Code-Example-050.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module 5: Regression\n",
    "\n",
    "The following tutorial contains Python examples for solving regression problems. You should refer to the Appendix chapter on regression of the \"Introduction to Data Mining\" book to understand some of the concepts introduced in this tutorial. The notebook can be downloaded from http://www.cse.msu.edu/~ptan/dmbook/tutorials/tutorial5/tutorial5.ipynb.\n",
    "\n",
    "Regression is a modeling technique for predicting quantitative-valued target attributes. The goals for this tutorial are as follows:\n",
    "1. To provide examples of using different regression methods from the scikit-learn library package.\n",
    "2. To demonstrate the problem of model overfitting due to correlated attributes in the data.\n",
    "3. To illustrate how regularization can be used to avoid model overfitting. \n",
    "\n",
    "Read the step-by-step instructions below carefully. To execute the code, click on the corresponding cell and press the SHIFT-ENTER keys simultaneously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.1 Synthetic Data Generation\n",
    "\n",
    "To illustrate how linear regression works, we first generate a random 1-dimensional vector of predictor variables, x, from a uniform distribution. The response variable y has a linear relationship with x according to the following equation:  y = -3x + 1 + epsilon, where epsilon corresponds to random noise sampled from a Gaussian distribution with mean 0 and standard deviation of 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 1,
     "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": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "seed = 1            # seed for random number generation \n",
    "numInstances = 200  # number of data instances\n",
    "np.random.seed(seed)\n",
    "X = np.random.rand(numInstances,1).reshape(-1,1)\n",
    "y_true = -3*X + 1 \n",
    "y = y_true + np.random.normal(size=numInstances).reshape(-1,1)\n",
    "\n",
    "plt.scatter(X, y,  color='black')\n",
    "plt.plot(X, y_true, color='blue', linewidth=3)\n",
    "plt.title('True function: y = -3X + 1')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.2 Multiple Linear Regression\n",
    "\n",
    "In this example, we illustrate how to use Python scikit-learn package to fit a multiple linear regression (MLR) model. Given a training set {X,y}, MLR is designed to learn the regression function $f(X,w) = X^T w + w_0$ by minimizing the following loss function given a training set $\\{X_i,y_i\\}_{i=1}^N$:\n",
    "$$L(y,f(X,w)) = \\sum_{i=1}^N \\|y_i - X_i w - w_0\\|^2,$$\n",
    "where $w$ (slope) and $w_0$ (intercept) are the regression coefficients.\n",
    "\n",
    "Given the input dataset, the following steps are performed:\n",
    "1. Split the input data into their respective training and test sets.\n",
    "2. Fit multiple linear regression to the training data.\n",
    "3. Apply the model to the test data.\n",
    "4. Evaluate the performance of the model.\n",
    "5. Postprocessing: Visualizing the fitted model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 1: Split Input Data into Training and Test Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "numTrain = 20   # number of training instances\n",
    "numTest = numInstances - numTrain\n",
    "\n",
    "X_train = X[:-numTest]\n",
    "X_test = X[-numTest:]\n",
    "y_train = y[:-numTest]\n",
    "y_test = y[-numTest:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 2: Fit Regression Model to Training Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "# Fit regression model to the training set\n",
    "regr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 3: Apply Model to the Test Set "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply model to the test set\n",
    "y_pred_test = regr.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 4: Evaluate Model Performance on Test Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error = 1.0476\n",
      "R-squared = 0.4443\n"
     ]
    },
    {
     "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": [
    "# Comparing true versus predicted values\n",
    "plt.scatter(y_test, y_pred_test, color='black')\n",
