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": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "</style>\n",
       "<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": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(Xarray)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([130.        , 165.        , 150.        , 150.        ,\n",
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       "        92.        ,  79.        ,  83.        , 140.        ,\n",
       "       150.        , 120.        , 152.        , 100.        ,\n",
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       "        60.        ,  70.        ,  53.        , 100.        ,\n",
       "        78.        , 110.        ,  95.        ,  71.        ,\n",
       "        70.        ,  75.        ,  72.        , 102.        ,\n",
       "       150.        ,  88.        , 108.        , 120.        ,\n",
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       "       105.        ,  95.        ,  85.        ,  88.        ,\n",
       "       100.        ,  90.        , 105.        ,  85.        ,\n",
       "       110.        , 120.        , 145.        , 165.        ,\n",
       "       139.        , 140.        ,  68.        ,  95.        ,\n",
       "        97.        ,  75.        ,  95.        , 105.        ,\n",
       "        85.        ,  97.        , 103.        , 125.        ,\n",
       "       115.        , 133.        ,  71.        ,  68.        ,\n",
       "       115.        ,  85.        ,  88.        ,  90.        ,\n",
       "       110.        , 130.        , 129.        , 138.        ,\n",
       "       135.        , 155.        , 142.        , 125.        ,\n",
       "       150.        ,  71.        ,  65.        ,  80.        ,\n",
       "        80.        ,  77.        , 125.        ,  71.        ,\n",
       "        90.        ,  70.        ,  70.        ,  65.        ,\n",
       "        69.        ,  90.        , 115.        , 115.        ,\n",
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       "        92.        ,  75.        ,  65.        , 105.        ,\n",
       "        65.        ,  48.        ,  48.        ,  67.        ,\n",
       "        67.        ,  67.        , 104.46938776,  67.        ,\n",
       "        62.        , 132.        , 100.        ,  88.        ,\n",
       "       104.46938776,  72.        ,  84.        ,  84.        ,\n",
       "        92.        , 110.        ,  84.        ,  58.        ,\n",
       "        64.        ,  60.        ,  67.        ,  65.        ,\n",
       "        62.        ,  68.        ,  63.        ,  65.        ,\n",
       "        65.        ,  74.        , 104.46938776,  75.        ,\n",
       "        75.        , 100.        ,  74.        ,  80.        ,\n",
       "        76.        , 116.        , 120.        , 110.        ,\n",
