INDUS    0.41 -0.53   1.00  0.06  0.76 -0.39  0.64 -0.71  0.60  0.72     0.38   \n",
       "CHAS    -0.06 -0.04   0.06  1.00  0.09  0.09  0.09 -0.10 -0.01 -0.04    -0.12   \n",
       "NOX      0.42 -0.52   0.76  0.09  1.00 -0.30  0.73 -0.77  0.61  0.67     0.19   \n",
       "RM      -0.22  0.31  -0.39  0.09 -0.30  1.00 -0.24  0.21 -0.21 -0.29    -0.36   \n",
       "AGE      0.35 -0.57   0.64  0.09  0.73 -0.24  1.00 -0.75  0.46  0.51     0.26   \n",
       "DIS     -0.38  0.66  -0.71 -0.10 -0.77  0.21 -0.75  1.00 -0.49 -0.53    -0.23   \n",
       "RAD      0.63 -0.31   0.60 -0.01  0.61 -0.21  0.46 -0.49  1.00  0.91     0.46   \n",
       "TAX      0.58 -0.31   0.72 -0.04  0.67 -0.29  0.51 -0.53  0.91  1.00     0.46   \n",
       "PTRATIO  0.29 -0.39   0.38 -0.12  0.19 -0.36  0.26 -0.23  0.46  0.46     1.00   \n",
       "B       -0.39  0.18  -0.36  0.05 -0.38  0.13 -0.27  0.29 -0.44 -0.44    -0.18   \n",
       "LSTAT    0.46 -0.41   0.60 -0.05  0.59 -0.61  0.60 -0.50  0.49  0.54     0.37   \n",
       "MEDV    -0.39  0.36  -0.48  0.18 -0.43  0.70 -0.38  0.25 -0.38 -0.47    -0.51   \n",
       "\n",
       "            B  LSTAT  MEDV  \n",
       "CRIM    -0.39   0.46 -0.39  \n",
       "ZN       0.18  -0.41  0.36  \n",
       "INDUS   -0.36   0.60 -0.48  \n",
       "CHAS     0.05  -0.05  0.18  \n",
       "NOX     -0.38   0.59 -0.43  \n",
       "RM       0.13  -0.61  0.70  \n",
       "AGE     -0.27   0.60 -0.38  \n",
       "DIS      0.29  -0.50  0.25  \n",
       "RAD     -0.44   0.49 -0.38  \n",
       "TAX     -0.44   0.54 -0.47  \n",
       "PTRATIO -0.18   0.37 -0.51  \n",
       "B        1.00  -0.37  0.33  \n",
       "LSTAT   -0.37   1.00 -0.74  \n",
       "MEDV     0.33  -0.74  1.00  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.options.display.float_format = \"{:,.2f}\".format\n",
    "df_boston.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_boston = df_boston['DIS'].values\n",
    "y_boston = df_boston['NOX'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.scatter(X_boston, y_boston);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score = 0.59\n"
     ]
    },
    {
     "data": {
      "image/png": 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105MysQXAHADoySFuUJ4URXEAgAxJkg6HOMakMGP8oKjfw+HsxqIqz8caaPtnLeFcQ0REREQeegLiVwC0i6K4FcBvADwgiuKDoije3HN+HICmKI0v7jbtORaT+8j5xsp6wgI8tYCXzi0IuDgunGuIiIiIyCNoyoQkSd0A7vM7vEdx/gN4KlH0SZHkEIdCrjwBhFfXl7WAiYiIiMLDneqCyO3Z+S3a5B3liIiIiCi2GBAHoZafGw3zpgyP+j2IiIiIqDcGxEGo5ecWjxnondE1CwKKxwxETpYlaF/yJHB2uhnyfLBZEDC/aETQ7ZGJiIiIKDr0lF1LeczPJSIiIuq7GBBHQVWdHZXVEo60OJBrs6JsltgroK6qs+Ox13bjZJvT53h2uhndbjccPXtBmwSg2+2Zmb6j4BwkYIk/IiIioqTGgNhgVXV2LFzb4N1K2d7iwMK1nhrDclBcVWdH2cv1qltCt3b6bsHc3dPE3uLA01vbkZdr52w1ERERkYGYQ2ywymrJGwzLHE4XKqslnzZqwXAwHS63Tz9EREREFDkGxAbTqlusPB5JbeNY1UUmIiIiShUMiA2mVbdYeTyS2saxqotMRERElCqYQ6wgL4azB5iFzetZJAdAdeFc2SzRJ4cYAKwWs/cawFPbWCuHOJAMs+DTDxERERFFLiUC4kVVDVhVc9hne+Q8v+oP/ovhtNhbHChbUw8I8Aa0agvnAlWZkP8cTpUJLqgjIiIiMlafD4gXVTVgxfbmXsf9g1i1xXBanN29Z3blhXNyzeJggWs4tY0bGxtDak9EREREwfX5HOJVNYc1zymrPxixWI0L3oiIiIiST58PiJVpEmrkINaIxWpc8EZERESUfPp8QGwWhIDn5SC2bJYIq8Wsq0+LSYDF7Nuv/8I5IiIiIkoOfT4gnjdleMDz9hYHPj5yGqUT87B0bgHygszy5tmsqLytEJW3FiLPZoXQc2zp3AIueCMiIiJKQn1+Ud2S0gIA6FVlQgAgv5rz9Gbv8TybFU/dfqmu4JYBMBEREVHy6/MzxIAnKH7ym4U+KRFueNIcZoiDfNraWxz4yZp6rN35aYxHSURERETx0OdniGVqZdUcThfe/eR4r7Zd3W48+Pd6/O2Dw3ju25PRL9MSq2H2SfKGJ8q6zIB6rWa1tpyJJyIiomhKmYBYqyRaoCoU7x88gYLF/0KmxYT1P5qO0YPOidbw+iz/DU/sLQ6UvVwPuM/Wc5ZrQu84dAL/qLX7tPXf8ISIiIjIaCmRMgFol0TTqkKROyAT931tDACg3dmNa558ByPL12Hjni+iNsa+SG1m3uly99rcxOF0YVXNYdVZfLlWNBEREVE0pExArFZWzWoxY96U4arHf3rDeJTPHo+mihI8c8dl3nPffWEHRpavw9P/3gt3kBrHFNpmJVqz9dzwhIiIiKIpZQJiZVk1Zam0JaUFqseVX9GXXDIUTRUleOPH073Hlm34BKMWrseCF3egXeeWz6kolM1KNGfrueEJERERRVHK5BADnqBYLRdV67i//KH90VRRgpa2Tsx/rgYf2U/jrcYvMP4Xb2JQvwxU/aA4aB1jWaCFZvYWB8yCAJfbDZvVAqerG62dnqDbZj2MGwuHYtOeY7C3OHzKx3nOW7D45ot93k88F6qVzRJ9cogBeDY1UeQQA55Z+W9MyvPJIZaPc8MTIiIiiqaUCoiNYstKx+s/nA5XtxuP/PMjrKxpxrEzHSiu2AgA+Nv3ilA0+lzN61UXmq2pBwRPfi1wNn2gxeH0ubbF4cSK7c3e1/5JBi0Op6cvwFu1wf9esVyoJt9Db5WJyRcMZJUJIiIiiikGxBEwmwQ8/vUCPP71Aqz+oBk/+4cn0Px/f9oOAFh800X4TvGoXtepLjTrNi4f2dntRmW1hNKJeZrl5uTzsRBoZl5vWyIiIqJoSZkc4mi7/fIRaKoowSv/eaX32OLXPsbI8nV4YPUuOF3d3uOxWCQm30PrXlyoRkREROTBgNhgE0fkoKmiBO8/fC1GnpsFAHilzo6xD7+Ba/7nbRw70xGTRWLyPbTuxYVqRERERB4MiKNkcL9MvF02A58smY1bLs0FABw43orLH38L9hYHMsy+H73FJHgWmxnAYhK8ebpa5ea4UI2IiIjIgwFxlKWnmfDb/zcRTRUlWFSS7z3eoUihyLNZUXlbISpvLfRWqZBLkNmsFmSnnw1obVYL5heN8LbzD6FtVgsqbyv05uFqlZtjni4RERGRBxfVxdCC6aOxYPpobN13HHc8W+M9bm9xYGfzSTx608UBA9XGxkbk5+drntfChWpERERE2jhDHAdXXngemipKsPmnM3BudjoA4C/bDmHMz9fjlme24FSbM0gPRERERGSUlJohljeoUG58kedX67aqzo7Fr+721v/NybKoztwasdnF8IFZqP3FTDg6XfjPlbXYJB1D/eEWFP7yXwCAfz1wFcYN6WfAOyciIiIiLSkTEPtvUCFvfKHcqAIAytbU+9QEPtnmRNnLZze6UOsr0s0urOlmPH/3FXC73fjtv/fiqbf2AgCu/827AIA/zr8MN0wYGnK/RERERBRcyqRMqG1QIZM3qqisllQ3yHC6PBtdBOpL7iMSgiDg/uvGoamiBMu/Ndl7/L4VOzGyfB1e2HkCbrdxG3gQERERUQoFxME2ojjS4gjYRnkuFptdzLxoCJoqSvDWg19Dek+JttUNLRi1cD3mP1uD1o4uw+5FRERElMpSJmUi12aFPUDAKm9UodXGlmVBccVGHGlxwNSTfxyoTa7NipHnWrH9wEm43G6YBQHzpgzHktIC1VxmtZzmqjo7HnttNzp7SrSZBcDlBt7bdxwXP1oNi1mAy+VGN+DTv5Iy13mA1YLOLhfanJ7+/POjjciLJiIiIko2KRMQl80SffJ+lZQbVfjnEAOA2STgq/YunOyp/qAWDFvMvm3sLQ6f4NrldmPF9mYcPPYVdjaf6pXL7J/TvOPQCaz+4DCcLreiDyBNAIrHDsI7nxzzO+fpH4A3KPbPdZYXCsqU+dEADM2LJiIiIkoWKRMQy0FdsCoTAHpVmXC7eweTgGdWttvtRq7NitaOLtU2/rbsPxG0jcPpwqqaw6qBd5cb2Hf0K+/4/a3c3oxf3TIBgiAEzJuWKfOjtfKiGRATERFRX5YyATGgb4MKtTajyteptu12u3GwoiRgm3CpBbuyIy0OaJ11Axi1cD1mTzg/YIqIf3/hnCMiIiLqC1JmUV0k5PziQMe12oRL3rpZ676BzgPAGx99rvteuTarrvdIRERE1BcxINahbJYIq8Xsc0yZd6zVRk3xmIFB21ktZsybMhwWc++g12ISUDZLxLwpw1WvnV80Avsen41vTh4WdCyAJ/e5bJao6z0SERER9UUMiHUonZiHpXMLkGezQgCQZ7Ni6dwCn9QKtTbFYwZ6Z3LNgoD5RSOw8t6p3nbyceW/5b4BwOW3uE8A4Ow+m/Obne4bwGanm7FyezO+Vvk2rhzj2R761knagXFOlgWVtxZ600SU47dZLci0mPDA6l0ortiIqjp7uB8fERERUUJLqRziSISbfxxOu0VVDd6KEUpyeGxvcaieb+3sXSHif24rxLQLz8NPX/7QW75NNm5IP9x4ydkd8ORxGb0THxEREVEi4wxxAlpVczjiPpQ751VWS72CYQCoOXgCFz78Bmb95l2caO30Ho/WTnxEREREiYgzxDHkv/GFcuMOAUBWuhltnS7NChKhkitEBKsUIX1xBpf9agMA4PUfTovJTnxEREREiYIzxDEipyHYe0qm2Vsc2LL/hLe8mhuelAejgmHgbIUIrUoReTYrDi6dg/LZ473Hbvzde5pjYMUJIiIi6os4QxwjejbJMJLFLGDG+EEortioWo/YYhbQ2tGFUQvX6+qPFSeIiIior+IMcYzo3STDKC6XG6s/OKx5X1e3W3NnvctGDEBOlsX7Os0k4JZLczG74PyojJWIiIgonjhDHCNaWy1HSzeAbpf2/boDDGVn8yk0VZSgs6sbr9UfwfLNB/C3Dw7jrcaj+NbUCzC/6AIMzE43ftBEREREccCAOEZiGQwbJT3NhG9MGoa5l+Vh6/4v8ezmA1i24RM8s2kfvjFpGO6ZNgpjBp0T72ESERERRSRoQCyKognAHwAUAugAsECSpH2K87MBPNrzcieAH0iSlHzRX5Tl2awxT5swiiAIKL7wPBRfeB72fnEGz713EC/XfoqXappxXf5g3DNtNIpGD4QQZDtpIiIiokSkZ4a4FECmJElTRVEsAvAkgFsAQBTFfgAqAVwtSdJxURR/CuA8AMeiNeBYU5ZKU5ZFMwsCikbnYPeRM95cXJPgSUXIs1lRNkv02cSibJbos9lFMBaTAAiAM0DaQ7jXB+u7eMxAzX7HDumHim9cgp/MEvHXbYfw1+2H8Nby7ZiQ1x8Lpo1GySVDYTEzNZ2IiIiSh+AO8lW+KIrLALwvSdLfel7bJUnK6/nzLADfAdAJYDSAZyVJejFQf7t27XJnZGQYMPTo23jgDJ7eehwdYQSlGWYBP7ryPFwzup9Pfy/uPIljrV04J12AIAg409GNQdlpuHyYFR986sCx1i4Myk7Dty/LAQBv+0HZaTg/W8BHx5ze/F9rmoD2LnfQ64+2dnmD9cEq55QuPT8DS2fp342uo6sbGw98hVc+PoXDp5w4N8uMW/IHYPa4fjjHb2vpVNbe3o7MzMx4D4NCxOeWvPjskhOfW/JK1GfX1tZWO2nSpMnB2ukJiJ8F8A9Jkt7oed0MYLQkSV2iKN4Jz4zxpQC+ArAZwO2SJH2i1V9jY6M7Pz9f/zuJI62SZXrl2azYUn6NYeNpbGxEon523d1uvP3JUTy7+SC27v8S2elmfPPy4fhu8SgMH5gV7+HFXSI/O9LG55a8+OySE59b8krUZ1dbW6srINaTMnEaQD/Fa5MkSfK04pcAPpAk6XMAEEXxXXiCY82AOJlEujNbKu3sZjIJuGb8EFwzfgg+sp/Cn987iL9uO4QXtzbhhgnnY8H00bhsRE68h0lERETUi55kzy0A5gBATw5xg+JcLYAJoiieJ4piGoAiAB8bPso4iXRntlTd2W1C3gAsu/1SvPeza/D9r43Be3uPY+4ftmLuH7bgjYbP4ApU842IiIgoxvQExK8AaBdFcSuA3wB4QBTFB0VRvFmSpGMAFgKoBlADYK0kSR9Fb7ixVTZLhNUSXh4sd3YDzh+QiZ/dMB7bFl6LxTddhONfdeI/Vu7E1f+zCc9vOYjWjq7gnRARERFFWdCUCUmSugHc53d4j+L83wD8zeBxJQS5SoQRVSZSWXZGGr5TPAp3TR2JDR9/jmc3H8Rjr32MZRs+wR1TRuA7V47E0AGpOZtORERE8ceNOYIonZjXJwPbRVUNWLm9GcrkBZvVghsLh2LTnmM40uJAbpiB/aKqBqyqOQyX2w2zIGDelOGYfMFA7y8WuTYr7r9uLPZ+8RWWv3sAz20+iBsvGYoF00djQt4AY98oERERURAMiJOAshay1dIER1c3lMVBlDPSasHoktICn/4WVTVgxfbmXvdpcTh9jttbHHhg9S7cv3qX7llv/75dbjdWbG/GqvcPe3OH7S0O/N87B7B0bgHKZ4/H81uasPqDZlTtOoKi0QNx7/TRmCEOhskk9Hr/4Qbp/vT2Gcm9ldcOyk7Dz2/s3yd/uSIiIkp2DIhjKJTgSm7rX/atzdndq629xYGyl+uxZkcztuw/4T0uB6Mrtjf7BLSrag7rHrMcd9tbHFi41rOeMlBQp9W3/0I6h9OFymoJW8qvwSM3XYQfXzcWqz9oxvNbmnDPizswelA27pk2ChaTCY++utu7oYnecQRSVWf32SRFq0+97fTc42hrV8TjJiIioujglmIxIgdI9hYH3DgbXFXV2QO21cvpcvsEw/6U93MFqT2tRQ5iAwmlb+X727TnKF7cegifnWpHTpYFzq5uPPzKRyhf+2Gv3f30jCOQympJV59620VyDyIiIoo/BsQxEkqApNbWCPL9zIIQdh/BaiuH2ndVnb3XLwAn25w4dqYDP5xxIbQqtEVS41nrWv/jettFcg8iIiKKPwbEMRJKgBTNoOlIiwPzpgwP+/pgtZVD7buyWlLa0uYcAAAgAElEQVT9BaC9qxtr6+zI07jfwOx0BNtlUYvWe/A/rrddJPcgIiKi+GNAHCOhBEjRDJpybVYsKS3A/KIR0JrLFfz+LdNTW9l/AV8wR1ocAX9Z0KoF/WVrJ2b/djNerv0UHV2hzaar9an23vS2i+QeREREFH8MiGMklAApnA1BTACy04Nf09bZhao6OyZfMBC2LItqG7nOsvxvwFPJYuncAl0LwrRmddXk2qwBf1konZiHpXMLkGezQujp+39uvQS/vvUSuN3AT9bUY/p/b8Izm/ahpa1T1z3V+lR7b3rb6bnH4Ow03dcSERFRbAnhfu0crsbGRnd+fn5M75kowqkycaTFgUyLCR1d3eh2Q7Wu7wCrBa2dXXC6fJ9llsUENwCHX2UKi0kABPRqr8VqMYcUzPlXWNBiMQmovK0QAHq113NPt9uNzXuPY/nmA9i89zisFjNunTQM90wbhZHnZesaa6w0NjYiVX/ukxmfW/Lis0tOfG7JK1GfXW1tbe2kSZMmB2vHsmsxFMomH2pt/X/Y5PPFFRu9u+Up5WRnAECvahVOrZVqGuTFeKGMHYBq2TilytsKffoMtd6vIAi4atwgXDVuEKTPz+DZzQew+oPDWFFzCDPzh2DB9NG4fGQOhAgWERIREVHfx4C4D4hFRYNQ+5ID+uKKjapBcV5POoR/+3CJ5/dD5W2FKLtBxF+3HcKK7Yfwr4+/QOGwAbhn+mjMmXA+0szMECIiIqLeGCH0AYFycI1aoBduP7FeXDa4XyYeul7E1vJrsaR0As60d+FHq+rwtcq38ezmAzjd3nsmnYiIiFIbA+I+IFDQqXbOYhJgMetPI4gkgI1kYVokrOlmzC+6AG89+DU8+63JGJZjxZJ1jbhy6UYsef1jfHqyLar3JyIiouTBlIk+QJmzq5WD638u0DF7iwNmQYDL7fbZ8jmS8cWruoLJJOC6i4bguouGoOHTU3j2vQN4fmsTnt/ahNkTzseC6aNx6XBbXMZGREREiYEBcR8RKOjUOqf3WF9RMGwAfvv/JuJnN4zHC1ubsKqmGa9/+BkuH5mDBdNH47r8ITCbuACPiIgo1TBlglJOrs2Kn8/Jx7afX4tf3HgRjrS04/t/rcW1T76Nv2xrQltnV7yHSERERDHEgJhS1jkZabhn2ii8U3Y1nrnjMtiy0vHIP3dj6tKN+PWbe/DF6fZ4D5GIiIhigCkTlPLSzCaUXDIUJZcMRe2hE1j+7kH87zv7sXzzAdxUmIsF00bjotz+8R4mERERRQkDYiKFSRcMxKS7BuLQl614fksT/r7jMNbutGPahefhnumjcPW4Qdzog4iIqI9hygSRigvOzcbimy/GtvJr8bMbxmPv0TO4+/kPcP1v3sXf3m9Ge5BtqYmIiCh5cIaYYqKqzh7S1syhtte6bsb4Qdi051jI/cgGZFnwH1ePwT3TRmFdwxEsf/cgytc2oLJawl1TL8BdRRfg3HMydPdHREREiYcBMUVdVZ0dC9c2wNEzq2pvcWDh2gYA6mXeQm0f6LoV25u95/X2oyY9zYSvTxyG0kvzsG3/l3j2vYN46q29+N+392PuZcNwz7RRuHDwOSH1SURERImBAXEfpjbLCmhv4LGoqgGrag7D5XbDLAgoGp2Dpi8dqm2VfQ+wWtDZ5UKbs9t775wsCx696WKUTsxDZbXkDVJlDqcLldWSamAaavtA1/nT008ggiDgygvPw5UXnod9R8/gufeasHbnp1j1fjOuGT8YC6aPwtTR5zLPmIiIKIkwIO6j1GZLy16uB9yAs9vtPSbPmO44dMJnNtXldmPL/hPe18q2AHz6bnE4e93/ZJvTcz8AR1ocqmM06rje86G2C+bCwf2wdG4BfnL9OKzY3oy/bGvCHctrcHFufyyYPgolBblIT2OaPhERUaJjQNxHqc2WOl3uXu3kGdPPTwWvuetwurD41d04094Fl7t3X/6cLjce+ns9tFrm2qyax+0qQat/e+UstS3LEnQ8yn6MzDU+95wM/Pi6sfj+10bj0X/uxj92fooHVtfjwdX1SDMJ3l9AgAOwWS1YfPPFfXpHQCIiomTD6as+KpRZ0CMtDl0BLuCZDdbbFoBmW6vF7E3h8Ddj/KCgx+UZcHuLA254ZqT1jMpqMWPG+EE+18q5xsrXC9c2oKrOrqPHs9786HO8Wn8EXT0BsBtQBMMeLQ4nytbUh9w3ERERRQ8D4j5Ka/ZVq605hjmveTYrls4t0Jwl3bTnWNDjevKFzYKA+UUjkGezQlDcd9OeY7pzjUOhZ0yAJ0gOtW8iIiKKHqZM9FFls0SfPF8AsJgFnxxi4OxMrX8OcbQIALaUXxOwjZ4cYj0z4N1uN5aUFvQ6/sDqXUGv1XuPcNvbWxz4wUs7seybhchIM4d0HyIiIjIWA+I+Sp591VtlQm4vV5lQYxKAbpVTggBY00w+VSa02uqZudaTQ6zVRs+99Fzrf72cc+x/3djB2djw4NUh9Stb9+FnWPfhZ8jOMKNfhgVfnG6HLcuCDqdvxQ61vGNlDrQAoNuvb7MgYN6U4aq/ECjfi1kQ4HK7kRdGjWYiIqK+ggFxH6YMdP2Pq1lSWoAlpQW9KlQAnpnkb0zKwz9q7b2Oq6U/aPWhlTespDa77X+tWhulQPcKdq3/9WrvRbb3aCtmLnsbGx68Wle/alo7XGjt8Fxzsq13xQ457xjwPDv/8aj9+uJyu70z/sqg2P9a+ZefSGo0ExERJTvmEFMvpRPzsHRuQa/c2yWlBarHtYJuvW3Duda/TU6WBTarRde91PpXyzVWzrIHCnL3Hm316Tca+djKvGO9ucqAZ8ZfKdC14eRNExER9QWcISZVgWaX9c4ghtI2HP79K9MIKqsl7Dh0Aus+/Mw766pMPQhlbKHkBpdOzNOdoxwqeRyhjMc//cWoWs5ERER9CWeIKeH4l1TTUwZN7ZoV25t9UhDCLXkWSsWOcNrrNaR/Zsj9+89WB7s2WmMnIiJKZAyIKeEE2ro5lGvUhFPyrGyWCKtFuxLE2MHZvdpbTManTXx+uh0jy9fhjitGBByP0rwpw3uNTetavTneREREfQ0DYko44WzdHOpGJKFQ5hz7U1aZULavvK0QNqvv7nn+r/3JudBZFt+/lgMy01BSMNT7uvJfnuA/J8uTM632l1iuwexfZcL/vcgzyKHkeBMREfU1zCGmhKN362Y912i1DVWo+dD+7RsbG5Gfn4/iio2q48yzWYPWZ34GwCbpKO5+/gMAZytSLJg+Cgtn58Okc1Y62rndREREyYYBMSUcPWXX9FyjxmIS4poWEM57U5ohDkZTRQkOHm/FjU9vRmunC8s3H8TyzQdxxaiBeO7bk9EvM/BMdDJRLpRU1s3WOm70vcTM4GOJ1lij8R6JiEidefHixTG94fHjxxcPGjQopvfsK44fP45U+OzGD+2PYTlWNNhP4av2LuTZrHjkposCBgNq19xyaS4On2hDe88mFzarBU/EKS1AfnbhvDc1OVnp+MGMC7Fg+mjUNbfg05MO2Fsc+N+39+OP7+zHnIKhyMlOj9K7iQ15oeSJtk4AwJn2LrzzyTF8ftqB323c1+v4sBwrxg/tb+i9BmWbccW4PM3z8j2NHmuw+1FwqfLfy76Gzy15Jeqz++yzzz7Lzc39U7B2gltjV7JoaWxsdOfn58f0nn2F/LW7rKrOjsWv7kaLw/PVeU6WBY/edDEA9d3o1Gj1oXdma1FVg3d3O7MgYPSgLBw41uZ9XTQ6B01fOlJ+lsv/2Rmtu9uN/67eg/9754DP8T9/ZzKuGT8kaveNJq30Enl3PX960k5Cvdfg7DS8/4tZQVNdjB5rJKk15BHtv3MUHXxuyStRn11tbW3tpEmTJgdrx5SJJFVVZ0fZmno4Ffsjn2xz4qE19TAB3uOBdiDT6qPs5XrsOHTCZ1c6tX4WVTV4d0MDPDVv5U0q5Ndb9p/wvuZuaNFjMglYODsfC2fn4/UPj+C/XqoDAHz3hR0AgAdnjsMPr7kQQhQ2DYkWrcWPWluLR1JDWevaY61dAc8Hqw0d7ljDWVhKREThY5WJJFVZLfkEsjJXt7vXca2SZVp9OF1urKo5HLT0mf8uaHpwN7Tou/GSXDRVlOCNH0/3Hlu24ROMWrgeC178AO0hbi0dL1qLH7V2AoykhrLWtYOy0wKel48bXas62P2IiMhYDIiTVKgzRWrtA/WhZ2ZLq004YyHj5Q/tj6aKEux6ZCYm5HnyTt9qPIrxv3gTk5e8pfqV/J3Lt2Fk+TrvP3cu32bomKrq7Ciu2IhR5etQXLEx4CYpajWTrRYz5k0Z3uu4AM83EMH6DOVeANDe1e35JkVjLPJiyGC1qtWuW1TVgDEL12Nk+TqMWbgei6oaAo6HdaKJiKKHAXGSMmJGKlAfembhtNqEMxaKHltWOl7/4XTsf2IO7pwyAgBw/KsOFFdsxMjyddh+4EsAnmBYmeICAFv2nzAsKA51B0JlzWQBZ2slLykt8KmlLACQfzXTs6thoHv514