    "plt.title('Comparing true and predicted values for test set')\n",
    "plt.xlabel('True values for y')\n",
    "plt.ylabel('Predicted values for y')\n",
    "\n",
    "# Model evaluation\n",
    "print(\"Root mean squared error = %.4f\" % np.sqrt(mean_squared_error(y_test, y_pred_test)))\n",
    "print('R-squared = %.4f' % r2_score(y_test, y_pred_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 5: Postprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope =  -3.242354544656501\n",
      "Intercept =  1.0805993038584834\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 6,
     "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": [
    "# Display model parameters\n",
    "print('Slope = ', regr.coef_[0][0])\n",
    "print('Intercept = ', regr.intercept_[0])### Step 4: Postprocessing\n",
    "\n",
    "# Plot outputs\n",
    "plt.scatter(X_test, y_test,  color='black')\n",
    "plt.plot(X_test, y_pred_test, color='blue', linewidth=3)\n",
    "titlestr = 'Predicted Function: y = %.2fX + %.2f' % (regr.coef_[0], regr.intercept_[0])\n",
    "plt.title(titlestr)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3 Effect of Correlated Attributes\n",
    "\n",
    "In this example, we illustrate how the presence of correlated attributes can affect the performance of regression models. Specifically, we create 4 additional variables, X2, X3, X4, and X5 that are strongly correlated with the previous variable X created in Section 5.1. The relationship between X and y remains the same as before. We then fit y against the predictor variables and compare their training and test set errors. \n",
    "\n",
    "First, we create the correlated attributes below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Correlation between X4 and X5 = 0.9190')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "seed = 1\n",
    "np.random.seed(seed)\n",
    "X2 = 0.5*X + np.random.normal(0, 0.04, size=numInstances).reshape(-1,1)\n",
    "X3 = 0.5*X2 + np.random.normal(0, 0.01, size=numInstances).reshape(-1,1)\n",
    "X4 = 0.5*X3 + np.random.normal(0, 0.01, size=numInstances).reshape(-1,1)\n",
    "X5 = 0.5*X4 + np.random.normal(0, 0.01, size=numInstances).reshape(-1,1)\n",
    "\n",
    "fig, ((ax1, ax2),(ax3,ax4)) = plt.subplots(2, 2, figsize=(12,9))\n",
    "ax1.scatter(X, X2, color='black')\n",
    "ax1.set_xlabel('X')\n",
    "ax1.set_ylabel('X2')\n",
    "c = np.corrcoef(np.column_stack((X[:-numTest],X2[:-numTest])).T)\n",
    "titlestr = 'Correlation between X and X2 = %.4f' % (c[0,1])\n",
    "ax1.set_title(titlestr)\n",
    "\n",
    "ax2.scatter(X2, X3, color='black')\n",
    "ax2.set_xlabel('X2')\n",
    "ax2.set_ylabel('X3')\n",
    "c = np.corrcoef(np.column_stack((X2[:-numTest],X3[:-numTest])).T)\n",
    "titlestr = 'Correlation between X2 and X3 = %.4f' % (c[0,1])\n",
    "ax2.set_title(titlestr)\n",
    "\n",
    "ax3.scatter(X3, X4, color='black')\n",
    "ax3.set_xlabel('X3')\n",
    "ax3.set_ylabel('X4')\n",
    "c = np.corrcoef(np.column_stack((X3[:-numTest],X4[:-numTest])).T)\n",
    "titlestr = 'Correlation between X3 and X4 = %.4f' % (c[0,1])\n",
    "ax3.set_title(titlestr)\n",
    "\n",
    "ax4.scatter(X4, X5, color='black')\n",
    "ax4.set_xlabel('X4')\n",
    "ax4.set_ylabel('X5')\n",
    "c = np.corrcoef(np.column_stack((X4[:-numTest],X5[:-numTest])).T)\n",
    "titlestr = 'Correlation between X4 and X5 = %.4f' % (c[0,1])\n",
    "ax4.set_title(titlestr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create 4 additional versions of the training and test sets. The first version, X_train2 and X_test2 have 2 correlated predictor variables, X and X2. The second version, X_train3 and X_test3 have 3 correlated predictor variables, X, X2, and X3. The third version have 4 correlated variables, X, X2, X3, and X4 whereas the last version have 5 correlated variables, X, X2, X3, X4, and X5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train2 = np.column_stack((X[:-numTest],X2[:-numTest]))\n",
    "X_test2 = np.column_stack((X[-numTest:],X2[-numTest:]))\n",
    "X_train3 = np.column_stack((X[:-numTest],X2[:-numTest],X3[:-numTest]))\n",
    "X_test3 = np.column_stack((X[-numTest:],X2[-numTest:],X3[-numTest:]))\n",
    "X_train4 = np.column_stack((X[:-numTest],X2[:-numTest],X3[:-numTest],X4[:-numTest]))\n",
