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Contents Preface vii 1 Introduction 1 2 Statistical Learning 15 2.1 What Is Statistical Learning? . . . . . . . . . . . . . . . . . 15 2.1.1 Why Estimate f? . . . . . . . . . . . . . . . . . . . . 17 2.1.2 How Do We Estimate f? . . . . . . . . . . . . . . . 21 2.1.3 The Trade-Off Between Prediction Accuracy and Model Interpretability . . . . . . . . . . . . . . 24 2.1.4 Supervised Versus Unsupervised Learning . . . . . . 26 2.1.5 Regression Versus Classification Problems . . . . . . 28 2.2 Assessing Model Accuracy . . . . . . . . . . . . . . . . . . . 29 2.2.1 Measuring the Quality of Fit . . . . . . . . . . . . . 29 2.2.2 The Bias-Variance Trade-Off . . . . . . . . . . . . . 33 2.2.3 The Classification Setting . . . . . . . . . . . . . . . 37 2.3 Lab: Introduction to R . . . . . . . . . . . . . . . . . . . . . 42 2.3.1 Basic Commands . . . . . . . . . . . . . . . . . . . . 42 2.3.2 Graphics . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3.3 Indexing Data . . . . . . . . . . . . . . . . . . . . . 47 2.3.4 Loading Data . . . . . . . . . . . . . . . . . . . . . . 48 2.3.5 Additional Graphical and Numerical Summaries . . 49 2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 ix
x Contents 3 Linear Regression 59 3.1 Simple Linear Regression . . . . . . . . . . . . . . . . . . . 61 3.1.1 Estimating the Coefficients . . . . . . . . . . . . . . 61 3.1.2 Assessing the Accuracy of the Coefficient Estimates . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.3 Assessing the Accuracy of the Model . . . . . . . . . 68 3.2 Multiple Linear Regression . . . . . . . . . . . . . . . . . . 71 3.2.1 Estimating the Regression Coefficients . . . . . . . . 72 3.2.2 Some Important Questions . . . . . . . . . . . . . . 75 3.3 Other Considerations in the Regression Model . . . . . . . . 82 3.3.1 Qualitative Predictors . . . . . . . . . . . . . . . . . 82 3.3.2 Extensions of the Linear Model . . . . . . . . . . . . 86 3.3.3 Potential Problems . . . . . . . . . . . . . . . . . . . 92 3.4 The Marketing Plan . . . . . . . . . . . . . . . . . . . . . . 102 3.5 Comparison of Linear Regression with K-Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.6 Lab: Linear Regression . . . . . . . . . . . . . . . . . . . . . 109 3.6.1 Libraries . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.6.2 Simple Linear Regression . . . . . . . . . . . . . . . 110 3.6.3 Multiple Linear Regression . . . . . . . . . . . . . . 113 3.6.4 Interaction Terms . . . . . . . . . . . . . . . . . . . 115 3.6.5 Non-linear Transformations of the Predictors . . . . 115 3.6.6 Qualitative Predictors . . . . . . . . . . . . . . . . . 117 3.6.7 Writing Functions . . . . . . . . . . . . . . . . . . . 119 3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4 Classification 127 4.1 An Overview of Classification . . . . . . . . . . . . . . . . . 128 4.2 Why Not Linear Regression? . . . . . . . . . . . . . . . . . 129 4.3 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . 130 4.3.1 The Logistic Model . . . . . . . . . . . . . . . . . . . 131 4.3.2 Estimating the Regression Coefficients . . . . . . . . 133 4.3.3 Making Predictions . . . . . . . . . . . . . . . . . . . 134 4.3.4 Multiple Logistic Regression . . . . . . . . . . . . . . 135 4.3.5 Logistic Regression for >2 Response Classes . . . . . 137 4.4 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . 138 4.4.1 Using Bayes’ Theorem for Classification . . . . . . . 138 4.4.2 Linear Discriminant Analysis for p = 1 . . . . . . . . 139 4.4.3 Linear Discriminant Analysis for p>1 . . . . . . . . 142 4.4.4 Quadratic Discriminant Analysis . . . . . . . . . . . 149 4.5 A Comparison of Classification Methods . . . . . . . . . . . 151 4.6 Lab: Logistic Regression, LDA, QDA, and KNN . . . . . . 154 4.6.1 The Stock Market Data . . . . . . . . . . . . . . . . 154 4.6.2 Logistic Regression . . . . . . . . . . . . . . . . . . . 156 4.6.3 Linear Discriminant Analysis . . . . . . . . . . . . . 161
Page 1 and 2: Springer Texts in Statistics Gareth
Page 4 and 5: Gareth James • Daniela Witten •
Page 6: To our parents: Alison and Michael
Page 9: viii Preface disciplines who wish t
Page 13 and 14: xii Contents 6.6 Lab 2: Ridge Regre
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46 2. Statistical Learning We will
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48 2. Statistical Learning [3,] 3 7
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50 2. Statistical Learning > plot(c
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52 2. Statistical Learning 2.4 Exer
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54 2. Statistical Learning (b) What
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56 2. Statistical Learning 9. This
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3 Linear Regression This chapter is
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3.1 Simple Linear Regression 3.1 Si
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3.1 Simple Linear Regression 63 3 2
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3.1 Simple Linear Regression 65 con
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3.1 Simple Linear Regression 67 In
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Quantity Value Residual standard er
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3.2 Multiple Linear Regression 71 a
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3.2 Multiple Linear Regression 73 Y
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3.2 Multiple Linear Regression 75 T
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3.2 Multiple Linear Regression 77 w
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3.2 Multiple Linear Regression 79 i
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3.2 Multiple Linear Regression 81 S