       "       105.        ,  88.        ,  85.        ,  88.        ,\n",
       "        88.        ,  88.        ,  85.        ,  84.        ,\n",
       "        90.        ,  92.        , 104.46938776,  74.        ,\n",
       "        68.        ,  68.        ,  63.        ,  70.        ,\n",
       "        88.        ,  75.        ,  70.        ,  67.        ,\n",
       "        67.        ,  67.        , 110.        ,  85.        ,\n",
       "        92.        , 112.        ,  96.        ,  84.        ,\n",
       "        90.        ,  86.        ,  52.        ,  84.        ,\n",
       "        79.        ,  82.        ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(199, 2)\n"
     ]
    }
   ],
   "source": [
    "X = Xarray.reshape(-1, 2)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(398, 1)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = Xarray.reshape(-1, 1)\n",
    "Y = Yarray.reshape(-1, 1)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, 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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       "       [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": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [2984],\n",
       "       [1965],\n",
       "       [4464],\n",
       "       [3012],\n",
       "       [2870],\n",
       "       [4042],\n",
       "       [4422],\n",
       "       [3988],\n",
       "       [3940],\n",
       "       [2600],\n",
       "       [3410],\n",
       "       [3820],\n",
       "       [3850],\n",
       "       [3230],\n",
       "       [2035],\n",
       "       [3570],\n",
       "       [2800],\n",
       "       [3353],\n",
       "       [1867],\n",
       "       [3282],\n",
       "       [2223]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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)\n",
    "X_train\n",
    "X_test\n",
    "Y_train"
   ]
  },
  {
   "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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L8sUjcNAXkX5AM7BZVS8UkTE4e+YOAV4CLlfVvSIyAHgImABsA76kqm+6z3EzMB04AHxDVZ/K5JsxJtf8AmYqx0eNGkVTUxMffu45Ji1dGndp47jWrw92nilqyXTvXAe8HnX/+8DdqloJbMcJ5rg/t6vqccDd7nmIyMeAS4CPA+cDP3MvJMaYKFXHHsvMsjImJxPwwenrN8ZHoKAvIiOAicAD7n0BzgEec0+Zj7M5OsAk9z7u8Rr3/EnAIlXdo6obcPbQPTUTb8KYPiMyUPu1r0EyAX/YMCeLxxgfQVv69wA3AJG8r6OA91R1v3t/E1Dh3q4A3gJwj3e453eXx3lMNxGZISLNItLc1taWxFsxpsB5DdT6GTYMli+Pn7ZpTAzfoC8iFwLvqGpLdHGcU9XnWKLHHCxQvV9Vq1W1eujQoX7VM6awPfMMDBwI/frB4MHBA/655zqTrxYscPL1Tzklu/U0fUaQgdwzgItE5ALgUGAQTsv/SBHp77bmRwBb3PM3ASOBTSLSHygH2qPKI6IfY0xW5HIbuqSddBKsWnXw/p49wR5XUgKPPBJoFUxjYvkGfVW9GbgZQETOBq5X1UtF5DfA53EyeKYCS92HLHPv/9E9/jtVVRFZBiwUkbuAY4BK4M+ZfTvGHJTrbei86tDronPssXDHHT0DflBJLHtsTDzp5OnfCCwSke8CLwPz3PJ5wK9EZB1OC/8SAFVdIyKPAq8B+4FrVPVA76c1JjOCLCaWzW8C8S46zXPn8tFHH6V027bknqy0FKZNg+99zwK+SUtSQV9VnwWedW+vJ072jaruBr7g8fjbgduTraQxqfBb+ybb3wRiLzr99+3jCw89ROnOnck9UWSg1vrtTQbYjFzTZ/ktJpbtDak7Ojo4dOdOznnmGY7atg0V4fCgAX/AAPj2txMvqJYjoR4XMUmzoG/6LL+13rO969Ppb7zBpx9+OLUFrn77W/jkJzNSj3SEYVzEZJYFfZOysLcA/da+yequT+3tnLdoUdw85UQUkBNPDEXAh+x/GzK5Z0HfpKRQWoCJ1r7J6q5Ps2YhScyo7QL2lZbyqyuu4LTrriMsn6Dtgdv3WNA3KekLLcBMbEjt+W3Hb3/aKB8MHMjDU6awpcKZoN7Y2Biaz9D2wO17LOiblBR6CzA2WF988cVJB9rW1lZ+X1/Plxcs4IgdO9gxaBCPbdwI06ZR5bc/7bnn8rsDB9g+eDB/Of549ketq9/ptS5+HtgeuH2PBX2TkkJuAWaqa0q/8hW+/uKL3f32h+3ezdV3303rH/4ATz4J993Xc5vCCHdG7e9/+tN030og6Yy9ZOLbkAkXC/omJYXcAsxI19S6dVRFBfwIAapefBHa2333py0rK4vbqi/LYHpmJi5wtslK32JB36SkkFuAGemamjzZMzNH3OO0tjqrZs6a5fTxjxvnLJLmzqitra1l8eLFvR5fW1sbvB4+cjH2EvYsLtOTBX1TdDLSNbV5c7Djkf1pPfTr148DBw70uJ9J2R57KZQsLnOQBX2TkiB/7H4twCeeeIKWlhZUFRFhwoQJTJw4Met1z0jXVEUFbN+e+LiPpqamHgEf4MCBAxlthWd77KUvZHEVm5QmCxqT6I8dDl4UIgEnclFobW0FnIDf3NyMurnsqkpzczNPPPFE1uteVVVFXV1dd+ArLy+nrq4uuSDV0JDecXKTAVVTU0NpVGYQZHbspdCzuIqRtfQLTFj6T/3+2P1agC0tLfEeTktLS05a+2kPTh53HEyfDvPm9T42fbpz3EcuMqCyPfZSyFlcxcqCfgEJU/+p3x+730VBPWarepWH0gMPwE03OYO2mzc7XToNDYECPuQuA8rvApdOQ6KQs7iKlXXvFBC/LpVc8us28GrpRcpF4ue+eJWH1nHHOVk67e3Oz4ABHzLUzZQmv244P2F4DyY51tIvIGHqP/XrNvBrAU6YMIHm5uZezzthwoQc1D488p0Dn4mB2Hy/B5Mc36AvIocCzwMD3PMfU9VbRORB4CwgEnGuVNVV4jTVfgxcAOxyy19yn2sq8G33/O+q6vxMvpm+Lmz9p4n+2P0uCqNGjeKll16iK2riUklJCaNGjcp+xaO9+y7Mng1//WuvPPpiEKaGhMmNIC39PcA5qvqBiJQCL4hIo3vsP1T1sZjza3H2v60ETgPmAqeJyBDgFqAaZwXZFhFZpqoJ8t5MtELrP010UWhqauoR8AG6urpyl+q3axd885vw859HV8pZOqG+HqZOzX4dQiBsDQmTfUE2RlfgA/duqfsv0WjbJOAh93F/EpEjRWQ4cDawQlXbAURkBXA+8HDq1S8uhTYLNtEAYV5bmCtXwsSJ0NbW+1hXl7N0Ql1dUbT4C60hYdIXqE9fRPoBLcBxwL2q+qKIfB24XURmA03ATaq6B6gA3op6+Ca3zKs89rVmADOA3H/VLwCF0n/ql2mUtxZmZ6cT0OMF/IiuLmfphAQzaSPCkkKbSKI6FlpDwqQvUNBX1QPAiSJyJNAgIicANwP/AA4B7gduBG6DuEuSaILy2Ne6330+qqurCyh/Lz2FEDyS4TdAWFNTw9KlS3stQZD1FmZDA2zd6n9egPXww5RC6yVIHQulIWEyI6nsHVV9T0SeBc5X1R+6xXtE5JfA9e79TcDIqIeNALa45WfHlD+bfJX7nkIIHskK0n0Tm5OfSo6+78Vy1y4n0G/Y4GwyHnRzk3HjfE8phCUICqGOJreCZO8MBfa5Ab8MOBf4vogMV9W33WydzwKvug9ZBlwrIotwBnI73POeAv5LRAa7552H822h6PXFP0y/7ptMDOT6XixXrnS6cqJb9kG6j0pKnCweH4WQ+VIIdTS5FWRy1nDgGRF5BViJMxj7OLBARFqBVuBo4Lvu+U8C64F1wC+AqwHcAdw57nOsBG6LDOoWu774h+k3eSsT7znhZLVI331sV05HhxPUvYh0r3fvx28CWhgUQh1NbgXJ3nkFOClO+Tke5ytwjcexeqA+yTr2eX0xbc5vgDAT7znhhSNR331XFwwaBO+/f7DskEPgooucFM6AWTuFkPlSCHU0uWUzckOgr/5hJhogzMR7TnjhWL8+8YNnznT67devd/r6J0+GJHesKoTMl0Koo8ktC/ohUIx/mJl4zzU1NaxYtIgzn36ao7Zt492jj+aF885zLhx+a8eMGwdTpqTzFoDCyHwphDqa3JEwr2pYXV2t8dZnMeGQ9zTT+fPRadOQqN9hFUF++Uv44hdhzJj4XTzDhjnZPBnci9aYMBGRFlWtjnfMVtk0KUl3dca0tbfDVVf1CPiAc/+qq5yB3OXLnQAfbdgwp9wCvilS1r2TI3lvFWdYrtJMPT+3WbOcAdl4omfUbtjgDOqm0XdvTF9iQT8HinXyVboin5vu3EnVX/7Ckdu387c//hG5/npO8JtkFTleVpaRvntj+goL+jkQ1slX6Xz7yEWaaVNTE/+0bh1TFi7k0D17ust3NjbCZz6T+MEBZtQaU4ws6OdAolZxvrp90v32kYs000GvvMKVv/xlr4GngTt2wHPPOROp4iUiBJxRa0wxsoHcHPBq/ZaVlfUaDF28eDF33nln1gdE0916Mevb5HV2cunDD3v/gra1wYwZvWfXlpQEnlFrTDGyln4OeLWKgV6BF6CzszPrff6Z6JPPeP539C5WIgzYvTvx+SNGOMF/1iynD78Id74yJlkW9HPAayLS4sWLPR+T7T7/0C39MH++k2rplZETz9ixToAPsO69McZhQT9H4rWKIxcBL9lccC0