    "X_test4 = np.column_stack((X[-numTest:],X2[-numTest:],X3[-numTest:],X4[-numTest:]))\n",
    "X_train5 = np.column_stack((X[:-numTest],X2[:-numTest],X3[:-numTest],X4[:-numTest],X5[:-numTest]))\n",
    "X_test5 = np.column_stack((X[-numTest:],X2[-numTest:],X3[-numTest:],X4[-numTest:],X5[-numTest:]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we train 4 new regression models based on the 4 versions of training and test data created in the previous step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr2 = linear_model.LinearRegression()\n",
    "regr2.fit(X_train2, y_train)\n",
    "\n",
    "regr3 = linear_model.LinearRegression()\n",
    "regr3.fit(X_train3, y_train)\n",
    "\n",
    "regr4 = linear_model.LinearRegression()\n",
    "regr4.fit(X_train4, y_train)\n",
    "\n",
    "regr5 = linear_model.LinearRegression()\n",
    "regr5.fit(X_train5, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All 4 versions of the regression models are then applied to the training and test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_train = regr.predict(X_train)\n",
    "y_pred_test = regr.predict(X_test)\n",
    "y_pred_train2 = regr2.predict(X_train2)\n",
    "y_pred_test2 = regr2.predict(X_test2)\n",
    "y_pred_train3 = regr3.predict(X_train3)\n",
    "y_pred_test3 = regr3.predict(X_test3)\n",
    "y_pred_train4 = regr4.predict(X_train4)\n",
    "y_pred_test4 = regr4.predict(X_test4)\n",
    "y_pred_train5 = regr5.predict(X_train5)\n",
    "y_pred_test5 = regr5.predict(X_test5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For postprocessing, we compute both the training and test errors of the models. We can also show the resulting model and the sum of the absolute weights of the regression coefficients, i.e., $\\sum_{j=0}^d |w_j|$, where $d$ is the number of predictor attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "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>Model</th>\n",
       "      <th>Train error</th>\n",
       "      <th>Test error</th>\n",
       "      <th>Sum of Absolute Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.24 X + 1.08</td>\n",
       "      <td>0.891873</td>\n",
       "      <td>1.047626</td>\n",
       "      <td>4.322954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-5.90 X + 5.92 X2 + 1.00</td>\n",
       "      <td>0.856157</td>\n",
       "      <td>1.087601</td>\n",
       "      <td>12.817040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.22 X + -2.30 X2 + 17.14 X3 + 1.08</td>\n",
       "      <td>0.834238</td>\n",
       "      <td>1.094661</td>\n",
       "      <td>26.744867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12</td>\n",
       "      <td>0.825722</td>\n",
       "      <td>1.128861</td>\n",
       "      <td>29.453660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...</td>\n",
       "      <td>0.799399</td>\n",
       "      <td>1.146546</td>\n",
       "      <td>48.614927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                               Model  Train error  Test error  \\\n",
       "0                                     -3.24 X + 1.08     0.891873    1.047626   \n",
       "1                           -5.90 X + 5.92 X2 + 1.00     0.856157    1.087601   \n",
       "2               -6.22 X + -2.30 X2 + 17.14 X3 + 1.08     0.834238    1.094661   \n",
       "3      -7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12     0.825722    1.128861   \n",
       "4  -7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...     0.799399    1.146546   \n",
       "\n",
       "   Sum of Absolute Weights  \n",
       "0                 4.322954  \n",
       "1                12.817040  \n",
       "2                26.744867  \n",
       "3                29.453660  \n",
       "4                48.614927  "
      ]
     },
     "execution_count": 11,
     "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": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "columns = ['Model', 'Train error', 'Test error', 'Sum of Absolute Weights']\n",
    "model1 = \"%.2f X + %.2f\" % (regr.coef_[0][0], regr.intercept_[0])\n",
    "values1 = [ model1, np.sqrt(mean_squared_error(y_train, y_pred_train)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test)),\n",
