Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression with the mpg dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(398, 9)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = sns.load_dataset('mpg')\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             False\n",
       "cylinders       False\n",
       "displacement    False\n",
       "horsepower       True\n",
       "weight          False\n",
       "acceleration    False\n",
       "model_year      False\n",
       "origin          False\n",
       "name            False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['horsepower'] = df['horsepower'].fillna(df['horsepower'].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model_year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.775396</td>\n",
       "      <td>-0.804203</td>\n",
       "      <td>-0.771437</td>\n",
       "      <td>-0.831741</td>\n",
       "      <td>0.420289</td>\n",
       "      <td>0.579267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cylinders</th>\n",
       "      <td>-0.775396</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.950721</td>\n",
       "      <td>0.838939</td>\n",
       "      <td>0.896017</td>\n",
       "      <td>-0.505419</td>\n",
       "      <td>-0.348746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>displacement</th>\n",
       "      <td>-0.804203</td>\n",
       "      <td>0.950721</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.893646</td>\n",
       "      <td>0.932824</td>\n",
       "      <td>-0.543684</td>\n",
       "      <td>-0.370164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>-0.771437</td>\n",
       "      <td>0.838939</td>\n",
       "      <td>0.893646</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.860574</td>\n",
       "      <td>-0.684259</td>\n",
       "      <td>-0.411651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>-0.831741</td>\n",
       "      <td>0.896017</td>\n",
       "      <td>0.932824</td>\n",
       "      <td>0.860574</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.417457</td>\n",
       "      <td>-0.306564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>acceleration</th>\n",
       "      <td>0.420289</td>\n",
       "      <td>-0.505419</td>\n",
       "      <td>-0.543684</td>\n",
       "      <td>-0.684259</td>\n",
       "      <td>-0.417457</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.288137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_year</th>\n",
       "      <td>0.579267</td>\n",
       "      <td>-0.348746</td>\n",
       "      <td>-0.370164</td>\n",
       "      <td>-0.411651</td>\n",
       "      <td>-0.306564</td>\n",
       "      <td>0.288137</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   mpg  cylinders  displacement  horsepower    weight  \\\n",
       "mpg           1.000000  -0.775396     -0.804203   -0.771437 -0.831741   \n",
       "cylinders    -0.775396   1.000000      0.950721    0.838939  0.896017   \n",
       "displacement -0.804203   0.950721      1.000000    0.893646  0.932824   \n",
       "horsepower   -0.771437   0.838939      0.893646    1.000000  0.860574   \n",
       "weight       -0.831741   0.896017      0.932824    0.860574  1.000000   \n",
       "acceleration  0.420289  -0.505419     -0.543684   -0.684259 -0.417457   \n",
       "model_year    0.579267  -0.348746     -0.370164   -0.411651 -0.306564   \n",
       "\n",
       "              acceleration  model_year  \n",
       "mpg               0.420289    0.579267  \n",
       "cylinders        -0.505419   -0.348746  \n",
       "displacement     -0.543684   -0.370164  \n",
       "horsepower       -0.684259   -0.411651  \n",