USz80NsJnPwt79yb/2EGDnPRLY0xSrE8/j+KtRBktm63uqqoqxo8fj7MyNogI48ePz1020bhxcMEFqQX8khJ4/HHLtzcmBdbSz6NIgG1sbKSzs7PHsUy0uuNlBkH8bxiqyurVqxk1alT2A39Tk9Nvn4rycmdG7ZlnZrZOxhQJW3snJDKduhmbkgnOdoSq2mvzkmjl5eXMnDkz5ddNKLKL1dSpELVNoq9zz4WzzrIZtcYElGjtHWvph0SmM2HipWQeCBBoszaOEG8XqyBKSuCRRywjx5gM8e3TF5FDReTPIrJaRNaIyK1u+RgReVFE1orIIyJyiFs+wL2/zj0+Ouq5bnbL3xARnymVJh2pBu+MjSO8+y5cfrkTrAcNgk98IrWAbzn3xmRUkIHcPcA5qjoeOBE4X0ROB74P3K2qlcB2YLp7/nRgu6oeB9ztnoeIfAy4BPg4cD7wMxHpl8k3Yw5KJXhnLHtn/nwYOhR+/WvYvh127ID9+wM9VAFOPBGuvtrJwZ86Nf36GGO6+QZ9dXzg3i11/ylwDvCYWz4fZ3N0gEnufdzjNe7m6ZOARaq6R1U34Oyhe2pG3oXppbKyMqnzMzajdtMmmDYtpYcqsO3oo+Hll53ce2vhG5Nxgfr03RZ5C3AccC/wN+A9VY003zYBFe7tCuAtAFXdLyIdwFFu+Z+injb6MdGvNQOYATBq1Kgk30545XqNnTVr1mTleRO+j5UrnQHXJJMDuoAD/frx0JQp/NOXvsTEzFfbGOMKFPRV9QBwoogcCTQAx8c7zf0pHse8ymNf637gfnCyd4LUL+zysbRybAqonyB1Svg+jjvOGahN8nU/GDiQH8+cyX53vsLmlhaam5sDXxj72j4FxmRbUtk7qvqeiDwLnA4cKSL93db+CGCLe9omYCSwSUT6A+VAe1R5RPRj+rSwLq0cK7ZOsQF17969Pd7HP23cyOULFzJg1iwnjXLnzqRe74OBA3l4ypTugA/OfAHoeUGB+Hvp9sV9CozJNt+gLyJDgX1uwC8DzsUZnH0G+DywCJgKLHUfssy9/0f3+O9UVUVkGbBQRO4CjgEqgT9n+P2EUi42HIlVVlaWdGsfDtYpXkCNdnl9PWM2bjz49S2ZgH/99TT+4x+89OEP9wj4sfbt20djYyP79++PG9gL5WJqTJgEyd4ZDjwjIq8AK4EVqvo4cCPwTRFZh9NnP889fx5wlFv+TeAmAFVdAzwKvAb8L3CN223U53ll0mRzmYXa2lpKYpcdDiBSp3gBFaD/3r2c8eyzPQN+MmbPhh/8gBE33IAcdpjv6Z2dnZ6BPR8XU2MKnW9LX1VfAU6KU76eONk3qrob+ILHc90O3J58NQtbPhY3i7ey5969exO2/qPrFBs4D925k7rHH+cjb7xB/2RWwsQZqH1r1Ch2zpvHx849N279khV5T6FaKdSYAmAzcnPAa2nlbHdBxM7yvfXWWz3Pja1TdECd8OKLTGxsTKllH+m331JRQfmrr3YH/dj63XnnnXEvSCJCvKVCIvXN+0qhxhQYC/o5kvENR1KQqGUcu95OZWUl6xobmfbggxyxc2dSAX9PaSn/98lPsn3wYP5y/PHd/faJWvRe30BUldLS0riBPV8XU2MKmQX9Pi46A6esrIySkpIeC655tYxHzpnDBS++mHTrXoH6K6/knYpeUzASdrskuiDV1NR4BvYwXEyNKSQW9Puw2Ayczs5O+vXr153ZE7dlvGsXzJ1LVYoBf8OoUXEDvl+3S6KuGgvsxmSOBf0+LNFKm5GWdWQj9Krhw+FrX3PWqt+7N6mAr0DnoYcy//LL4wZ8gP79E/+qWVeNMblhQb+PiDcz1asPvbOzs7sPvaOjg3WzZ/PxJUtS2kbtg8MO4+FLL2WLR7CPfs3YiVPx6py1tfyNMYAF/T7Ba2aq3wStsa+9xpd/8xv6qabUlfPy+PE0XnhhjwlWZWVlHHLIIXEvONETp2w2rTH5YUG/D/Camdq/f/9emS/gTLC67q67GLh7d0ppmAq8eNll/O7449kf0wdfW1tLVVWVZ3po5GJgs2mNyQ8L+gUsunskns7OTi6++OLuc0SEj7S28sXHHkupK0eBd446igenT2fA8OHUJciq8Zs4ZbNpjckPC/oFKt4euLGcbQyczJgVixZx6X338aH29pS6ct4ZOpRFl1zCe0cdBcDujo6EWTV+E6e8up7KbP9bY7LKgn4IBVku2GttnGiqyopFi7h40SJmrl+f2kBt1IzaaJELihfLxjEmnCzoh0zQAc4g3SCfeOYZzn3uudQWRhOBGTP48dFHx10JU1V9L06Jvgl4DTCnsjKoMSa4VBp/JosSDXCCc+bQykcAABM3SURBVFG45557Ej7H4e+9xze/973UA/4FFzgbm993HwOPPjruKWVlZSxfvrz74hO5OLW2tgZ6iXysPGqMsaAfGpFgnmiAM/ItIFEr/zPLl/PNe+7hiD17Ugv4o0bBE090709bU1NDaUxLP3I/0cXJj9fz2mJpxmSXBf0QCBLMRYTGxkbPfvyjysq4ZuFCTmtpSWmg9gCw7r//G/7+9x7HqqqqqKur6zHA2r9/f89umKDZN5HnjbTsM7YxuzEmIevTD4Ggg7JegfaYzZv5yuLFsG1b0q+twEvjx/P45MmUdnRQ19oaN/Du37+/+3aifvdkumdsTR1jcs+3pS8iI0XkGRF5XUTWiMh1bvl3RGSziKxy/10Q9ZibRWSdiLwhIp+JKj/fLVsnIjdl5y0VnlRz0w/duZOJy5Yxrb4+6YCvQMcRR/CTf/s3Hp88GfDunglyUQLrnjGmEARp6e8H/l1VXxKRI4AWEVnhHrtbVX8YfbKIfAy4BPg4zl64vxWRj7iH7wU+jbNJ+koRWaaqr2XijRQyr4lMify/VauYlMJ6