    "           np.absolute(regr.coef_[0]).sum() + np.absolute(regr.intercept_[0])]\n",
    "\n",
    "model2 = \"%.2f X + %.2f X2 + %.2f\" % (regr2.coef_[0][0], regr2.coef_[0][1], regr2.intercept_[0])\n",
    "values2 = [ model2, np.sqrt(mean_squared_error(y_train, y_pred_train2)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test2)),\n",
    "           np.absolute(regr2.coef_[0]).sum() + np.absolute(regr2.intercept_[0])]\n",
    "\n",
    "model3 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f\" % (regr3.coef_[0][0], regr3.coef_[0][1], \n",
    "                                                regr3.coef_[0][2], regr3.intercept_[0])\n",
    "values3 = [ model3, np.sqrt(mean_squared_error(y_train, y_pred_train3)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test3)),\n",
    "           np.absolute(regr3.coef_[0]).sum() + np.absolute(regr3.intercept_[0])]\n",
    "\n",
    "model4 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f\" % (regr4.coef_[0][0], regr4.coef_[0][1], \n",
    "                                        regr4.coef_[0][2], regr4.coef_[0][3], regr4.intercept_[0])\n",
    "values4 = [ model4, np.sqrt(mean_squared_error(y_train, y_pred_train4)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test4)),\n",
    "           np.absolute(regr4.coef_[0]).sum() + np.absolute(regr4.intercept_[0])]\n",
    "\n",
    "model5 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f X5 + %.2f\" % (regr5.coef_[0][0], \n",
    "                                        regr5.coef_[0][1], regr5.coef_[0][2], \n",
    "                                        regr5.coef_[0][3], regr5.coef_[0][4], regr5.intercept_[0])\n",
    "values5 = [ model5, np.sqrt(mean_squared_error(y_train, y_pred_train5)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test5)),\n",
    "           np.absolute(regr5.coef_[0]).sum() + np.absolute(regr5.intercept_[0])]\n",
    "\n",
    "results = pd.DataFrame([values1, values2, values3, values4, values5], columns=columns)\n",
    "\n",
    "plt.plot(results['Sum of Absolute Weights'], results['Train error'], 'ro-')\n",
    "plt.plot(results['Sum of Absolute Weights'], results['Test error'], 'k*--')\n",
    "plt.legend(['Train error', 'Test error'])\n",
    "plt.xlabel('Sum of Absolute Weights')\n",
    "plt.ylabel('Error rate')\n",
    "\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results above show that the first model, which fits y against X only, has the largest training error, but smallest test error, whereas the fifth model, which fits y against X and other correlated attributes, has the smallest training error but largest test error. This is due to a phenomenon known as model overfitting, in which the low training error of the model does not reflect how well the model will perform on previously unseen test instances. From the plot shown above, observe that the disparity between the training and test errors becomes wider as the sum of absolute weights of the model (which represents the model complexity) increases. Thus, one should control the complexity of the regression model to avoid the model overfitting problem.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "## 5.4 Ridge Regression\n",
    "\n",
    "Ridge regression is a variant of MLR designed to fit a linear model to the dataset by minimizing the following regularized least-square loss function:\n",
    "$$L_{\\textrm{ridge}}(y,f(X,w)) = \\sum_{i=1}^N \\|y_i - X_iw - w_0\\|^2 + \\alpha \\bigg[\\|w\\|^2 + w_0^2 \\bigg],$$\n",
    "where $\\alpha$ is the hyperparameter for ridge regression. Note that the ridge regression model reduces to MLR when $\\alpha = 0$. By increasing the value of $\\alpha$, we can control the complexity of the model as will be shown in the example below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the example shown below, we fit a ridge regression model to the previously created training set with correlated attributes. We compare the results of the ridge regression model against those obtained using MLR. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>Model</th>\n",
       "      <th>Train error</th>\n",
       "      <th>Test error</th>\n",
       "      <th>Sum of Absolute Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.24 X + 1.08</td>\n",