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3.3 Other Considerations in the Reg
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x i = 3.3 Other Considerations in t
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3.4 The Marketing Plan 103 units wh
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y x 2 y x 2 3.5 Comparison of Linea
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3.5 Comparison of Linear Regression
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3.6 Lab: Linear Regression 109 p=1
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3.6 Lab: Linear Regression 111 Coef
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3.6 Lab: Linear Regression 113 > pl
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3.6 Lab: Linear Regression 115 > lm
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3.6 Lab: Linear Regression 117 > lm
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3.6 Lab: Linear Regression 119 Shel
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3.7 Exercises 121 (b) Answer (a) us
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3.7 Exercises 123 10. This question
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3.7 Exercises 125 (d) Create a scat
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4 Classification The linear regress
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4.2 Why Not Linear Regression? 129
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4.3 Logistic Regression 131 0 500 1
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4.3 Logistic Regression 133 β 1 do
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4.3 Logistic Regression 135 Coeffic
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4.3 Logistic Regression 137 Default
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4.4 Linear Discriminant Analysis 13
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4.5 A Comparison of Classification
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4.5 A Comparison of Classification
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4.6 Lab: Logistic Regression, LDA,
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4.7 Exercises 169 we will use obser
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Applied 4.7 Exercises 171 10. This
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4.7 Exercises 173 return(result) Th
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176 5. Resampling Methods 5.1 Cross
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178 5. Resampling Methods Mean Squa
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180 5. Resampling Methods LOOCV 10
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182 5. Resampling Methods Mean Squa
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184 5. Resampling Methods has highe
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186 5. Resampling Methods Error Rat
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188 5. Resampling Methods Y −2
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190 5. Resampling Methods Obs X Y Z
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192 5. Resampling Methods > mean((m
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194 5. Resampling Methods first is
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196 5. Resampling Methods Next, we
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198 5. Resampling Methods (f) When
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200 5. Resampling Methods predict.g
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6 Linear Model Selection and Regula
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6.1 Subset Selection 205 6.1 Subset
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6.1 Subset Selection 207 p = 20, th
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6.1 Subset Selection 209 #Variables
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6.1 Subset Selection 211 C p 10000
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6.1 Subset Selection 213 will lead
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6.2 Shrinkage Methods 215 obvious w
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6.2 Shrinkage Methods 217 regressio
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6.2 Shrinkage Methods 219 discussed
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6.2 Shrinkage Methods 221 respectiv
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6.2 Shrinkage Methods 223 Mean Squa
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6.2 Shrinkage Methods 225 To simpli
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6.2 Shrinkage Methods 227 (β j ) 0
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6.3 Dimension Reduction Methods 229
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6.4 Considerations in High Dimensio
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6.5 Lab 1: Subset Selection Methods
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6.6 Lab 2: Ridge Regression and the
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6.7 Lab 3: PCR and PLS Regression 2
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6.8 Exercises 259 final seven-compo
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6.8 Exercises 261 (a) As we increas
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6.8 Exercises 263 (d) Repeat (c), u
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7 Moving Beyond Linearity So far in
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|| 7.1 Polynomial Regression 267 De
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|| 7.2 Step Functions 269 Piecewise
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7.4 Regression Splines 271 7.4 Regr
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7.4 Regression Splines 273 plot is