       "weight           -0.417457   -0.306564  \n",
       "acceleration      1.000000    0.288137  \n",
       "model_year        0.288137    1.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xarray = df['horsepower'].values\n",
    "Yarray = df['weight'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(Xarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "metadata": {},
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    "Xarray"
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  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(199, 2)\n"
     ]
    },
    {
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       "       [ 69.        ,  90.        ],\n",
       "       [115.        , 115.        ],\n",
       "       [ 90.        ,  76.        ],\n",
       "       [ 60.        ,  70.        ],\n",
       "       [ 65.        ,  90.        ],\n",
       "       [ 88.        ,  90.        ],\n",
       "       [ 90.        ,  78.        ],\n",
       "       [ 90.        ,  75.        ],\n",
       "       [ 92.        ,  75.        ],\n",
       "       [ 65.        , 105.        ],\n",
       "       [ 65.        ,  48.        ],\n",
       "       [ 48.        ,  67.        ],\n",
       "       [ 67.        ,  67.        ],\n",
       "       [104.46938776,  67.        ],\n",
       "       [ 62.        , 132.        ],\n",
       "       [100.        ,  88.        ],\n",
       "       [104.46938776,  72.        ],\n",
       "       [ 84.        ,  84.        ],\n",
       "       [ 92.        , 110.        ],\n",
       "       [ 84.        ,  58.        ],\n",
       "       [ 64.        ,  60.        ],\n",
       "       [ 67.        ,  65.        ],\n",
       "       [ 62.        ,  68.        ],\n",
       "       [ 63.        ,  65.        ],\n",
       "       [ 65.        ,  74.        ],\n",
       "       [104.46938776,  75.        ],\n",
       "       [ 75.        , 100.        ],\n",
       "       [ 74.        ,  80.        ],\n",
       "       [ 76.        , 116.        ],\n",
       "       [120.        , 110.        ],\n",
       "       [105.        ,  88.        ],\n",
       "       [ 85.        ,  88.        ],\n",
       "       [ 88.        ,  88.        ],\n",
       "       [ 85.        ,  84.        ],\n",
       "       [ 90.        ,  92.        ],\n",
       "       [104.46938776,  74.        ],\n",
       "       [ 68.        ,  68.        ],\n",
       "       [ 63.        ,  70.        ],\n",
       "       [ 88.        ,  75.        ],\n",
       "       [ 70.        ,  67.        ],\n",
       "       [ 67.        ,  67.        ],\n",
       "       [110.        ,  85.        ],\n",
       "       [ 92.        , 112.        ],\n",
       "       [ 96.        ,  84.        ],\n",
       "       [ 90.        ,  86.        ],\n",
       "       [ 52.        ,  84.        ],\n",
       "       [ 79.        ,  82.        ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = Xarray.reshape(-1, 2)\n",
    "print(X.shape)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = Xarray.reshape(-1, 1)\n",
    "Y = Yarray.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model1 = LinearRegression()\n",
    "model1.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[977.34076621]\n",
      "[[19.07816155]]\n"
     ]
    }
   ],
   "source": [
    "print(model1.intercept_)\n",
    "print(model1.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model1.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [2484.51552888],\n",
       "       [2541.75001353]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y,  color='gray')\n",