o+3dHtTfNRG4uc+iNfH4jyuh2HTmDF9mbvL5Uutxsrtjd7g2Kt985UIyKi6OCiuiSiTFhXy/8FALNJ8MkhBjwzS2r/M9Xqw2IWcPvlw31yiNX68c8h1kNrLH1doi02WP1BM372j4bgDXs0VZREfM9oLBQzus9I+9N7/ZiF61W/YTELAvYvnRPiqElNov2dI3343JJXoj47Lqrr4+SAMpIqE4H6KJ2Yh8kXDPT2M8BqgSAAD6zehcWv7oYgAC1tTqSbBXS6zv6PfUi/dBz/yqlZZWLG+EGorJbwwOpduqpO6K3FGk7N1lSu83r75SNw++UjsLP5JOb+YWtM7hmNhWJG9xlpf3rrTGulG4WbhkRERJFhQJzEAu04pjewC9aHXH5N+T95OXgG4BMMA8Dpdhee/GahZtCq7CdY1Qm97UPtN9xr+qLLRuSgqaIER0+344on/h3Ve4WzA2Gs+4y0P/lnJ9gvWlrl2MJNQyIiosgwIKagKquloDvAyeQqEmo7eKkFGsr2/jO2rR1dmpUuSifm+dRA1jOOYO/J4XShbM0u3L96l/dY8ZiBWHnvVNU+jJhh9q/jPG/KcCwpDZyLGg2D+2eieMzAXjnEsvrDLSgcbovoHpHu0heLPo3oT8/W2POmDFdNN5o3Zbj+wRIRkWG4qI6CiqSihXIhVaD2aguulDPRSvYWB0aWr/NZlKTVzn/1vtoYlXo2tfPasv8Epjy+oVe7UBeIqZFzsLUWVsXaynunonjMQNVztzyzBSPL12HNjtBL7cmisVDM6D79+xucnRaVnPclpQWYXzTCOyNsFgTMLxoRl1+GiIiIi+qSSrwS1rUWCmlRLiDSc61cLSCUe4TKP9gI9T3pvV5r8ZXas0uWhVVb9x3HHc/W+By7q+gCLL75YphNffsr/kRdJELB8dklJz635JWoz07vojrOEFNQ4dRYlQWbXZbbR7s2sf8mIqG8J7XrjVjMlSwLq6688Dw0VZRg809nYGB2OgDgr9sPYczP1+OW37+HU23qM/lERETJImgOsSiKJgB/AFAIoAPAAkmS9inOPw2gGMCZnkO3SJJ0KgpjpTjxXygkV5xoaXP6/Fktj1ZrkZJM/jpaK8c4J8uCrPQ0HOlJTQiXf5Cptvgp0Dj9r9dqb8uyoLhio6684mRbWDV8YBZ2/mImHJ0u/MfKWrwtHUP9p6dQ+Mt/AQD+9cBVGDekX5xHSUREFDo9i+pKAWRKkjRVFMUiAE8CuEVx/jIAsyRJOh6NAVJi0LNQSE3ZLNFnkZqSWRC8fWotZpJLwAHaKQZ6qH2z7/+e1DamUI5Vacb4QaqLok61OXGyZ8ZUWblCzOzdZ7IurLKmm/HC3VfA7Xbjqbf24rf/3gsAuP437wIA/jj/MtwwYWg8h0hERBQSPSkT0wC8CQCSJG0H4M3D6Jk9HgvgT6IobhFF8btRGSUlrdKJeZoLtZSBn57FUYECRbMgwGrR/nHOSAv+o77y3qkY0i896FgBYNOeY6rt/NbkeatdqEn2hVWCIOCBmePQVFGC5d86m55134qdGFm+DpXVexDrNQpEREThCLqoThTFZwH8Q5KkN3peNwMYLUlSlyiK/QD8GMAyAGYAmwB8V5KkD7X627VrlzsjI8Oo8aeU9vZ2ZGaqTDUmgd9vP4Y3PjmDbrdntnb2uH74r6JBhvYz58UDmmkVAoD13x5t2FgD3Uvt3mtvz03aZxeKw6c68Z+vfoouxW8GE4da8YsZQwL+wpKokvnvXKrjs0tOfG7JK1GfXVtbm2E71Z0GoEwMNEmS1CXfB8BvJUlqAwBRFDfCk2usGRBnZGQk5CrEZJCoKzj1eMagcQfqJ9f2mWYecK7Nqvuz0zPWQPdSu3dmZmbMnp3e2sb+KSKBai7rlQ9gX1EhTrc78d3nP8COQydR95kDc19qQr+MNLz+o2m44NzsoP1EY2zhSOa/c6mOzy458bklr0R9drW1tbra6Zmy2QJgDgD05BAri6SOA/CeKIpmURQt8KRX7AxtqETGKJslwqKSLGwxCxFt/qB1L/8qFRaz0Ov+kW48ESq9tY3V8qW37D+BO5dvM2Qc/TMtePk/rsSBJ+bgu8WjAABnOrrwtcq3MbJ8Hd79RD3lJBZjIyIi8qdnhvgVADNFUdwKz7e/d4ui+CCAfZIkvSqK4koA2wE4AfxFkqTd0RsupYJwd2+T840Xv7rbu6mHAMDpcuP+1buw+NXdWHzzxb0WByp3nLNlWdDhdKGtZ4cOm9Wieo2ySoU8U+x09U6iGJaTidKJeWhsPK37/WvtgKfnc/EvD6c8rmyrtXhQ63i4TCYBj9x0ER656SK8UvcpHlhdDwD41p/fBwCUzx6P7181GoJi0WKsxkZERCQLGhBLktQN4D6/w3sU538N4NcGj4sSjFaQptyWWS4jltdzHvANTnOyLD5VI9T6HXmu1SfwkWc4AWDyBQN7jQFAr2O7Hr0eVXV2lL1c7xOktjicKFvjCcjkMcg7zsnVLU761dRVu0ZWOjEPOw6dUK0UIdt7tBV3Lt+GRdP0bXvsPx65UsWaHc2an4sy0E3k2sZfnzgMX584DB/ZT+HG370HAKh4Yw8q3tiD2RPOx29uvxSZIdSGJiIiMoqeGWJKcVpB2o5DJ/CPWrv3uBx02VscKHu5Hi6X26fqwsk2J8pePhtcqvWrlZe7cnuzz73ke8ANOLvP3lcuc1ZZLanO2Dq73aislnxmeJWl3tT4X6OkNSOrtGX/CUBnQKw2HofTpTk76j/zmwy1jSfkDUBTRQm+/KoDdyyvgfTFGbzx0ed446M3kTsg8RZkEBFR35d8y74p5rSCtFU1hzWDSadfMKw8Lpch0xOMytw99/TvSw6GleOSZ4y1KM/p3VlOq53RM6+h7tjnf3+t0nT+x7VK4Wkdj4Zzz8lA9QNXYd/js/HNycMAAEdOtWu2D3VsVXV2FFdsxKjydSiu2IiqOntE442GZBgjEVEqYEBMQRkdDMr9RWu7Zjl9QovyXKB2WtcoGT3zqnc8WvfXW9t45b1TewWY8arkkGY24de3FqKpogS/Kp2g2ibUscnfPth7djiUvz1IpIAzGcZIRJQqGBBTUEYHg3J/oQR/2en6c0vlXGKLWaXihMm34oRatYhg1yjp2VUulJlNtfFYLWZdm5vIlpQWYP/SOWiqKMH+pXM0FySuvHcqmipKvP/EIxj2d1fRBWiqKMGa+3zHsmX/Cfz05Xp0udS+d+hN61sNrU1S4iEZxkhElCoYEFNQWkHavCnDNYNJi1lQ/eFSlkALFPz5z3A+/vWCkMqclU7MQ+WthcjJsnjP2awWVN5W6JML7L9DXk6WBVmKDSTUrlHyn5H1F+rMptaOfSvvnZrUu9qF6vKRA9FUUYJtC6/x5hX/fcenuPDhNzDrN+/iRGtnwOu1vn2I1rcS4UiGMRIRpQouqqOglAvQ/KtMyJUfwqkyEahfLXqqTCj7D9SX8v3paadlSWmBoYGp1niMvk8yGDrAiq0Lr0W704X7/7YLb+7+HNIXZ3DZrzYAAF7/4TRMyBvQ67pcm1V1gWaoKSnRlAxjJCJKFQyISRetIC1YMBks0AwlGA00BurbMi1m/PGuSXC73fjjOwfw3296Kj/K5dueuv1Sn5+DslmiTwUTIPabpASTDGMkIkoVTJkgoqQhCAL+4+oxaKoowYvfvcJ7/P7VuzCyfB1+9frH6O52a6aeJNIvT8kwRiKiVMEZYkpI/ht2zBg/CJv2HNOVWqG1iUi8VNXZ8cTrzTjWeiAhxtNXfG3cIDRVlODQl6248en3cKajC8+9dxDPvXcQky/IwZ/vvjzhP+dI03WIiMgYDIgp4aht2KHcDU65AYfaNsxqm4iotY2FRBtPX3TBudloeGwWWju68P2/1uK9fcex49BJXLL4X7CYBbzx46tw4eBz4j1MIiJKYEyZoISjZ8MOrfJUiVbKKtHGY4RFVQ0Ys3A9Rpavw5iF67GoqiHeQwIAZGekYcWCKTi4dA5+MGMMAM/mLdctewcjy9fhrY+/iPMIiYgoUTEgpoQTye5xiVbKKtHGE6lFVQ1Ysb3ZuymLy+3Giu3NCRMUA54847JZ49FUUYI/3HmZ9/iCv+zAyPJ1eOqtT+A2eIdBIiJKbgyIKeFEsnuc1rXxKmWVaOOJ1KqawyEdj7c5BUPRVFGC6vuv8h576q29GLVwPe5+/n04OvVtHU5ERH0bc4gp4aiVo/KnVZ4q3FJWyoV4WelmtHW64IZnA4x5U4brqv+7qKoBq2oOw+V2e68zurSWEeOMhNZ23eFu4x0r4vn90FRRglNtTnzrzzWo//QUNknHkP/ImxiYnY5//qAYwwdmxXuYREQUJ5whpoSjVo5qftEIXeWpwillJS98s7c44AbQ2hNkAvpTArRSCXYcOoGlcwswODst4tJaRowzUlo78oW7jXesDciy4J//NQ37n5iDu4ouAACcaO3E9F9vwsjyddi673icR0hERPHAGWJKSJGUowr1Wj2L+FbVHA44+xoolWBJaQHEzNPIz8/XPaZojTNS86YM96n4oTwejNoMerx23jObBEy6IAcb9xz12S3ujmdrAAC/uPEi3DNtVFzGRkREsceAmFKengVuwVICYpFKYMQ4IyUHsKEGtvIMunKc8ut4BMX+5fAAIMNsQoerGwDwq9c/xq9e/xhXj8rGn8aKuPv5GmzZf8LbtnjMQKy8d2rMx01ERNHBlAlKeXoWuAVLCYhFKoER4zTCktIC7F86B00VJdi/dI6ugDbRFuOpzbZ3uLqRZ7Pi/YevxejzsgEAbx9sxbhFb/gEwwCwZf8J3Ll8W8zGS0RE0cWAmFJe2SwRVos5YJtgKQFa5/WkEuhlxDjjJdEW4wUqhze4XyY2/uRqfLJkNmaM1t7Qwz9IJiKi5MWUCUp5cr5xJNUbwk0liPU448UsCKrBb7wW4+XarD65w8rjsvQ0E346fTA2HfgqlkMLW6AtyyPdzjwR8r/1vAdlm0HZafj5jf25IyQR6cKAmAiRLeKTLSktiHqQYMQ44yGSxXjRYFQ5vJHl63DnlBH45S0TYDbFr9JGoC3CAUS0fXgi5H/r2QLdv83R1i5uk05EujFlgoiibklpAeYXjfDOCJsFAfOLRsRtRjuU8nzFYwaq9mExe97LyppmjPn5etz4u81oaeuM5rA1BdoiPNLtwxMh/1vPe+iL26QTUexwhphIh0i/co7WmB57bTdOtjkBADarBYtvvjjscRnxHgN9tR6LGXTg7PvwT4kYOzgbGx68OuT+Vt47FXcu3+aTM5yRZsJ/f+MS3DDhfPxg5U78e89RfGQ/jUt/uQEA8Ob90zH+/P4RvY9QhLNFuN7twxMh/1vP++tr26QTUWwxICYKQs/XtaH0JQedA6wWCALQ0uYMOeezqs6Ospfr4XSdDUpaHE6UrakPe1xla+rh7HZ73+ODq3fhsdd2q45PTSJ+ta6092grZi57GxsevDrkZ3rb5BHY2XzK276jq9vb/rnvXA63243fbdyHZRs+AQDc8NRmAMAzd1yGkkuGGv9G/QTLiQ6WLx1IIuR/68n51tOGiEgLUyYopUx5fANGlq/z/jPl8Q1BrzHqq1j/neZaHE6cbHPCjbMBWVWdvVc75TnlmJTBsMzZ7Q7rK+LFr+72BsOybkB1fFoS9at1pb1HWzXbBXqmwdoLgoAfXTsWTRUleO7bk71tfvDSTowsX4eKN/bAHcUZVbUKJHJOdKBzesSigkowet5DpO+TiFIbZ4gpZUx5fAO+OOOb4/nFmU5MeXwDah6eqXmdUV/FBgvWlAGWVvAlz15G+lW4/wx0i8MZ9Br/MfgL9tW60SkeavQ+k1CfaSjHr80f4qnRfOwrzPntZnR0deOP7+zHH9/Zj6mjz8Xyb0/GORnG/qfXvwKJ2ox+uOkwsaigEoye9+ffxlNlYkLcU5uIKDkwIKaU4R8MBzsuM+qrWD3Bmt5AV2tMesalli6gV6DxBfpq3egUDy2BPhc97bQ+u3B+BsYMOgfSktk40+7EPS/uwPsHT2DbgS8x4dFqZKebse5H0zGyZwMQIwSqQKJ1Tm/eeKzyvwPRU2FFbrOoqgEv1TTj/tW78NDf6xO6JCERJQamTBAFYdRXsXoC6FybNWBQphyTXOVAyWISgo4r2Ex1sPFpCfTVutEpHlqCbV4ydnC2ZrtAzzSSn4F+mRb8/ftTceCJOfjeVaMBAK2dLlz9P29jZPk6vC0dDdqHHjOXve2TDjRz2dsB2+tJzUlGci67nAEk57IvqmoIfCERpTQGxERBhFKiK5BgwVMoOZ+lE/NQeWshcrIs3mM2qwWVtxUGHVe4q+6DBYCBSqsZUe1AD+Wz8qesMhHqMzXiZ8BkEvDzOfloqijB0/Mmeo9/5/kPMLJ8HZ7ZtE8zz3hRVQPGLFyPkeXrMGbh+kXxchcAACAASURBVF7B3cxlb3vzo2XyIkItfbVMWSLkshNR8mHKBKWMIf3SVdMjhvRLD3qt/FWs/BXzA6t3obJa0p2LufHAGbzU8JnmebMgeAOsqjo7MtJM3mAlJ8uCR2/qnWvr/xXyoqoGPPT3ety/ehfMgoDRg7Jw4Fhbr7xPra//c7IsyEpP8359PmP8IGzac0z3zmByG7WvpiNJ8VC+Pz15rHo3L1Fr53+PG8adg2fy80PqV0krJeHmwlzcXJiL3UdOoeTp9wDAWzN4YLYFW8uvRWbPL0V6qnf4B8MyreNA3y1Tlghl4ogo+TAgppRR8/DMXgvrhvRLD7igTinc8mtVdXY8vfU4OlRSBmTzpgz3BsP+ZcPand1Bx6YWNCmDIWUQpbVLm1rQHUgon0fZLLFXDjGgL8VD6/0ZXdJN7R7rpDPIqWoI6x56Pp8n1n3c67oTrU6M/8WbOL9/Jtb+55UBZzwjee99tUyZkWXiErH+OBFFB1MmKKXUPDwTTRUl3n/0BsNA+F8xV1ZLAYNhANi051hE99D7dfCqmsOGpYCEMtZIUjwAqG77LL8foxj9Vbuez0e52Ye/z0+348qKjVGb8eyrZcqMKhPXV3OsiUgdZ4iJdAr3K+ZQqkuEew+9wZHcLpyv//WOSet4uPe8c/k2zXNGfg1udOAZaUrCE18vwM9f0V4IppzxHDs4WzU9Ql5EqEZPKbNQ6E1pCVeg/v3PjR2cjf3HWqEsrS3/YqN3TIF+oYnFLHG0P08i8sWAmEincL9i1lMKTO4j3HtofU2s1s4osfrKPdAsqpHvx+gd2SL9fO6YMgJ3TBmB7/91B6p3f9Hr/O2XD/P+ecODV/daWKdnq2ojfjECop/SEqh/AKrpQiP6m9F82qV6jZ4xhfILTSSpFWqBr9p7ivWuj0SphikTRDqF+xVz2SwRGSol0tT6CPceer8ONnJ3sWh95e5fUSEQI99PuF+1a1WA0CoBN/LcswFx8ZiBqn0qj//fXZMxv2hEr/9Yv/T+YVy37B0c/6oDgCcoVqYDBQuGg1WuCEW0KzsE6l/rnDIYDmdMesofApGlVsiBvvyLmBz4xiJFiIh8MSAm0inc3NvSiXn40ZXnea+zWS3IybKo9hHuPdRKno0dnK1aAs0oRuUiK6kFCIEY+X7UPsMSsV/Ae2gFNIuqGlA6MQ+XjRjQ65ot+094g8+V907tFRQXjxmIlfdO7TW2Az2BrrTkBpQUDAUA7Dv6FSYveQsjy9eh4dNTut9roHGHI9qVHQL1H+o99LbX+wtfJOXrQg1wWSmDKHqYMkEUgnC/Yr5mdD/8oOSKqN4jHruJGfWVu0xrZkyN1uxqJPw/w8bGxoDtg1WA2H7gZMDzAHoFv8FkpJnxzJ2X4fduN5ZvPoAn1u8BANz0e0/5tmXfLMTcy4YF6sLwyhVGp5uE2n8ogaLeMenNsY4kVzzUANfIFCEi8sWAmIiSjtosajxKZAWbGY3mzKkgCPjeVWPwvavGYPPeY7jrufcBAA/+vR4P/r0e37lyJB658SKYTL2DKKPHNW/KcNVfZoxKaQnWv9o5/xzicMak5xe+SHLFtQJ9AYDakzAyRYiIfDEgJqKk0FRRonku3BrRkQo2cxntmVPZ9LGD0FRRguYv23DT79/DKYcTL2xtwgtbmzBxhA0v3H0FBljPlrwzelzyrHK0qiLo6d//3J1iGlZKXVGv1KBV11tPLr1WoH9n0QgA0fs8iag3BsRElPTiVSIr2MxltGdO/Y04Nwv1j16Pts4u3LdiJ9795BjqmltQ+Ni/YBKA6vuvwtgh/aIyrmin7ATqX+1cY2NjTNKIIilfFyzQZwBMFDsMiIkoYYRTTxeI3zbEegOaWM/0ZaWn4S/fvQJutxvLNnyC323ch243MPM37wIA/u+uSXEZV18VSS59PHL/iag3BsREZKhINhQIt55uPLch9g9o5HJmyve/f+mcqI9DjSAIeOh6EQ9dL+LNjz7HfStqAQDf/6vn3z+85kI8OHMcBC7W6pO49TSRfgyIicgwRmzQECz4VRNJHqeRor1BRSRumHA+mipKsPeLM5j11LvodgO/27gPv9u4D1eNG4Q/zr8MWen8X0JfEa+8eqJkxf/6EZFhQinnFc5MsBajtyEOl9HlzKJh7