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7.4 Regression Splines 275 Natural
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7.5 Smoothing Splines 277 Wage 50 1
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7.5 Smoothing Splines 279 to the nu
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7.6 Local Regression 281 Local Regr
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7.7 Generalized Additive Models 283
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7.7 Generalized Additive Models 285
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7.8 Lab: Non-linear Modeling 287 25
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7.8 Lab: Non-linear Modeling 289 po
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7.8 Lab: Non-linear Modeling 291 po
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7.8.2 Splines 7.8 Lab: Non-linear M
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7.8 Lab: Non-linear Modeling 295 In
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7.9 Exercises 297 It is easy to see
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7.9 Exercises 299 5. Consider two c
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7.9 Exercises 301 (a) Generate a re
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304 8. Tree-Based Methods Years < 4
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306 8. Tree-Based Methods have been
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308 8. Tree-Based Methods R5 R2 t4
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310 8. Tree-Based Methods Years < 4
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312 8. Tree-Based Methods E =1− m
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314 8. Tree-Based Methods Figure 8.
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316 8. Tree-Based Methods ▼ Unfor
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318 8. Tree-Based Methods Error 0.1
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320 8. Tree-Based Methods 8.2.2 Ran
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322 8. Tree-Based Methods of the ot
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324 8. Tree-Based Methods stumps wi
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326 8. Tree-Based Methods > tree.ca
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328 8. Tree-Based Methods Residual
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330 8. Tree-Based Methods The test
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332 8. Tree-Based Methods 8.4 Exerc
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334 8. Tree-Based Methods (e) Use r
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9 Support Vector Machines In this c
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9.1 Maximal Margin Classifier 339 X
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9.1 Maximal Margin Classifier 341 h
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9.1 Maximal Margin Classifier 343 m
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9.2 Support Vector Classifiers 345
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9.2 Support Vector Classifiers 347
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9.3 Support Vector Machines 349 X2
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9.3 Support Vector Machines 351 in
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9.3 Support Vector Machines 353 X2
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9.4 SVMs with More than Two Classes
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9.5 Relationship to Logistic Regres
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9.6 Lab: Support Vector Machines 35
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9.6.3 ROC Curves 9.6 Lab: Support V
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Obs. X 1 X 2 Y 1 3 4 Red 2 2 2 Red
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9.7 Exercises 371 (b) Compute the c
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10 Unsupervised Learning Most of th
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10.2 Principal Components Analysis
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10.2.4 Other Uses for Principal Com
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10.3 Clustering Methods 387 K=2 K=3
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10.3 Clustering Methods 389 Data St
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10.3 Clustering Methods 391 X2 −2
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10.3 Clustering Methods 393 0.0 0.5
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Algorithm 10.2 Hierarchical Cluster
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10.3 Clustering Methods 397 Average
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10.3 Clustering Methods 399 0 2 4 6
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10.4 Lab 1: Principal Components An
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10.4 Lab 1: Principal Components An
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10.5 Lab 2: Clustering 405 Cluster
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10.6 Lab 3: NCI60 Data Example 407
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10.7 Exercises 413 differ: for inst
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10.7 Exercises 415 (b) At a certain
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10.7 Exercises 417 10. In this prob
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Index C p , 78, 205, 206, 210-213 R
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Index 421 Wage, 1, 2, 9, 10, 14, 26
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Index 423 noise, 22, 228 non-linear
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Index 425 read.table(), 48, 49 regs
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