    "plt.plot(X, Y_pred, color='red', linewidth=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Need to split dataset into Training and Testing set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split \n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(318, 1)\n",
      "(80, 1)\n",
      "(318, 1)\n",
      "(80, 1)\n",
      "318.40000000000003\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)\n",
    "print(0.8 * df.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[942.42861007]\n",
      "[[19.48576276]]\n"
     ]
    }
   ],
   "source": [
    "model2 = LinearRegression()\n",
    "model2.fit(X_train, Y_train)\n",
    "print(model2.intercept_)\n",
    "print(model2.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Compare with model1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[977.34076621]\n",
      "[[19.07816155]]\n"
     ]
    }
   ],
   "source": [
    "print(model1.intercept_)\n",
    "print(model1.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = model2.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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"
    }
   ],
   "source": [
    "plt.scatter(X_test, Y_test,  color='gray')\n",
    "plt.scatter(X_test, Y_pred, color='red', linewidth=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now check model performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error: 368.1337619437148\n",
      "Mean Squared Error: 201176.0818221282\n",
      "Root Mean Squared Error: 448.52656757669126\n",
      "R-squared: 0.7232751145017162\n"
     ]
    }
   ],
   "source": [
    "print('Mean Absolute Error:', metrics.mean_absolute_error(Y_test, Y_pred))  \n",
    "print('Mean Squared Error:', metrics.mean_squared_error(Y_test, Y_pred))  \n",
    "print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(Y_test, Y_pred)))\n",
    "print('R-squared:', metrics.r2_score(Y_test, Y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pick another training set and build another model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(238, 1)\n",
      "(160, 1)\n",
      "(238, 1)\n",
      "(160, 1)\n",
      "238.79999999999998\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.4, random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)\n",
    "print(0.6 * df.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[885.63517611]\n",
      "[[20.05543059]]\n"
     ]
    }
   ],
   "source": [
    "model3 = LinearRegression()\n",
    "model3.fit(X_train, Y_train)\n",
    "print(model3.intercept_)\n",
    "print(model3.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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"
    }
   ],
   "source": [
    "Y_pred = model3.predict(X_test)\n",
    "plt.scatter(X_test, Y_test,  color='gray')\n",
    "plt.scatter(X_test, Y_pred, color='red', linewidth=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error: 343.7676698648614\n",
      "Mean Squared Error: 188633.05036591887\n",
      "Root Mean Squared Error: 434.3190651651374\n",
      "R-squared: 0.7285281245558992\n"
     ]
    }
   ],
   "source": [
    "print('Mean Absolute Error:', metrics.mean_absolute_error(Y_test, Y_pred))  \n",
    "print('Mean Squared Error:', metrics.mean_squared_error(Y_test, Y_pred))  \n",
    "print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(Y_test, Y_pred)))\n",
    "print('R-squared:', metrics.r2_score(Y_test, Y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Note that the RMSE changes. If the RMSE is still good when we pick various training set, it means model passes (one of the ) model validation test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## how are we going to do this automatically?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Idea is to pick random testing set, and display the model performance metric.  First we need some random number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "844\n",