       "      <td>0.891873</td>\n",
       "      <td>1.047626</td>\n",
       "      <td>4.322954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-5.90 X + 5.92 X2 + 1.00</td>\n",
       "      <td>0.856157</td>\n",
       "      <td>1.087601</td>\n",
       "      <td>12.817040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.22 X + -2.30 X2 + 17.14 X3 + 1.08</td>\n",
       "      <td>0.834238</td>\n",
       "      <td>1.094661</td>\n",
       "      <td>26.744867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12</td>\n",
       "      <td>0.825722</td>\n",
       "      <td>1.128861</td>\n",
       "      <td>29.453660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...</td>\n",
       "      <td>0.799399</td>\n",
       "      <td>1.146546</td>\n",
       "      <td>48.614927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ridge</th>\n",
       "      <td>-2.24 X + -0.43 X2 + -0.14 X3 + -0.10 X4 + 0.0...</td>\n",
       "      <td>0.917456</td>\n",
       "      <td>1.052388</td>\n",
       "      <td>3.765759</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                   Model  Train error  \\\n",
       "0                                         -3.24 X + 1.08     0.891873   \n",
       "1                               -5.90 X + 5.92 X2 + 1.00     0.856157   \n",
       "2                   -6.22 X + -2.30 X2 + 17.14 X3 + 1.08     0.834238   \n",
       "3          -7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12     0.825722   \n",
       "4      -7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...     0.799399   \n",
       "Ridge  -2.24 X + -0.43 X2 + -0.14 X3 + -0.10 X4 + 0.0...     0.917456   \n",
       "\n",
       "       Test error  Sum of Absolute Weights  \n",
       "0        1.047626                 4.322954  \n",
       "1        1.087601                12.817040  \n",
       "2        1.094661                26.744867  \n",
       "3        1.128861                29.453660  \n",
       "4        1.146546                48.614927  \n",
       "Ridge    1.052388                 3.765759  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "ridge = linear_model.Ridge(alpha=0.4)\n",
    "ridge.fit(X_train5, y_train)\n",
    "y_pred_train_ridge = ridge.predict(X_train5)\n",
    "y_pred_test_ridge = ridge.predict(X_test5)\n",
    "\n",
    "model6 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f X5 + %.2f\" % (ridge.coef_[0][0], \n",
    "                                        ridge.coef_[0][1], ridge.coef_[0][2], \n",
    "                                        ridge.coef_[0][3], ridge.coef_[0][4], ridge.intercept_[0])\n",
    "values6 = [ model6, np.sqrt(mean_squared_error(y_train, y_pred_train_ridge)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test_ridge)),\n",
    "           np.absolute(ridge.coef_[0]).sum() + np.absolute(ridge.intercept_[0])]\n",
    "\n",
    "ridge_results = pd.DataFrame([values6], columns=columns, index=['Ridge'])\n",
    "pd.concat([results, ridge_results])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By setting an appropriate value for the hyperparameter, $\\alpha$, we can control the sum of absolute weights, thus producing a test error that is quite comparable to that of MLR without the correlated attributes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.5 Lasso Regression\n",
    "\n",
    "One of the limitations of ridge regression is that, although it was able to reduce the regression coefficients associated with the correlated attributes and reduce the effect of model overfitting, the resulting model is still not sparse. Another variation of MLR, called lasso regression, is designed to produce sparser models by imposing an $\\ell_1$ regularization on the regression coefficients as shown below:\n",
    "$$L_{\\textrm{lasso}}(y,f(X,w)) = \\sum_{i=1}^N \\|y_i - X_iw - w_0\\|^2 + \\alpha \\bigg[ \\|w\\|_1 + |w_0|\\bigg]$$\n",
    "\n",
    "The example code below shows the results of applying lasso regression to the previously used correlated dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "        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>Model</th>\n",
       "      <th>Train error</th>\n",
       "      <th>Test error</th>\n",