OQrIqady59lnszvOdoXx6pGobpG6W0qmMYUhyHaJbwNvu7d3iMjrQKLVtSYBi1R1D7DB3Ss3sq3iOnebRURkkXtu0Qf9eBOZvAzfsYPPPfQQQ9raUuq7l/PPh8ZGBtxzD7sDbjWYzOYriQSZf2CMya6kGooiMhpnv9wX3aJrReQVEakXkcFuWQXwVtTDNrllXuWxrzFDRJpFpLmtrS2Z6hWseIOa1dXVvbJb6pYv5ys/+hFHJRnwFWc3K2lthcZGILnsmUxk2sQOVieb4mmMyYzAA7kicjjwP8BMVX1fROYCc3BiyhzgR8BVEDceKfEvML02P1XV+4H7Aaqrq3tvjtpHxRvUHDVqFP+3dCkTli5l+DvvULFxY0qt+9aqKmTBAqpOOKHH623cuJGWlhZUtXuG7eLFi2lqauq1OxX0nl0LdKeZ+rXcbYE1Y8IhUNAXkVKcgL9AVRcDqOrWqOO/AB53724CRkY9fASwxb3tVW7iqGpooOqWW1J6bBewffBgGr7+dU675JJegbW1tZWXX365e9NxVU04Czj2opTs0si2wJox4eAb9MVpAs4DXlfVu6LKh7v9/QCTgVfd28uAhSJyF85AbiXwZ5xvAJUiMgbYjDPYOyVTbyRs0uq/3rUL/vmf4ZVXUnrtTbNm0XD44bS7WyJ61SuRffv20dDQAMQP4sm23P1W3TTG5EaQlv4ZwOVAq4iscsv+E/iyiJyI04PwJvBVAFVdIyKP4gzQ7geuUdUDACJyLfAU0A+oV9U1GXwvoZHWBiErV0JtbUo595SU8Natt/KgKl1RO2MtWbKk+5SgA8bgtP4XL17M4sWLEREmTJjAxIkTu583Hq9yv1U3jTG5ESR75wXi99M/meAxtwO3xyl/MtHj+oqU+q83boQrr4Tnnwd3H9ukTJkCP/0pDz/wQHfAj+jq6qKxsZFDDjkkcMCPpao0NzcDMHHixKRb7rbqpjHhYDNysyCpVvC77zotezegpmT6dHjgASDx6pWZWMGypaWFiRMnptRytxm4xuSfrb2TBYFXkLzjDhg6NLWAX14OJ5wAa9d2B3w/mdigJDLwa2vnGFOYrKWfBb6t4HffdQZq161L+rkVkDlz4Nvfjns80Wboe/fupaSkhK6urriP279/v2/3T/TmKdZyN6bwWEs/CzxbwcceC1/9qtO6TzHgb/joRz0DPkBtbS39+vWLe+zAgQMMGDCgu16lpaXdQbyzszNQf/+ECROSrrcxJjyspR9HJpYL6NUKXrAAxo8HTX6+WRew87DDmD91KmMmTmSsz+uCM8kqns7OTm644QaeeOKJ7oFZL6Wlpezfv7978lZ09o4xpjBZ0I+RVrplPLt2wSc+AatXJ/1QBZ6orWX1ySd3b1m4f+3ahI+JXLC8RPr1W1pafF9/37593JLi5DBjTDhZ904Mv+0KA3vmGSgrg4EDUw74z551Fi2nndZjj9pEk6paW1tZsmRJwnP27NlDa2tr94BsIjZxypi+x1r6MTKyXMBJJ8GqVf7neTn2WO6eNIkdgwbFPey13k1jY2PcQdpoXV1dNDU1ISIJA79NnDKmb7KgHyPopKO4/f7HHuukYaYT8C+7DH71K3bceqvnKbErVYLT9RQ0D7+jo4Pq6mrPPn2bOGVM32VBP0aQSUfx+v1f/slPOH7RIvp/8EHSr9kF7Bw0iE0LF3K8O1AadGOVVFaqLC8v7x6QjV5l0wZqjen7LOjTu9U+fvx41q5d65m9E93v33/vXs544QXOev75lJY9/uuYMSz5whfYfdhhlK5ezf5Ro6iqqqKmpoaGhoZAfe+Ri0OiHP2I6AvYxIkTLcgbU2SKPujHa7WvXr064ezSjo4ODn/vPb706KMM37KF+FnxiSnwl8pKHr300u6y2FZ7kIAPB7ueamtrWbp0KQei1u4pKSlhwIABdLorblq3jTHFreiDfiqLo533hz9w+tNPJ92yB7crZ+BA5l9xBduGDet1PNJqD5otFN1yt0XNjDF+ij7oJ52ts3lzSgFfge3l5cy99toeKZixIq32RP35kcwbC+rGmGQVfdBPenOPK69MKuB3AftKS5l/2WW8/eEPJzw3utWeaCDXa8A14xPLjDF9TtFPzkp60+/16wM/dxfw4LRp3PGtb/kG/LKysh7jCIly5Nd6zMrN2MQyY0yf5Rv0RWSkiDwjIq+LyBoRuc4tHyIiK0RkrftzsFsuIvITEVknIq+IyMlRzzXVPX+tiEzN3tsKLuklgscmWvnmoN0DBvDgtGm85RPsRYSLL76YG264ocdrJmqZJ9slZfvQGmMignTv7Af+XVVfEpEjgBYRWQFcCTSp6h0ichNwE3AjUIuzL24lcBowFzhNRIYAtwDVOF3cLSKyTFW3Z/pNpUs6O50F0jZscIL85MnOkgoADz4II0Z4PnZP//7835ln8sdPfCJh332EqnoG+GS7nmwfWmOMH9+Wvqq+raovubd3AK8DFcAkYL572nzgs+7tScBD6vgTcKSIDAc+A6xQ1XY30K8Azs/ou0lBpB88EiwHvvYao2tqnJmxs2bBpZfCmDHO3rUAFRUwezaxyZQKvDZuHD+88UZ+f9ZZgQI+JA7IyXY9Jd1VZYwpOkkN5IrIaOAk4EVgmKq+Dc6FQUQ+5J5WAbwV9bBNbplXeexrzABmAIwaNSqZ6sXlt0xyU1MTA9ra+NLSpQzZvp0j3n+f/rHr12zdCnV1Tsu/rIzWz3+eZ3bvZuJjjzG4vZ3tQ4awZNIkPkiyRS0idHR0cOutt8adERsvBbOyspKmpiYWL17c6/1YyqYxxk/goC8ihwP/A8xU1fejd1CKPTVOmSYo71mgej9wP0B1dXXyi89HCZLNMn7JEs5+7jn/jJytW6GhAaZMcYLqYYfx6yuuSKd6PSZfRTYe37ZtG1