      "778\n",
      "211\n",
      "990\n",
      "657\n",
      "245\n",
      "669\n",
      "672\n",
      "205\n",
      "584\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "for i in range(10):\n",
    "    print(random.randint(1, 1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we can use different random_state value in the train_test_split so that it will generate different training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 0, R-squared: 0.659980399787172,  Slope: [[19.60461562]], Intercept: [921.9301468],  \n",
      "Trial 1, R-squared: 0.7031938642098073,  Slope: [[18.68661506]], Intercept: [1013.04369282],  \n",
      "Trial 2, R-squared: 0.6296753663290007,  Slope: [[19.57999381]], Intercept: [942.38390887],  \n",
      "Trial 3, R-squared: 0.7067313510634281,  Slope: [[19.37519413]], Intercept: [960.37677454],  \n",
      "Trial 4, R-squared: 0.755596996355267,  Slope: [[18.80257023]], Intercept: [993.44670511],  \n",
      "Trial 5, R-squared: 0.6120811977995035,  Slope: [[19.96367358]], Intercept: [905.17995578],  \n",
      "Trial 6, R-squared: 0.7301470416595965,  Slope: [[19.12065504]], Intercept: [988.36886906],  \n",
      "Trial 7, R-squared: 0.785402081044259,  Slope: [[18.80319497]], Intercept: [1013.4609685],  \n",
      "Trial 8, R-squared: 0.5998929687004237,  Slope: [[19.19321385]], Intercept: [973.46156886],  \n",
      "Trial 9, R-squared: 0.6909905493412003,  Slope: [[19.31092324]], Intercept: [948.85138553],  \n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state = random.randint(1,1000))\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_train, Y_train)\n",
    "    Y_pred = model.predict(X_test)\n",
    "    print('Trial {}, R-squared: {},  Slope: {}, Intercept: {},  '.format(i, metrics.r2_score(Y_test, Y_pred), \\\n",
    "                                                                      model.coef_, model.intercept_))\n",
    "    #plt.scatter(X_test, Y_test,  color='gray')\n",
    "    #plt.scatter(X_test, Y_pred, color='red', linewidth=2)\n",
    "    #plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collect the R-squared and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>trial</th>\n",
       "      <th>Rsquare</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.683479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.766308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>0.744655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>0.680372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>0.773008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.793346</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   trial   Rsquare\n",
       "0      0  0.723800\n",
       "1      1  0.771438\n",
       "2      2  0.763198\n",
       "3      3  0.780844\n",
       "4      4  0.683479\n",
       "5      5  0.766308\n",
       "6      6  0.744655\n",
       "7      7  0.680372\n",
       "8      8  0.773008\n",
       "9      9  0.793346"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsquare = []\n",
    "for i in range(10):\n",
    "    X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state = random.randint(1,1000))\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_train, Y_train)\n",
    "    Y_pred = model.predict(X_test)\n",
    "    rsquare.append(metrics.r2_score(Y_test, Y_pred))\n",
    "    \n",
    "rdf = pd.DataFrame( {'trial': range(10), 'Rsquare': rsquare})\n",