       "      <th>Sum of Absolute Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.24 X + 1.08</td>\n",
       "      <td>0.891873</td>\n",
       "      <td>1.047626</td>\n",
       "      <td>4.322954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-5.90 X + 5.92 X2 + 1.00</td>\n",
       "      <td>0.856157</td>\n",
       "      <td>1.087601</td>\n",
       "      <td>12.817040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.22 X + -2.30 X2 + 17.14 X3 + 1.08</td>\n",
       "      <td>0.834238</td>\n",
       "      <td>1.094661</td>\n",
       "      <td>26.744867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12</td>\n",
       "      <td>0.825722</td>\n",
       "      <td>1.128861</td>\n",
       "      <td>29.453660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...</td>\n",
       "      <td>0.799399</td>\n",
       "      <td>1.146546</td>\n",
       "      <td>48.614927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ridge</th>\n",
       "      <td>-2.24 X + -0.43 X2 + -0.14 X3 + -0.10 X4 + 0.0...</td>\n",
       "      <td>0.917456</td>\n",
       "      <td>1.052388</td>\n",
       "      <td>3.765759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lasso</th>\n",
       "      <td>-2.90 X + 0.00 X2 + 0.00 X3 + 0.00 X4 + 0.00 X...</td>\n",
       "      <td>0.895692</td>\n",
       "      <td>1.043334</td>\n",
       "      <td>3.856242</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                   Model  Train error  \\\n",
       "0                                         -3.24 X + 1.08     0.891873   \n",
       "1                               -5.90 X + 5.92 X2 + 1.00     0.856157   \n",
       "2                   -6.22 X + -2.30 X2 + 17.14 X3 + 1.08     0.834238   \n",
       "3          -7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12     0.825722   \n",
       "4      -7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...     0.799399   \n",
       "Ridge  -2.24 X + -0.43 X2 + -0.14 X3 + -0.10 X4 + 0.0...     0.917456   \n",
       "Lasso  -2.90 X + 0.00 X2 + 0.00 X3 + 0.00 X4 + 0.00 X...     0.895692   \n",
       "\n",
       "       Test error  Sum of Absolute Weights  \n",
       "0        1.047626                 4.322954  \n",
       "1        1.087601                12.817040  \n",
       "2        1.094661                26.744867  \n",
       "3        1.128861                29.453660  \n",
       "4        1.146546                48.614927  \n",
       "Ridge    1.052388                 3.765759  \n",
       "Lasso    1.043334                 3.856242  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "lasso = linear_model.Lasso(alpha=0.02)\n",
    "lasso.fit(X_train5, y_train)\n",
    "y_pred_train_lasso = lasso.predict(X_train5)\n",
    "y_pred_test_lasso = lasso.predict(X_test5)\n",
    "\n",
    "model7 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f X5 + %.2f\" % (lasso.coef_[0], \n",
    "                                        lasso.coef_[1], lasso.coef_[2], \n",
    "                                        lasso.coef_[3], lasso.coef_[4], lasso.intercept_[0])\n",
    "values7 = [ model7, np.sqrt(mean_squared_error(y_train, y_pred_train_lasso)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test_lasso)),\n",
    "           np.absolute(lasso.coef_[0]).sum() + np.absolute(lasso.intercept_[0])]\n",
    "\n",
    "lasso_results = pd.DataFrame([values7], columns=columns, index=['Lasso'])\n",
    "pd.concat([results, ridge_results, lasso_results])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that the lasso regression model sets the coefficients for the correlated attributes, X2, X3, X4, and X5 to exactly zero unlike the ridge regression model. As a result, its test error is significantly better than that for ridge regression. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.6 Hyperparameter Selection via Cross-Validation\n",
    "\n",
    "While both ridge and lasso regression methods can potentially alleviate the model overfitting problem, one of the challenges is how to select the appropriate hyperparameter value, $\\alpha$. In the examples shown below, we demonstrate examples of using a 5-fold cross-validation method to select the best hyperparameter of the model. More details about the model selection problem and cross-validation method are described in Chapter 3 of the book. \n",