JB+OLC0BKccTnzn+fdR19yCdz85hoseqYYty4LX/msahg/MivcwKULx3no6GXG77NTGgJiIDKO3nJd/MAwAe4+2YuaytyMKiuP9P/pob1BhpAFWC175z2K4ut341esf44WtTWhpc2L6rzcBAFbcMwXTxp6neX1f/zo+md9fVZ1dc7v4aOfVJ6tg3+4wWA5PMv09YkBMRDGntnAu0PFkEW45szuXb8OW/Se8r9XqLEeL2SRg8c0XY/HNF+MftZ/ioTX1AID5z9UAAB6ek497rxrtc01f/zo+md+fPHYtscirT0bBth9P1FSoRJZsf4+4dTMRkUG0ypYFKmfmHwwDnu2d71y+zdCx6fGNScPQVFGCV/+r2Hvs8fWNGFm+Dj94aSc6ujz/Y4tku+JkkMzvT23ssnjk1SeLQN/uBAuWSV2y/T3iDDERkUHCKbPmHwwHOx4LlwyzoamiBMe/6sDt/7cN+4+1Yt2Hn2Hdh59hWI56RQ+g73wdH68yfkYINMalcwsScmYuEQT6dieZUqESSbL9PWJATEQxF2694WTQl+rKnndOBv790NVwurrxs398iLU77fj0pPb/zNLC/M4x0fIzo1HGL1a5lFpjz7NZGQwHEGizGvln05/RO072NfEshxkOpkwQkWGKxwzUdXzDg1f3Cn4jqTJB0WUxm7Dsm5eiqaIEj918sWY7Z3fofcuLmeSAQ87PXFSlnQcbbWWzRFgtZp9jkaQbyLmU9hYH3DibS1lVZzdgtL6MHnuqWFJagPlFI3y2XZ9fNAJLSgvCSoWi5PtZ5AwxERlm5b1TdS8QS4Tg16hZu0hmOIvHDFRNj9D65SLevn3lSDz66m7N812ubqSZ9c+16C1VF8uFh0aX8YtlCbREKUGYjLS+3YnXjpPJLtl+FoMGxKIomgD8AUAhgA4ACyRJ2qfSZh2Af0qS9MdoDJSIkkOsqiNEyqgV0JFuxhHol4hESyUAEHRW88KH30D+0P54acEU5GSnB+1PT35moIWH0QyKjfofd6xzKROhBGFf05dSoWIpmX4W9cwQlwLIlCRpqiiKRQCeBHCLX5slABJzOoOISIVRs3ZGbMahFtQl6q53elaIN352GhN/tQEAsP5H03FRbn/NtnpK1SXiwsNQJFsuJVEq0hMQTwPwJgBIkrRdFMXJypOiKN4KoBvAG3pu2NHRgcbGxlDHSQDa29v52SUpPrvEE2jWTn5Wep5boBnOSJ75SzW9F/jIx+8U45ftFmhW89LzM/DE9bn4W0ML/lJ3EgAw5+nNAIDyqwbja6PO6XXNDePOwTrpjOpxPZ+fVptE+jt3R8E5eHprOzpcZ39WMswC7ijQ9x5TSSI9NwpNsj87Pf9V7Q/glOK1SxTFNEmSukRRnADgDgC3AnhEzw0zMjKQn58f+kgJjY2N/OySFJ9d4sm1faY5ayc/Kz3PzSwc1JzhzM/PDztPudt9QOM44vqzpPW5ZaSZUHX/dQCAX14E/PJ2YNOeo7j7hQ8AABXvHkXFu0fxvatGo/yG8TCZPDPAz+TnIydoaoj6ZwFofxaJ9HcuPx/Iy02eHbviKZGeG4UmUZ9dbW2trnZ6AuLTAPopXpskSerq+fO3AOQB2AhgJIBOURSbJEl6U/9QiYhir2yW6JNDDIS3AjpQuaZI8pTD3fUu2rQ+t6Vze6dxzBg/GE0VJTh4vBUlT29GW6cLf3r3AP707gFcMWognvv2ZPTLtATNz0y2hYdq4pFLmYg56ESJSs9S4C0A5gBATw6xtxaOJEk/lSRpiiRJVwN4AcAyBsNElAxKJ+Zh6dwC5NmsEOCp0xrOxgWByjVFslNTopZ6CudzG3VeNv5/e3caJlV1r238rmZoFHCeh1ggskFUUFAZRImIDGWOJtGoJ2rUl0SNxjjkmEIEQRRKjUP0mBijRo2aaKLGoZhEERxQBAElwkKGQuOI4oBgM3WfD431EiJ2MzS7quv+fer6V9H1XKwLeNi9aq83r+rDzKG96dyyusROXrCYA4eMpc2gUcxf9OW3vucDP+3yH+V3Sx5vXYwK8XZ2UiGrzRXix4BeURS9BCSAs6IougSYG0J4ok7TSVId2lxX7dZ3hXNT7i5QH2/11Ky8IX/9WRcqK6u4dsxs/jBhPhUrKzn6hgkA3H1mJ45us+s3/lrL74bZHB/2lEpJjYU4hFAJnLvOePY3vG7IZsokSfXCpt5doBBv9bQ5bldXVpZgQN+2DOjblqdef48LHpwGwNn3TAHgkl6t+cXRrUh4EthG87hhacN4Up0k1ZFiO6mpNjZlG8g3Oe6gPchlUoz6Zff87Man59BiwEj63/sqFeu8l/7dP6a9S7fMs7RIZ+mWeTZ/n+j17TWPew+6VKgsxJJURzbXPuVCUleHTLTdfRtymRTTBvWi3Zr7Fo+b9RFtBo2m09XjvvFKe6n7tiOhC3UPulSoPLpZkupQMZ3UVBt1fcjE9k0bk72wO6tWVzL4iX/y4Ctv8/GXy+mWeRaAv/6sM51b7rhZ3qvYfdvV+hfTRwP1aw+6VJcsxJKkWttct6urScMGZQz//oEM//6BPPTq2/z6kep9yqfc8TIAQ763P2d2a7FZ37PY1HS1vhD3oEuFyi0TkqRai2MbyMmHfodcJsWjP++anw158k2S6SwXPzSdlasr6+y9C9n6rsp7JLS04bxCLEnaIHFtAznkO9uTy6T46IsKTvrDJBZ+sozHpr3LY9PepeVOTXnonC7s3Lx8i+eKy5a6Wi+VAguxJKmo7LJNEyb8z3dZsaqSS/82gydnvMf8j5dy6DXjAHj8/G40jjnjlvD1f0o8ElradBZiSVJRatywjFtPPZhbTz2YO5+fz9XZWQAcf9uLAFx/YjNO6lS/76pQ3z60KcXFPcSSpKLXv3tLcpkUD/Q/PD/7n7+/TjKdZfDjM1ld6YEUktbPQixJqje6tdqJXCbFPT/cmx2aVm+cuG/SQva9fCTH3/Yiny9bGXNCSYXIQixJqnd2bdaI1wb14s2retMj2hmAGe98RvurxpJMZ5nz4ZKYE0oqJBZiSVK9tXXjhtxz1mEsGNGPX/bcLz8/9qaJJNNZRs98P8Z0kgqFhViSVO8lEgku7tWaXCbFHad3zM/Pvf81kuks14+ZTVWV+4ylUmUhliSVlGPb7UYuk2LcJUfSsCwBwG3j59FiwEhOu/MVli5fFXNCSVuahViSVJJa7dKcucP78fqQY+m4z/YAvDD3Y9pdOYYDrxzDwk+WxpxQ0pZiIZYklbRtmjTikfO6Mn94P87u1gKAJctXcdT1z5FMZ5k4Z1HMCSXVNQuxJElAWVmCwd/bn1wmxU0nt8/Pz7h7Msl0ltsnzHOfsVRPWYglSVrH9w/ei1wmxVO/OCI/y4yaTYsBIznv/qlUrFwdYzpJm5uFWJKk9Thgz23JZVJMveIYol2bAzBq5ge0GTSariOe4YPPK2JOKGlzsBBLklSDHZuVM+biI3nrmr6c1HEvAN77vILOI54hmc4yJbc45oSSNoWFWJKkWmrUoIzrT2pPLpNi2PHt8vMTb59EMp3l/pcXxphO0sayEEuStBFO75Ikl0nx8Dld8rMr/jGTZDrLZX+fwarVlTGmk7QhLMSSJG2Cw1rsQC6TYtKAo9lj2yYAPDzlX7QaOIreN01k8dIVMSeUVBMLsSRJm8Hu227FSwN6MntYH/q02w2A8OESDhn2NMl0lpnvfh5zQknr0zDuAJIk1SdNGjXg9tM7UlVVxe0T5nPt6NkAHHfrCwDcfHIHTjh4zzgjSlqHV4glSaoDiUSC83rsSy6T4p6zDs3PL3poOsl0lmFPvUllpQd9SIXAQixJUh3rEe1CLpPiuV/1oFl59Q9n73phAS0vH8mJv3+JLypWxpxQKm0WYkmStpDkTk2ZObQ3/xzam26tdgRgysJPOWjIWFoPHMW8RV/GnFAqTRZiSZK2sKblDXmgf2cWjOjHz3vsC8CK1ZX0vGECyXSWcW9+GHNCqbRYiCVJikkikeCyPm3IZVL87seH5Of975tCMp3l5nFzqKpyn7FU1yzEkiQVgH4H7k4uk2L0Rd3zs5vHvUWLASM560+T+WrF6hjTSfWbhViSpALSZrdtyGVSTB/ci4P22haA8WERbQeP5pBhT/PO4mUxJ5TqHwuxJEkFaLutG/PEBUcwb3g/Tu+8DwCLl66g+3XjSaazvDT345gTSvWHhViSpALWoCzBsBMOIJdJcd2JB+Xn/33nKyTTWe56YUGM6aT6wUIsSVKR+FGnvcllUvzj/G752bCn3iSZznLhX6axYlVljOmk4mUhliSpyHTYeztymRSTB/ak5U5NAXhixnu0vmIUPa4fz0dLKmJOKBUXC7EkSUVql+ZNePZXPZhzdV9O6LAHALlPlnHYNc+QTGeZ9vanMSeUioOFWJKkIte4YRk3n3IwuUyKwcftn59//3cvkUxnefjVd2JMJxU+C7EkSfXI2Ue0IJdJ8eBPD8/PLnvkdZLpLAMfe4PVlR70Ia3LQixJUj3Udd+dyGVSvPDr77JTs8YAPPDK2+x7+UiOu/V5Plu2IuaEUuGwEEuSVI/ttf3WTLmiF7Ou6kPPNrsAMPPdL+hw1dMk01lmf/BFzAml+FmIJUkqAVs1bsBdZx7KghH9uKRX6/y8z83Pk0xnyb7+fozppHhZiCVJKiGJRIILe+5HLpPirp90ys/Pf/A1kuksmVGzqapyn7FKi4VYkqQS1bPtruQyKZ659CgaN6yuBLdPmEeLASM59Y6X+XL5qpgTSluGhViSpBK3787NmHN1X94YciyHJXcAYNL8TzjgyjG0Gzya3MdLY04o1S0LsSRJAqB5k0Y8fG4X5g/vR/8jWgCwdMVqevzmOZLpLM+Fj2JOKNUNC7EkSfo3ZWUJrjhuf3KZFL89pUN+fuafXiWZznLb+LnuM1a9YiGWJEnrdXyHPcllUmQvPCI/u35MoMWAkfzsvilUrFwdYzpp87AQS5KkGrXbY1tymRSvDepFm92aAzD2zQ9pM2g0nYc/w3uffRVzQmnjWYglSVKt7dC0MaMvOpK51/Tl5E57A/DBFxV0zTxLMp3llfmfxJxQ2nANa3pBFEVlwO+A9sByoH8IYe5az58PnAlUAVeFEJ6qm6iSJKlQNGxQxrUnHsS1Jx7EA68sZOBjMwE4+Y6XAbjq+Hac0SUZY0Kp9mpzhfgEoEkIoQuQBm74+okoinYCfg50BXoCv4+iKFEXQSVJUmH68eH7kMukeOS8LvnZ4Mf/STKd5dKHZ7BydWWM6aSa1aYQHwGMBgghvAzkj7UJIXwMtA8hrAR2Az4LIfixU0mSSlDHfXYgl0nx8oCe7LndVgA88tq/2G/gKI65cQIff7k85oTSN0vUdNuUKIruBB4JIYxa8/htoGUIYdVar7kAGArcEkIY+m3fb/r06VXl5eWbHLwUVVRU0KRJk7hjaCO4dsXJdSterl1hWLG6it88/xHPL/z3gz1uOW5P9tvxP7uA61a8CnXtli1bNrVjx46danpdjXuIgS+A5ms9Llu7DAOEEP43iqI7gFFRFH03hDB+fd+svLyctm3b1uJtta5Zs2b5e1ekXLvi5LoVL9eucPz5gP2pqqrijonzGTFqNgAXPvUuADf+qD0/OGSv/Gtdt+JVqGs3derUWr2uNlsmXgT6AURR1Bl44+snomqPrtk3vJLqD925UUiSJOUlEgnOOWpfcpkU9519WH5+ycMzSKazDHnin1RWuuNS8anNFeLHgF5RFL0EJICzoii6BJgbQngiiqIZwCSq7zIxKoQwoe7iSpKkYnZk653JZVK8/ckyjrv1eb6oWMU9L+W456UcbXYu56FkK7bdqlHcMVViaizEIYRK4Nx1xrPXen4o1fuHJUmSauU7O27N60N6s2zFKs7581Sef+tjZi9aTvuhYylLwJiLjmS/XZvX/I2kzcCDOSRJUmy2btyQP/+/w1kwoh+nHrQdAJVV0OumiSTTWcb884OYE6oUWIglSVLsEokEZxxcfdu220/rmJ+f8+epJNNZbhwbqOnOWNLGshBLkqSC0ueA3chlUoy9+EjK1hz3dcuzc2kxYCRn3D2ZZStWffs3kDaQhViSJBWk1rs2Z/6IFDOuPJYOe1dvp5g4ZxH7Dx5Dh6vG8s7iZTEnVH1hIZYkSQVt260a8Y/zuzFveD9+0mUfAD5btpLu140nmc7ywlsfx5xQxc5CLEmSikKDsgRDjz+AXCbFb05qn5+fdtcrJNNZ/jhxfozpVMwsxJIkqeic2HEvcpkUj5/fLT+7ZuQskuks5z/4GstXrY4xnYqNhViSJBWt9ntvRy6T4tWBx7Dvzk0ByL7+PtEVozni2mf58IuKmBOqGFiIJUlS0du5eTnPXNqDt67pyw8O2ROAf336FYcPf4ZkOsvUhZ/GnFCFzEIsSZLqjUYNyrjxRx3IZVIM/a92+fkPf/8SyXSWv05+O8Z0KlQWYkmSVC/9pGuSXCbFX3/WOT9LP/oGyXSWAY++zqrVlTGmUyGxEEuSpHqtc8sdyWVSvJg+ml2alwPwl8nv0GrgKPr+9nk+Xboi5oSKm4VYkiSVhD2324rJA49h9rA+9Np/VwBmvf8FBw97mmQ6y5vvfRFzQsXFQixJkkpKk0YN+OMZnVgwoh+/OrZ1ft7vludJprM8OeO9GNMpDhZiSZJUkhKJBBccvR+5TIq7z+yUn//iL9NIprMMHzmLysqqGBNqS7EQS5Kkknd0m13JZVI8e+lRbNWoAQB3TJxPy8tH8qM/TGJJxcqYE6ouWYglSZLWaLlzM2YN68PMob3p3HIHACYvWMyBQ8bSZtAo5i/6MuaEqgsWYkmSpHU0K2/IX3/WhfnD+3HOkS0BqFhZydE3TCCZzvLs7A9jTqjNyUIsSZK0HmVlCQb0a0suk+LWUw/Oz8++ZwrJdJZbnnmLqir3GRc7C7EkSVItfK/9HuQyKUb9snt+duPTc2gxYCT9732VipWrY0ynTWEhliRJ2gBtd9+GXCbFtEG9aLfHNgCMm/URbQaN5tBrxvHuZ1/FnFAbykIsSZK0EbZv2pjshd2Ze01fTj3sOwAsWrKcbplnSaazvDz/k5gTqrYsxJIkSZugYYMyRvzgQHKZFCN+cGB+fsodL5NMZ7nnxQUxplNtWIglSZI2k1MP+w65TIpHzuuanw158k2S6SwXPzSdlasrY0yn9bEQS5IkbWYd99meXCbF5Mt78p0dtgbgsWnvst/AURz9m+dYtGR5zAm1NguxJElSHdllmyZMvOy7hKv78L32ewAw/+OlHHrNOJLpLDPe+SzmhAILsSRJUp0rb9iAW089mFwmxRWptvn58be9SDKd5W9T3okxnSzEkiRJW1D/7i3JZVI80P/w/Ox//v46yXSWwY/PZHWlB31saRZiSZKkGHRrtRO5TIrnL/su22/dCID7Ji1k38tHcvxtL/L5spUxJywdFmJJkqQY7b3D1kwbfCxvXtWbo1rvDMCMdz6j/VVjSaazzPlwScwJ6z8LsSRJUgHYunFD7j37MBaM6MeFPffLz4+9aSLJdJbRM9+PMV39ZiGWJEkqIIlEgkt6tSaXSfGH0zvm5+fe/xrJdJbrx8ymqsp9xpuThViSJKlA9W63G7lMinGXHEnDsgQAt42fR4sBIzntzldYunxVzAnrBwuxJElSgWu1S3PmDu/H60OOpeM+2wPwwtyPaXflGA68cgwLP1kac8LiZiGWJEkqEts0acQj53Vl/vB+nNUtCcCS5as46vrnSKazTJyzKN6ARcpCLEmSVGTKyhJc+b125DIpbjq5fX5+xt2TSaaz3D5hnvuMN4CFWJIkqYh9/+C9yGVSPHnBEflZZtRsWgwYyXn3T6Vi5eoY0xUHC7EkSVI9cOBe25LLpJhyxTG03rUZAKNmfkCbQaPpOuIZPvi8IuaEhctCLEmSVI/s1KycsRcfxVvX9OWkjnsB8N7nFXQe8QzJdJYpucUxJyw8FmJJkqR6qFGDMq4/qT25TIphx7fLz0+8fRLJdJb7X14YY7rCYiGWJEmq507vkiSXSfHwOV3ysyv+MZNkOstlf5/BqtWVMaaLn4VYkiSpRBzWYgdymRSTBhzN7ts2AeDhKf+i1cBR9L5pIouXrog5YTwsxJIkSSVm9223YtKAnswe1oc+7XYDIHy4hEOGPU0ynWXmu5/HnHDLahh3AEmSJMWjSaMG3H56R6qqqvj9hHlcNzoAcNytLwBw88kdOOHgPeOMuEV4hViSJKnEJRIJft6jFblMinvOOjQ/v+ih6STTWYY99SaVlfX3oA8LsSRJkvJ6RLuQy6R47lc9aFZevZngrhcW0PLykZx0+0ssqVgZc8LNz0IsSZKk/5DcqSkzh/Zm5tDedN13RwBezX3KgUPG0nrgKOYt+jLmhJuPe4glSZK0Xs3KG/LgTztTVVXFdWMCv39uHitWV9LzhgkA3HlGJ/ZMxBxyE3mFWJIkSTVKJBL8uk8bcpkUt/33Ifl5//um0Pfe+dw8bg5VVcW5z9hCLEmSpA2SOmh3cpkUoy/qnp/dPO4tWgwYyVl/msxXK1bHmG7D1bhlIoqiMuB3QHtgOdA/hDB3recvBk5Z83BkCGFoXQSVJElSYWmz2zbkMikmT5/J1S98xuv/+pzxYRFtB49mh6aNefz8buy9w9Zxx6xRba4QnwA0CSF0AdLADV8/EUVRS+DHQFegC3BsFEUH1UVQSZIkFabm5Q144oIjmDe8H6d33geAxUtX0P268fz4zpdjTlez2hTiI4DRACGEl4FOaz33DtAnhLA6hFAJNAIq4fJmPgAABMhJREFUNntKSZIkFbwGZQmGnXAAuUyK635YfY105arC31ecqGnzcxRFdwKPhBBGrXn8NtAyhLBqrdckgOuB5iGEc77t+02fPr2qvLx8k4OXooqKCpo0aRJ3DG0E1644uW7Fy7UrTq5b8SrUtVu2bNnUjh07dqrpdbW57doXQPO1HpetU4abAHcDS4Cf1/TNysvLadu2bS3eVuuaNWuWv3dFyrUrTq5b8XLtipPrVrwKde2mTp1aq9fVZsvEi0A/gCiKOgNvfP3EmivDjwMzQgjnhBCK6yOFkiRJKnm1uUL8GNAriqKXgARwVhRFlwBzgQbAUUB5FEV917x+QAhhUp2klSRJkjazGgvxmg/LnbvOePZaXxfehhFJkiSpljyYQ5IkSSXNQixJkqSSZiGWJElSSbMQS5IkqaRZiCVJklTSLMSSJEkqaRZiSZIklTQLsSRJkkqahViSJEklzUIsSZKkkmYhliRJUkmzEEuSJKmkWYglSZJU0izEkiRJKmmJqqqqLfqGU6dOXQQs3KJvKkmSpFK0T8eOHXeu6UVbvBBLkiRJhcQtE5IkSSppFmJJkiSVNAuxJEmSSpqFWJIkSSXNQixJkqSSZiGWJElSSWsYdwB9uyiKGgF3A0mgHLg6hPBErKG0QaIo2gWYCvQKIcyOO49qJ4qiAcB/AY2B34UQ7oo5kmqw5u/Le6n++3I18FP/zBW+KIoOB64NIfSIoqgVcA9QBcwEzg8hVMaZT99snXXrANxK9Z+75cAZIYQPYw24gbxCXPhOAz4JIXQH+gL/G3MebYA1/0D/Afgq7iyqvSiKegBdgW7AUcDesQZSbfUDGoYQugJXAdfEnEc1iKLoMuBOoMma0Y3AFWv+zUsAx8eVTev3Dev2W+AXIYQewKPAr2OKttEsxIXvb8CgtR6viiuINspvgNuB9+IOog3SG3gDeAx4Engq3jiqpTlAwyiKyoBtgJUx51HN5gE/WOtxR2DCmq9HAcds8USqjXXX7ZQQwvQ1XzcEKrZ8pE1jIS5wIYQvQwhLoihqDvwduCLuTKqdKIrOBBaFEMbEnUUbbCegE3AScC7wQBRFiXgjqRa+pHq7xGzgj8AtsaZRjUIIj/Dv/3FJhBC+PkJ3CbDtlk+lmqy7biGE9wGiKOoKXADcFFO0jWYhLgJRFO0NjAf+HEJ4MO48qrWzgV5RFD0HdADui6Jot3gjqZY+AcaEEFaEEALVVzt2jjmTanYx1evWGmgP3BtFUZMafo0Ky9r7hZsDn8UVRBsmiqKTqf6JaCqEsCjuPBvKD9UVuCiKdgXGAheEEJ6JO49qL4Rw5NdfrynF54YQPogvkTbAC8Avoyi6EdgdaEp1SVZh+5T/f9VqMdAIaBBfHG2EaVEU9QghPEf152bGx5xHtRBF0WnAOUCPEMLiuPNsDAtx4bsc2B4YFEXR13uJ+4YQ/JCWVEdCCE9FUXQkMJnqn6SdH0JYHXMs1ewm4O4oip6n+u4gl4cQlsacSRvmUuCPURQ1BmZRvVVQBSyKogZUb096G3g0iiKACSGEK2MNtoESVVVVNb9KkiRJqqfcQyxJkqSSZiGWJElSSbMQS5IkqaRZiCVJklTSLMSSJEkqaRZiSZIklTQLsSRJkkra/wENSKSCiN9LYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(X_boston.reshape(-1, 1), y_boston)\n",
    "model_pred = lr.predict(X_boston.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.scatter(X_boston, y_boston);\n",
    "plt.plot(X_boston, model_pred);\n",
    "print(\"R^2 score = {:.2f}\".format(r2_score(y_boston, model_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadratic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_reg = PolynomialFeatures(degree=2)\n",
    "X_poly_b = poly_reg.fit_transform(X_boston.reshape(-1, 1))\n",
    "lin_reg_2 = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg_2.fit(X_poly_b, y_boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_fit = np.arange(X_boston.min(), X_boston.max(), 1)[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.1296],\n",
       "       [ 2.1296],\n",
       "       [ 3.1296],\n",
       "       [ 4.1296],\n",
       "       [ 5.1296],\n",
       "       [ 6.1296],\n",
       "       [ 7.1296],\n",
       "       [ 8.1296],\n",
       "       [ 9.1296],\n",
       "       [10.1296],\n",
       "       [11.1296]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lin_reg_2.predict(poly_reg.fit_transform(X_fit.reshape(-1,1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score = 0.70\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(X_boston, y_boston);\n",
    "plt.plot(X_fit, y_pred);\n",
    "print(\"R^2 score = {:.2f}\".format(r2_score(y_boston, \n",
    "                                          lin_reg_2.predict(X_poly_b))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cubic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_reg = PolynomialFeatures(degree=3)\n",
    "X_poly_b = poly_reg.fit_transform(X_boston.reshape(-1, 1))\n",
    "lin_reg_3 = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg_3.fit(X_poly_b, y_boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_fit = np.arange(X_boston.min(), X_boston.max(), 1)[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lin_reg_3.predict(poly_reg.fit_transform(X_fit.reshape(-1,1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score = 0.71\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(X_boston, y_boston);\n",
    "plt.plot(X_fit, y_pred);\n",
    "print(\"R^2 score = {:.2f}\".format(r2_score(y_boston, \n",
    "                                          lin_reg_3.predict(X_poly_b))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}