    "rdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2bbbd9bfe48>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEGCAYAAACevtWaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAF7FJREFUeJzt3X+UVPV9//HnywWCgoFENtbsoksVGoiEFTcIsSUmSoLNKeSbX0L7TeI3KbRRqm08PZI0Rzl8bY6NbXKaczjfb2iMRo+GqK1fNuk2GJHUxNZkF1yDLEFXgjLijw01pvhrWXl//5jBM1kH5i47OzP74fU4h+Pcez9772tn1tfevXPvHUUEZmaWlhNqHcDMzCrP5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSVoTK02PGXKlGhpaanV5s3MRqWtW7f+KiIay42rWbm3tLTQ1dVVq82bmY1Kkp7IMs6HZczMEuRyNzNLkMvdzCxBmY65S1oM/CPQAHwzIq4ftPx04NvA5MKY1RHRUeGslpiDBw+Sy+V45ZVXah1lVBg/fjzNzc2MHTu21lFsFChb7pIagHXAIiAHdEpqj4ieomFfAu6IiP8jaRbQAbSMQF5LSC6X4+STT6alpQVJtY5T1yKC/fv3k8vlmDZtWq3j2CiQ5bDMPKA3InZHRD+wAVg6aEwAby48ngTsq1xES9Urr7zCKaec4mLPQBKnnHKK/8qxzLIclmkC9hZN54DzBo1ZA9wj6S+ACcBFFUlnyXOxZ+fnyoYiy557qZ+owZ/Ntxy4OSKagT8EbpX0hnVLWimpS1JXX1/f0NOamVkmWfbcc8DUoulm3njY5bPAYoCI+E9J44EpwHPFgyJiPbAeoK2tzR/ear+lZfW/VnR9e67/UNkxDQ0NzJ49m4GBAaZNm8att97K5MmTK5rDjh+/s6V72Ot45n2tFUiSbc+9E5guaZqkccAyoH3QmCeBCwEkzQTGA941t7p34okn0t3dzSOPPMJb3/pW1q1bV/UMEcGhQ4eqvl1LW9lyj4gBYBWwCdhJ/qyYHZLWSlpSGHYVsELSw8B3gEsjwnvmNqosWLCAp556CoCnn36ahQsX0traytlnn82Pf/xjAG666SZmzJjBe9/7XlasWMGqVasAuPTSS7nrrrteX9fEiRMBOHDgABdeeCFz585l9uzZbNy4EYA9e/Ywc+ZMLrvsMubOncvevXu55557WLBgAXPnzuXjH/84Bw4cqOa3b4nJdBFTRHRExIyIODMi/rYw75qIaC887omI8yNiTkS0RsQ9IxnarNJee+01Nm/ezJIl+f2V22+/nQ9+8IN0d3fz8MMP09raytNPP821117LAw88wA9/+EN6enrKrDV/bvrdd9/Ntm3b2LJlC1dddRWH93t27drFpz71KR566CEmTJjAddddx7333su2bdtoa2vjq1/96oh+z5a2mt04zEafne+YOex1zPzFzgokqZyXX36Z1tZW9uzZw7nnnsuiRYsAePe7381nPvMZDh48yIc//GFaW1vZvHkzF1xwAY2N+RvyXXLJJTz66KNHXX9E8MUvfpH777+fE044gaeeeopnn30WgDPOOIP58+cD8OCDD9LT08P5558PQH9/PwsWLBipb9uOA779gB3XDh9zf+KJJ+jv73/9mPvChQu5//77aWpq4pOf/CS33HILcOTTEceMGfP6cfOIoL+/H4DbbruNvr4+tm7dSnd3N6eeeurr56pPmDDh9a+PCBYtWkR3dzfd3d309PRw4403jtj3benznns5ayZVYB0vDH8dNqImTZrE17/+dZYuXcrnPvc59u3bR1NTEytWrODFF19k27ZtXH311Vx55ZXs37+fN7/5zdx5553MmTMHyN/CeuvWrXziE59g48aNHDx4EIAXXniBt73tbYwdO5YtW7bwxBOl79Y6f/58Lr/8cnp7eznrrLN46aWXyOVyzJgxo2rPwWi2+b4zh72OC9//eAWS1A+Xu9WNLKcujqRzzjmHOXPmsGHDBg4dOsQNN9zA2LFjmThxIrfccgunnXYaa9asYcGCBZwyeTLvnDWTl174Nc88/hhLF13IpX/2Oc75wb/x+wsWcNJJJ/HM449x0Xvmc+vNNzNn9mzOnvkOzjrzd+l74pdv2HZjYyM333wzy5cv59VXXwXguuuuc7nbMVOtTmppa2uLUfFhHXWw5z7727OHHWH7p7cPex2VPua+c+dOZs4c/jpr4ZnHH+O7//wvPLx9O19ec+0xreN3zpw+5K8Zzc/ZSKqXPfdqnOcuaWtEtJVbj4+5m5klyIdlzI7RJR/9CJd89CO1jmFWkvfcraZ8rVt2fq5sKFzuVjPjx49n//79Lq0MDt/Pffz48bWOYqOED8tYzTQ3N5PL5RiNdwj9Td9z5QeV8Xz/wJDGH/4kpsNyq3887AzN1//BsNdh9cnlbjUzduzYUfupQv+w5q+HvY6rvvv9CiQxK82HZczMEuRyNzNLkMvdzCxBdXvMvRKfylPry9nNzGrFe+5mZglyuZuZJShTuUtaLGmXpF5Jq0ss/5qk7sK/RyX9uvJRzcwsq7LH3CU1AOuARUAO6JTUHhGvf8ZYRPxV0fi/AM4ZgaxmZpZRlj33eUBvROyOiH5gA7D0KOOXk/+QbDMzq5Es5d4E7C2azhXmvYGkM4BpwH3Dj2ZmZscqS7mX+tDII93paRlwV0S8VnJF0kpJXZK6RuP9RMzMRoss5Z4DphZNNwP7jjB2GUc5JBMR6yOiLSLaDn+CvJmZVV6Wcu8EpkuaJmkc+QJvHzxI0u8BbwH+s7IRzcxsqMqWe0QMAKuATcBO4I6I2CFpraQlRUOXAxvCN+c2M6u5TLcfiIgOoGPQvGsGTa+pXCyz0tb9+fDfq7/8/76/AknM6lvd3lvGzEaHNWvW1MU67Lf59gNmZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZgnKVO6SFkvaJalX0uojjPmEpB5JOyTdXtmYZmY2FGU/Zk9SA7AOWATkgE5J7RHRUzRmOvAF4PyIeF7S20YqsJmZlZdlz30e0BsRuyOiH9gALB00ZgWwLiKeB4iI5yob08zMhiJLuTcBe4umc4V5xWYAMyQ9IOlBSYtLrUjSSkldkrr6+vqOLbGZmZWVpdxVYl4Mmh4DTAcuAJYD35Q0+Q1fFLE+Itoioq2xsXGoWc3MLKMs5Z4DphZNNwP7SozZGBEHI+KXwC7yZW9mZjWQpdw7gemSpkkaBywD2geN+X/A+wAkTSF/mGZ3JYOamVl2Zcs9IgaAVcAmYCdwR0TskLRW0pLCsE3Afkk9wBbgryNi/0iFNjOzoyt7KiRARHQAHYPmXVP0OIDPF/6ZmVmN+QpVM7MEudzNzBLkcjczS5DL3cwsQS53M7MEudzNzBLkcjczS5DL3cwsQS53M7MEudzNzBLkcjczS5DL3cwsQS53M7MEudzNzBLkcjczS5DL3cwsQS53M7MEZSp3SYsl7ZLUK2l1ieWXSuqT1F3496eVj2pmZlmV/Zg9SQ3AOmARkAM6JbVHRM+god+NiFUjkNHMzIYoy577PKA3InZHRD+wAVg6srHMzGw4spR7E7C3aDpXmDfYRyX9XNJdkqaWWpGklZK6JHX19fUdQ1wzM8siS7mrxLwYNP09oCUi3gXcC3y71IoiYn1EtEVEW2Nj49CSmplZZlnKPQcU74k3A/uKB0TE/oh4tTD5T8C5lYlnZmbHIku5dwLTJU2TNA5YBrQXD5B0WtHkEmBn5SKamdlQlT1bJiIGJK0CNgENwLciYoektUBXRLQDV0haAgwA/wVcOoKZzcysjLLlDhARHUDHoHnXFD3+AvCFykYzM7Nj5StUzcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwSlKncJS2WtEtSr6TVRxn3MUkhqa1yEc3MbKjKlrukBmAdcDEwC1guaVaJcScDVwA/rXRIMzMbmix77vOA3ojYHRH9wAZgaYlx/xv4CvBKBfOZmdkxyFLuTcDeoulcYd7rJJ0DTI2I7x9tRZJWSuqS1NXX1zfksGZmlk2WcleJefH6QukE4GvAVeVWFBHrI6ItItoaGxuzpzQzsyHJUu45YGrRdDOwr2j6ZOBs4EeS9gDzgXa/qWpmVjtZyr0TmC5pmqRxwDKg/fDCiHghIqZEREtEtAAPAksiomtEEpuZWVllyz0iBoBVwCZgJ3BHROyQtFbSkpEOaGZmQzcmy6CI6AA6Bs275ghjLxh+LDMzGw5foWpmliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mlqBM5S5psaRdknolrS6x/M8lbZfULeknkmZVPqqZmWVVttwlNQDrgIuBWcDyEuV9e0TMjohW4CvAVyue1MzMMsuy5z4P6I2I3RHRD2wAlhYPiIjfFE1OAKJyEc3MbKiyfEB2E7C3aDoHnDd4kKTLgc8D44D3l1qRpJXASoDTTz99qFnNzCyjLHvuKjHvDXvmEbEuIs4Erga+VGpFEbE+Itoioq2xsXFoSc3MLLMs5Z4DphZNNwP7jjJ+A/Dh4YQyM7PhyVLuncB0SdMkjQOWAe3FAyRNL5r8EPBY5SKamdlQlT3mHhEDklYBm4AG4FsRsUPSWqArItqBVZIuAg4CzwOfHsnQZmZ2dFneUCUiOoCOQfOuKXp8ZYVzmZnZMPgKVTOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBLnczcwS5HI3M0uQy93MLEEudzOzBGUqd0mLJe2S1CtpdYnln5fUI+nnkjZLOqPyUc3MLKuy5S6pAVgHXAzMApZLmjVo2ENAW0S8C7gL+Eqlg5qZWXZZ9tznAb0RsTsi+oENwNLiARGxJSJeKkw+CDRXNqaZmQ1FlnJvAvYWTecK847ks8C/lVogaaWkLkldfX192VOamdmQZCl3lZgXJQdK/xNoA24otTwi1kdEW0S0NTY2Zk9pZmZDMibDmBwwtWi6Gdg3eJCki4C/Ad4bEa9WJp6ZmR2LLHvuncB0SdMkjQOWAe3FAySdA3wDWBIRz1U+ppmZDUXZco+IAWAVsAnYCdwRETskrZW0pDDsBmAicKekbkntR1idmZlVQZbDMkREB9AxaN41RY8vqnAuMzMbBl+hamaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJcjlbmaWoEzlLmmxpF2SeiWtLrF8oaRtkgYkfazyMc3MbCjKlrukBmAdcDEwC1guadagYU8ClwK3VzqgmZkNXZbPUJ0H9EbEbgBJG4ClQM/hARGxp7Ds0AhkNDOzIcpyWKYJ2Fs0nSvMGzJJKyV1Serq6+s7llWYmVkGWcpdJebFsWwsItZHRFtEtDU2Nh7LKszMLIMs5Z4DphZNNwP7RiaOmZlVQpZy7wSmS5omaRywDGgf2VhmZjYcZcs9IgaAVcAmYCdwR0TskLRW0hIASe+WlAM+DnxD0o6RDG1mZkeX5WwZIqID6Bg075qix53kD9eYmVkd8BWqZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJcrmbmSXI5W5mliCXu5lZglzuZmYJylTukhZL2iWpV9LqEsvfJOm7heU/ldRS6aBmZpZd2XKX1ACsAy4GZgHLJc0aNOyzwPMRcRbwNeDvKh3UzMyyy7LnPg/ojYjdEdEPbACWDhqzFPh24fFdwIWSVLmYZmY2FIqIow+QPgYsjog/LUx/EjgvIlYVjXmkMCZXmH68MOZXg9a1ElhZmPw9YNcw808BflV21MiqhwxQHznqIQPUR456yAD1kaMeMkB95KhEhjMiorHcoDEZVlRqD3zwb4QsY4iI9cD6DNvMRFJXRLRVan2jNUO95KiHDPWSox4y1EuOeshQLzmqmSHLYZkcMLVouhnYd6QxksYAk4D/qkRAMzMbuizl3glMlzRN0jhgGdA+aEw78OnC448B90W54z1mZjZiyh6WiYgBSauATUAD8K2I2CFpLdAVEe3AjcCtknrJ77EvG8nQRSp2iGcY6iED1EeOesgA9ZGjHjJAfeSohwxQHzmqlqHsG6pmZjb6+ApVM7MEudzNzBLkcjczS1CW89zrgqR3kL8Ston8OfT7gPaI2FnTYMcxSfOAiIjOwi0pFgO/iIiOGma6JSI+VavtW+0VndW3LyLulfTHwHuAncD6iDhY04BVMireUJV0NbCc/K0PcoXZzeRfwA0RcX2tstVK4ZddE/DTiDhQNH9xRPygCtu/lvz9hsYAPwTOA34EXARsioi/rUKGwafkCngfcB9ARCwZ6QylSPp98rfteCQi7qnSNs8DdkbEbySdCKwG5gI9wJcj4oUq5bgCuDsi9lZje0fIcBv5n8uTgF8DE4F/AS4k33mfPsqXVzrLmcD/IH8d0ADwGPCdarweo6XcHwXeOfg3buE39I6ImF6bZL+V5X9FxE1V2tYVwOXk90RagSsjYmNh2baImFuFDNsL234T8AzQXFQsP42Id1Uhwzby5fVN8n/NCfgOhVNxI+LfRzpDIcfPImJe4fEK8q/N3cAHgO9VY+dD0g5gTuHU5fXASxTu81SY/5GRzlDI8QLwIvA4+dfizojoq8a2izL8PCLeVbig8ing7RHxWuF+Vw9X42ezkOMK4I+Afwf+EOgGnidf9pdFxI9GNEBE1P0/4Bfk76cweP4ZwK5a5ytkebKK29oOTCw8bgG6yBc8wENVyvBQqceF6e4qZTgB+Cvyfzm0FubtrsFrX/xcdAKNhccTgO1VyrCz6PG2Wrweh5+LwuvyAfLXv/QBPyB/kePJVcrwCDAOeAvw38BbC/PHFz9PVcixHWgoPD4J+FHh8enV+P90tBxz/0tgs6THgMN/7p0OnAWsOuJXVZiknx9pEXBqtXKQ/4E5ABAReyRdANwl6QxK3+dnJPRLOikiXgLOPTxT0iTgUDUCRMQh4GuS7iz891lq8z7SCZLeQr7UFIU91Yh4UdJAlTI8UvTX48OS2iKiS9IMoJrHmKPwutwD3CNpLPnDd8uBvwfK3vCqAm4kv0PYAPwNcKek3cB88od2q2kM8Br5v3BPBoiIJwvPy4gaFYdlACSdQP44ZhP5AssBnRHxWhUzPAt8kPyfVr+1CPiPiHh7lXLcB3w+IrqL5o0BvgX8SUQ0VCHDmyLi1RLzpwCnRcT2kc5QYtsfAs6PiC9Webt7yP9CE/nDQ++JiGckTQR+EhGtVcgwCfhH4A/I33VwLvkdob3AFRHx8EhnKOR4KCLOOcKyEyPi5SrleDtAROyTNJn8e0FPRsTPqrH9QoYryX/WxYPAQuDvIuImSY3AP0fEwhHd/mgp93og6Ubgpoj4SYllt0fEH1cpRzMwEBHPlFh2fkQ8UI0cdnSSTgJOjYhfVnGbJwO/S36PMRcRz1Zr24Xtz4iIR6u5zXom6Z3ATPJvrv+iqtt2uZuZpccXMZmZJcjlbmaWIJe7HVckTZZ02VGW/0eGdRwoN8as1lzudryZDLyh3CU1AETEe6qeyGwEjJbz3M0q5XrgTEnd5M//PgA8Tf5q21mSDkTExMJpjBvJXwgzFvhSFK4CNhsNfLaMHVcktQDfj4izCxd//Stw9uHTFYvKfQxwUuRvqTCF/LnK0yMiDo+p0bdglon33O1497MjnIcu4MuSFpK/QKmJ/FXIb7i2wKweudztePfiEeb/CflL5c+NiIOFq1DHVy2V2TD5DVU73vw3hXt8lDEJeK5Q7O8jf5M6s1HDe+52XImI/ZIekPQI8DJwpMvzbwO+J6mL/K1aq3rpuNlw+Q1VM7ME+bCMmVmCXO5mZglyuZuZJcjlbmaWIJe7mVmCXO5mZglyuZuZJej/A2pN7fsExzk4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rdf.plot.bar(x='trial', y='Rsquare')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7480448479939935\n"