    "\n",
    "In the first sample code below, we vary the hyperparameter $\\alpha$ for ridge regression to a range between 0.2 and 1.0. Using the RidgeCV() function, we can train a model with 5-fold cross-validation and select the best hyperparameter value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected alpha = 0.20\n"
     ]
    },
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>Train error</th>\n",
       "      <th>Test error</th>\n",
       "      <th>Sum of Absolute Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.24 X + 1.08</td>\n",
       "      <td>0.891873</td>\n",
       "      <td>1.047626</td>\n",
       "      <td>4.322954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-5.90 X + 5.92 X2 + 1.00</td>\n",
       "      <td>0.856157</td>\n",
       "      <td>1.087601</td>\n",
       "      <td>12.817040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.22 X + -2.30 X2 + 17.14 X3 + 1.08</td>\n",
       "      <td>0.834238</td>\n",
       "      <td>1.094661</td>\n",
       "      <td>26.744867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12</td>\n",
       "      <td>0.825722</td>\n",
       "      <td>1.128861</td>\n",
       "      <td>29.453660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...</td>\n",
       "      <td>0.799399</td>\n",
       "      <td>1.146546</td>\n",
       "      <td>48.614927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RidgeCV</th>\n",
       "      <td>-2.74 X + -0.16 X2 + 0.09 X3 + 0.01 X4 + 0.21 ...</td>\n",
       "      <td>0.899190</td>\n",
       "      <td>1.044401</td>\n",
       "      <td>4.112120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     Model  Train error  \\\n",
       "0                                           -3.24 X + 1.08     0.891873   \n",
       "1                                 -5.90 X + 5.92 X2 + 1.00     0.856157   \n",
       "2                     -6.22 X + -2.30 X2 + 17.14 X3 + 1.08     0.834238   \n",
       "3            -7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12     0.825722   \n",
       "4        -7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...     0.799399   \n",
       "RidgeCV  -2.74 X + -0.16 X2 + 0.09 X3 + 0.01 X4 + 0.21 ...     0.899190   \n",
       "\n",
       "         Test error  Sum of Absolute Weights  \n",
       "0          1.047626                 4.322954  \n",
       "1          1.087601                12.817040  \n",
       "2          1.094661                26.744867  \n",
       "3          1.128861                29.453660  \n",
       "4          1.146546                48.614927  \n",
       "RidgeCV    1.044401                 4.112120  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "ridge = linear_model.RidgeCV(cv=5,alphas=[0.2, 0.4, 0.6, 0.8, 1.0])\n",
    "ridge.fit(X_train5, y_train)\n",
    "y_pred_train_ridge = ridge.predict(X_train5)\n",
    "y_pred_test_ridge = ridge.predict(X_test5)\n",
    "\n",
    "model6 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f X5 + %.2f\" % (ridge.coef_[0][0], \n",
    "                                        ridge.coef_[0][1], ridge.coef_[0][2], \n",
    "                                        ridge.coef_[0][3], ridge.coef_[0][4], ridge.intercept_[0])\n",
    "values6 = [ model6, np.sqrt(mean_squared_error(y_train, y_pred_train_ridge)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test_ridge)),\n",
    "           np.absolute(ridge.coef_[0]).sum() + np.absolute(ridge.intercept_[0])]\n",
    "print(\"Selected alpha = %.2f\" % ridge.alpha_)\n",
    "\n",
    "ridge_results = pd.DataFrame([values6], columns=columns, index=['RidgeCV'])\n",
    "pd.concat([results, ridge_results])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this next example, we illustrate how to apply cross-validation to select the best hyperparameter value for fitting a lasso regression model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected alpha = 0.01\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\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>Model</th>\n",
       "      <th>Train error</th>\n",
       "      <th>Test error</th>\n",