dEPW/0uvxB3o/tZmWMSSRQ9o6IlOIE/AWqGtmdY6vbbYP78x23fBMwMurhI4AtCcqzxjebZfPmYAE/ws3cSTQwGtu9kqwNGzbQ2toa95jX+1m8eDH33HOP5+OMMSYiSPaOAPOA11X1rqhDy4BIBs5UYGlU+RVuFs/pQIfbDfQUcJ6IDHYzfc5zy7LGN5slyZz7SOaOVz+8iFBXV0eCb0GBeKVYJrrYRFr9FviNMYkEaemfAVwOnCMiq9x/FwB3AJ8WkbXAp937AE8C64F1wC+AqwFUtR2YA6x0/93mlmVNoiwXIKmce4YNc7J48B4wnTx5MlVVVWnvI+sV3P2ycCwn3xjjx7dPX1VfIH5/PECvtBB1Oqqv8XiueqA+mQqmw3eZ5LFjgwX+YcNg+fLutE2/AdN4yxaPHj2a9vb27vM/+OCDHgujRfMK7vHeTyzLyTfGJNKnl2GoqqpCOjt566c/ZcDmzeypqGDkN77BCZGBTp+ce66/3tkFKzpPPyC/ZYtbW1vjLp1cUlLimWIZe7GJJyw5+ZnYXN4Yk3l9OuizciUnXHQRJ2zderBsxQqn1X7KKd0599x2W+/Hzp4NHrtXZWKNm+gtDiNr4JeVlVFbW5vwOSLZObF1gPDk5NsaQMaElwRdsz0fqqur1WtLP1+dnc6kquiAHzFsWHfOPQCbN8OVVzpdPWPHOt8AKnpNIegW2aM2Vnl5OTNnzuxRls0Wb1hb08l8PsaYzBORFlWtjnes77b0GxriB3zokXMPOAF+xYrATx10jZtst3jDmpNvawAZE159d5VNvwHaZDJ3YvhmBbmKddXLoJ+PMSb3+m7Q91sNM+BqmfEEXeOmWFu8tgaQMeHVd7t3Jk92+u69+vTdnPtUBF3jplhXvbQ1gIwJr74b9MvKnCydurqegT8m5z5VQfrTfecJ9GFhHW8wptj13aAPTlrmhg3OoG0kMyeFnPtUWYvXGBM2fTdlMwlhTX00xphUFGfKZkA2kcgYU0yKPugnSqvMVtC3bxbGmHwp+qCf67RK+2ZhjMmnvpunH1CuJxIV64QtY0w4FH3Qz/VEomKdsGWMCYei797JdVplsU7YMsaEg2/QF5F64ELgHVU9wS37DvAVoM097T9V9Un32M3AdOAA8A1VfcotPx/4MdAPeEBV7yAkcjmRqJgnbBlj8i9IS/9B4L+Bh2LK71bVH0YXiMjHgEuAjwPHAL8VkY+4h+/F2VZxE7BSRJap6mtp1L0g2YQtY0w+Bdku8XkRGR3w+SYBi1R1D7BBRNYBp7rH1qnqegARWeSeW3RBH2yJAmNM/qQzkHutiLwiIvUiMtgtqwDeijpnk1vmVW6MMSaHUg36c4FjgROBt4EfueXxNlDXBOW9iMgMEWkWkea2trZ4pxhjjElRSkFfVbeq6gFV7QJ+wcEunE3AyKhTRwBbEpTHe+77VbVaVauHDh2aSvWMMcZ4SCnoi8jwqLuTgVfd28uAS0RkgIiMASqBPwMrgUoRGSMih+AM9i5LvdrGGGNSESRl82HgbOBoEdkE3AKcLSIn4nTRvAl8FUBV14jIozgDtPuBa1T1gPs81wJP4aRs1qvqmoy/G2OMMQmFemllEWkD/p7llzkaeDfLr5GusNcx7PWD8Ncx7PWD8Ncx7PWD3NXxw6oat3881EE/F0Sk2Wvd6bAIex3DXj8Ifx3DXj8Ifx3DXj8IRx2Lfu0dY4wpJhb0jTGmiFjQh/vzXYEAwl7HsNcPwl/HsNcPwl/HsNcPQlDHou/TN8aYYmItfWOMKSIW9I0xpogUXdAXkTdFpFVEVolIs1s2RERWiMha9+dgv+fJUt3GufWK/HtfRGaKyHdEZHNU+QU5rle9iLwjIq9GlcX9zMTxExFZ5y7Id3Ke6vcDEfmLW4cGETnSLR8tIp1Rn+V92a5fgjp6/r+KyM3uZ/iGiHwmT/V7JKpub4rIKrc8X5/hSBF5RkReF5E1InKdWx6K38UE9QvV7yKqWlT/cGYQHx1Tdidwk3v7JuD7IahnP+AfwIeB7wDX57EunwJOBl71+8yAC4BGnEX2TgdezFP9zgP6u7e/H1W/0dHn5fkzjPv/CnwMWA0MAMYAfwP65bp+Mcd/BMzO82c4HDjZvX0E8Ff3swrF72KC+oXqd7HoWvoeJgHz3dvzgc/msS4RNcDfVDXbM5J9qerzQHtMsddnNgl4SB1/Ao6MWaspJ/VT1adVdb979084i/zljcdn6KV7XwpV3QBE70uRFYnqJyICfBF4OJt18KOqb6vqS+7tHcDrOEu0h+J30at+YftdLMagr8DTItIiIjPcsmGq+jY4/3HAh/JWu4MuoecfWbz9C/LJ6zML494JV+G0+CLGiMjLIvKciJyZr0q5ktmXIl/OBLaq6tqosrx+huJs7HQS8CIh/F2MqV+0vP8uFmPQP0NVTwZqgWtE5FP5rlAscVYivQj4jVvktX9BGAXeOyEXRORbOIv/LXCL3gZGqepJwDeBhSIyKE/VS3Zfinz5Mj0bIHn9DEXkcOB/gJmq+n6iU+OUZf1z9KpfWH4Xiy7oq+oW9+c7QAPO1+atka997s938ldDwLkgvaSqWyHh/gX55PWZBd47IdtEZCpwIXCpup2obpfJNvd2C05/+Ue8nyV7Evy/hukz7A9cDDwSKcvnZygipTgBdYGqLnaLQ/O76FG/UP0uFlXQF5GBInJE5DbOAMurOGv7T3VPmwoszU8Nu/VoWYn3/gX55PWZLQOucDMnTgc6Il+9c0lEzgduBC5S1V1R5UNFpJ97eyzOng/rc10/9/WT3ZciH84F/qKqmyIF+foM3bGFecDrqnpX1KFQ/C561S90v4u5HjnO5z9gLE5WxGpgDfAtt/wooAlY6/4cksc6HgZsA8qjyn4FtAKv4PwiD89xnR7G+Sq6D6f1NN3rM8P5Sn0vTqulFajOU/3W4fTnrnL/3eee+zn3/3418BJQl8fP0PP/FfiW+xm+AdTmo35u+YPA12LOzddn+Emc7plXov5fLwjL72KC+oXqd9GWYTDGmCJSVN07xhhT7CzoG2NMEbGgb4wxRcSCvjHGFBEL+sYYU0Qs6BtjTBGxoG+MMUXk/wPBFjo/6gRgYQAAAABJRU5ErkJggg==\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": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "8\n",