     ]
    }
   ],
   "source": [
    "print(rdf['Rsquare'].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The above concept of re-running the same model but with different training set drawn from the data set is called Cross-Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We have just did a 10-fold Cross Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now Add a second variable, say, the horsepower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(318, 2) (80, 2)\n",
      "(318, 1) (80, 1)\n"
     ]
    }
   ],
   "source": [
    "X = df[['weight','horsepower']].values.reshape(-1, 2)\n",
    "Y = df['mpg'].values.reshape(-1, 1)\n",
    " \n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state=0)\n",
    "print(X_train.shape, X_test.shape)\n",
    "print(Y_train.shape, Y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3504.        ,  130.        ],\n",
       "       [3693.        ,  165.        ],\n",
       "       [3436.        ,  150.        ],\n",
       "       [3433.        ,  150.        ],\n",
       "       [3449.        ,  140.        ],\n",
       "       [4341.        ,  198.        ],\n",
       "       [4354.        ,  220.        ],\n",
       "       [4312.        ,  215.        ],\n",
       "       [4425.        ,  225.        ],\n",
       "       [3850.        ,  190.        ],\n",
       "       [3563.        ,  170.        ],\n",
       "       [3609.        ,  160.        ],\n",
       "       [3761.        ,  150.        ],\n",
       "       [3086.        ,  225.        ],\n",
       "       [2372.        ,   95.        ],\n",
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       "       [2900.        ,  116.        ],\n",
       "       [2930.        ,  120.        ],\n",
       "       [3415.        ,  110.        ],\n",
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       "       [2735.        ,   90.        ],\n",
       "       [2865.        ,   92.        ],\n",
       "       [3035.        ,  104.46938776],\n",
       "       [1980.        ,   74.        ],\n",
       "       [2025.        ,   68.        ],\n",
       "       [1970.        ,   68.        ],\n",
       "       [2125.        ,   63.        ],\n",
       "       [2125.        ,   70.        ],\n",
       "       [2160.        ,   88.        ],\n",
       "       [2205.        ,   75.        ],\n",
       "       [2245.        ,   70.        ],\n",
       "       [1965.        ,   67.        ],\n",
       "       [1965.        ,   67.        ],\n",
       "       [1995.        ,   67.        ],\n",
       "       [2945.        ,  110.        ],\n",
       "       [3015.        ,   85.        ],\n",
       "       [2585.        ,   92.        ],\n",
       "       [2835.        ,  112.        ],\n",
       "       [2665.        ,   96.        ],\n",
       "       [2370.        ,   84.        ],\n",
       "       [2950.        ,   90.        ],\n",
       "       [2790.        ,   86.        ],\n",
       "       [2130.        ,   52.        ],\n",
       "       [2295.        ,   84.        ],\n",
       "       [2625.        ,   79.        ],\n",