       "      <th>Sum of Absolute Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.24 X + 1.08</td>\n",
       "      <td>0.891873</td>\n",
       "      <td>1.047626</td>\n",
       "      <td>4.322954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-5.90 X + 5.92 X2 + 1.00</td>\n",
       "      <td>0.856157</td>\n",
       "      <td>1.087601</td>\n",
       "      <td>12.817040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.22 X + -2.30 X2 + 17.14 X3 + 1.08</td>\n",
       "      <td>0.834238</td>\n",
       "      <td>1.094661</td>\n",
       "      <td>26.744867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12</td>\n",
       "      <td>0.825722</td>\n",
       "      <td>1.128861</td>\n",
       "      <td>29.453660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...</td>\n",
       "      <td>0.799399</td>\n",
       "      <td>1.146546</td>\n",
       "      <td>48.614927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RidgeCV</th>\n",
       "      <td>-2.74 X + -0.16 X2 + 0.09 X3 + 0.01 X4 + 0.21 ...</td>\n",
       "      <td>0.899190</td>\n",
       "      <td>1.044401</td>\n",
       "      <td>4.112120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LassoCV</th>\n",
       "      <td>-3.07 X + 0.00 X2 + 0.00 X3 + 0.00 X4 + 0.00 X...</td>\n",
       "      <td>0.892829</td>\n",
       "      <td>1.043911</td>\n",
       "      <td>4.089598</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     Model  Train error  \\\n",
       "0                                           -3.24 X + 1.08     0.891873   \n",
       "1                                 -5.90 X + 5.92 X2 + 1.00     0.856157   \n",
       "2                     -6.22 X + -2.30 X2 + 17.14 X3 + 1.08     0.834238   \n",
       "3            -7.16 X + 0.93 X2 + 8.39 X3 + 11.85 X4 + 1.12     0.825722   \n",
       "4        -7.16 X + 4.50 X2 + 3.52 X3 + -6.55 X4 + 25.68...     0.799399   \n",
       "RidgeCV  -2.74 X + -0.16 X2 + 0.09 X3 + 0.01 X4 + 0.21 ...     0.899190   \n",
       "LassoCV  -3.07 X + 0.00 X2 + 0.00 X3 + 0.00 X4 + 0.00 X...     0.892829   \n",
       "\n",
       "         Test error  Sum of Absolute Weights  \n",
       "0          1.047626                 4.322954  \n",
       "1          1.087601                12.817040  \n",
       "2          1.094661                26.744867  \n",
       "3          1.128861                29.453660  \n",
       "4          1.146546                48.614927  \n",
       "RidgeCV    1.044401                 4.112120  \n",
       "LassoCV    1.043911                 4.089598  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "lasso = linear_model.LassoCV(cv=5, alphas=[0.01, 0.02, 0.05, 0.1, 0.3, 0.5, 1.0])\n",
    "lasso.fit(X_train5, y_train.reshape(y_train.shape[0]))\n",
    "y_pred_train_lasso = lasso.predict(X_train5)\n",
    "y_pred_test_lasso = lasso.predict(X_test5)\n",
    "\n",
    "model7 = \"%.2f X + %.2f X2 + %.2f X3 + %.2f X4 + %.2f X5 + %.2f\" % (lasso.coef_[0], \n",
    "                                        lasso.coef_[1], lasso.coef_[2], \n",
    "                                        lasso.coef_[3], lasso.coef_[4], lasso.intercept_)\n",
    "values7 = [ model7, np.sqrt(mean_squared_error(y_train, y_pred_train_lasso)), \n",
    "           np.sqrt(mean_squared_error(y_test, y_pred_test_lasso)),\n",
    "           np.absolute(lasso.coef_[0]).sum() + np.absolute(lasso.intercept_)]\n",
    "print(\"Selected alpha = %.2f\" % lasso.alpha_)\n",
    "\n",
    "lasso_results = pd.DataFrame([values7], columns=columns, index=['LassoCV'])\n",
    "pd.concat([results, ridge_results, lasso_results])"
   ]
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    "## 5.7 Summary\n",
    "\n",
    "This section presents example Python code for fitting linear regression models to a dataset. We also illustrate the problem of model overfitting and shows two alternative methods, called ridge and lasso regression, that can help alleviate such problem. While the model overfitting problem shown here is illustrated in the context of correlated attributes, the problem is more general and may arise due to other factors such as noise and other exceptional values in the data."
   ]
  }
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