      "9\n",
      "9\n",
      "8\n",
      "2\n",
      "10\n",
      "9\n",
      "3\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "for i in range(10):\n",
    "    print(random.randint(1, 10))"
   ]
  },
  {
   "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": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 0, R-squared: 0.7177621132779897,  Slope: [[19.32841916]], Intercept: [947.39991828],  \n",
      "Trial 1, R-squared: 0.6016957720250167,  Slope: [[19.39700249]], Intercept: [934.70484132],  \n",
      "Trial 2, R-squared: 0.5912799692881368,  Slope: [[19.18855903]], Intercept: [944.97992197],  \n",
      "Trial 3, R-squared: 0.7044380278504583,  Slope: [[18.67372858]], Intercept: [999.8518667],  \n",
      "Trial 4, R-squared: 0.7012224384487329,  Slope: [[19.15315442]], Intercept: [971.99993552],  \n",
      "Trial 5, R-squared: 0.8043394045734327,  Slope: [[18.92036524]], Intercept: [994.82650043],  \n",
      "Trial 6, R-squared: 0.7605777567754237,  Slope: [[18.85490209]], Intercept: [1012.5951756],  \n",
      "Trial 7, R-squared: 0.7366122906334873,  Slope: [[19.33118812]], Intercept: [963.75534953],  \n",
      "Trial 8, R-squared: 0.7459032319894745,  Slope: [[19.31768465]], Intercept: [946.03773117],  \n",
      "Trial 9, R-squared: 0.7781555308397314,  Slope: [[18.42095761]], Intercept: [1051.09755099],  \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": 57,
   "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>trial</th>\n",
       "      <th>Rsquare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.733568</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.747119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.704996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.691727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>0.757386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>0.694615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>0.755547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.758160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   trial   Rsquare\n",
       "0      0  0.761901\n",
       "1      1  0.733568\n",
       "2      2  0.637085\n",
       "3      3  0.747119\n",
       "4      4  0.704996\n",
       "5      5  0.691727\n",
       "6      6  0.757386\n",
       "7      7  0.694615\n",
       "8      8  0.755547\n",
       "9      9  0.758160"
      ]
     },
     "execution_count": 57,
     "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": 54,
   "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": [