       "       [2720.        ,   82.        ]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>weight</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3504</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3693</td>\n",
       "      <td>165.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3436</td>\n",
       "      <td>150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3433</td>\n",
       "      <td>150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3449</td>\n",
       "      <td>140.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   weight  horsepower\n",
       "0    3504       130.0\n",
       "1    3693       165.0\n",
       "2    3436       150.0\n",
       "3    3433       150.0\n",
       "4    3449       140.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['weight', 'horsepower']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.00521591 -0.06185685]]\n",
      "[45.44711105]\n"
     ]
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(X_train, Y_train)\n",
    "Y_pred = model.predict(X_test)\n",
    "print(model.coef_)\n",
    "print(model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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"
    }
   ],
   "source": [
    "plt.scatter(Y_test, Y_pred, color='red', linewidth=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared: 0.7030552754471302\n"
     ]
    }
   ],
   "source": [
    "print('R-squared:', metrics.r2_score(Y_test, Y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Do a 10-fold cross validation again with two variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 0, R-squared: 0.7394788901433109,  Slope: [[-0.00589103 -0.04695723]], Intercept: [45.87146109],  \n",
      "Trial 1, R-squared: 0.7030022961282528,  Slope: [[-0.00581111 -0.05081401]], Intercept: [45.96307329],  \n",
      "Trial 2, R-squared: 0.6810752276995626,  Slope: [[-0.00582756 -0.0454195 ]], Intercept: [45.64411764],  \n",
      "Trial 3, R-squared: 0.7720739541546723,  Slope: [[-0.00572728 -0.04634417]], Intercept: [45.28706059],  \n",
      "Trial 4, R-squared: 0.6901942972297512,  Slope: [[-0.006063   -0.04328103]], Intercept: [46.10922243],  \n",
      "Trial 5, R-squared: 0.743607034267757,  Slope: [[-0.00613194 -0.03902896]], Intercept: [45.80033424],  \n",
      "Trial 6, R-squared: 0.6985628470342096,  Slope: [[-0.00611105 -0.04303764]], Intercept: [46.28032798],  \n",
      "Trial 7, R-squared: 0.7601648112754598,  Slope: [[-0.00631528 -0.03423465]], Intercept: [45.8063684],  \n",
      "Trial 8, R-squared: 0.6229038216256992,  Slope: [[-0.00627284 -0.0395287 ]], Intercept: [46.45763961],  \n",
      "Trial 9, R-squared: 0.7675256934943115,  Slope: [[-0.00581441 -0.04625372]], Intercept: [45.59497169],  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2bbc306f198>"
      ]
     },
     "execution_count": 40,
     "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": [
    "rsquare = []\n",
    "for i in range(10):\n",
    "    X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state = random.randint(1,1000))\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_train, Y_train)\n",
    "    Y_pred = model.predict(X_test)\n",
    "    rsquare.append(metrics.r2_score(Y_test, Y_pred))\n",
    "    print('Trial {}, R-squared: {},  Slope: {}, Intercept: {},  '.format(i, metrics.r2_score(Y_test, Y_pred), \\\n",
    "                                                                      model.coef_, model.intercept_))\n",
    "\n",
    "    \n",
    "rdf = pd.DataFrame( {'trial': range(10), 'Rsquare': rsquare})\n",
    "rdf.plot.bar(x='trial', y='Rsquare')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7178588873052987\n"
     ]
    }
   ],
   "source": [
    "print(rdf['Rsquare'].mean())"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}