    "rdf.plot.bar(x='trial', y='Rsquare');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.73868256909141\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",
       "       [2833.        ,   95.        ],\n",
       "       [2774.        ,   97.        ],\n",
       "       [2587.        ,   85.        ],\n",
       "       [2130.        ,   88.        ],\n",
       "       [1835.        ,   46.        ],\n",
       "       [2672.        ,   87.        ],\n",
       "       [2430.        ,   90.        ],\n",
       "       [2375.        ,   95.        ],\n",
       "       [2234.        ,  113.        ],\n",
       "       [2648.        ,   90.        ],\n",
       "       [4615.        ,  215.        ],\n",
       "       [4376.        ,  200.        ],\n",
       "       [4382.        ,  210.        ],\n",
       "       [4732.        ,  193.        ],\n",
       "       [2130.        ,   88.        ],\n",
       "       [2264.        ,   90.        ],\n",
       "       [2228.        ,   95.        ],\n",
       "       [2046.        ,  104.46938776],\n",
       "       [2634.        ,  100.        ],\n",
       "       [3439.        ,  105.        ],\n",
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       "       [3230.        ,   80.        ],\n",
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       "       [2900.        ,  116.        ],\n",
       "       [2930.        ,  120.        ],\n",
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       "       [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: 0.706193418005814,  Slope: [[-0.00565645 -0.05310158]], Intercept: [45.89178369],  \n",
      "Trial 1, R-squared: 0.749772989661937,  Slope: [[-0.00600886 -0.04357085]], Intercept: [45.80075062],  \n",
      "Trial 2, R-squared: 0.7210768095612763,  Slope: [[-0.00565302 -0.04992271]], Intercept: [45.57184617],  \n",
      "Trial 3, R-squared: 0.7187242183570066,  Slope: [[-0.00545861 -0.05723   ]], Intercept: [45.71185202],  \n",
      "Trial 4, R-squared: 0.7236109186816309,  Slope: [[-0.0060021  -0.04471701]], Intercept: [46.27211189],  \n",
      "Trial 5, R-squared: 0.6589837872303446,  Slope: [[-0.00634425 -0.0383963 ]], Intercept: [46.48830539],  \n",
      "Trial 6, R-squared: 0.6467208794814854,  Slope: [[-0.00561841 -0.04897694]], Intercept: [45.30531008],  \n",
      "Trial 7, R-squared: 0.6678357733307807,  Slope: [[-0.00599335 -0.04005743]], Intercept: [45.56896775],  \n",
      "Trial 8, R-squared: 0.7262742459752446,  Slope: [[-0.0056876  -0.05178016]], Intercept: [45.8262037],  \n",
      "Trial 9, R-squared: 0.7595821067521407,  Slope: [[-0.00588404 -0.04479735]], Intercept: [45.52379616],  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1d3623c8>"
      ]
     },
     "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": [
      "0.707877514703766\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
}