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2.3 Lab: Introduction to R 51 > plot(horsepower ,mpg) > identify(horsepower ,mpg,name) The summary() function produces a numerical summary of each variable in summary() a particular data set. > summary(Auto) mpg cylinders displacement Min. : 9.00 Min. :3.000 Min. : 68.0 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 Median :22.75 Median :4.000 Median :151.0 Mean :23.45 Mean :5.472 Mean :194.4 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 Max. :46.60 Max. :8.000 Max. :455.0 horsepower weight acceleration Min. : 46.0 Min. :1613 Min. : 8.00 1st Qu.: 75.0 1st Qu.:2225 1st Qu.:13.78 Median : 93.5 Median :2804 Median :15.50 Mean :104.5 Mean :2978 Mean :15.54 3rd Qu.:126.0 3rd Qu.:3615 3rd Qu.:17.02 Max. :230.0 Max. :5140 Max. :24.80 year origin name Min. :70.00 Min. :1.000 amc matador : 5 1st Qu.:73.00 1st Qu.:1.000 ford pinto : 5 Median :76.00 Median :1.000 toyota corolla : 5 Mean :75.98 Mean :1.577 amc gremlin : 4 3rd Qu.:79.00 3rd Qu.:2.000 amc hornet : 4 Max. :82.00 Max. :3.000 chevrolet chevette: 4 (Other) :365 For qualitative variables such as name, R will list the number of observations that fall in each category. We can also produce a summary of just a single variable. > summary(mpg) Min. 1st Qu. Median Mean 3rd Qu. Max. 9.00 17.00 22.75 23.45 29.00 46.60 Once we have finished using R, wetypeq() inordertoshutitdown,or q() quit. When exiting R, we have the option to save the current workspace so workspace that all objects (such as data sets) that we have created in this R session will be available next time. Before exiting R, we may want to save a record of all of the commands that we typed in the most recent session; this can be accomplished using the savehistory() function.NexttimeweenterR, savehistory() we can load that history using the loadhistory() function. loadhistory()
52 2. Statistical Learning 2.4 Exercises Conceptual 1. For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer. (a) The sample size n is extremely large, and the number of predictors p is small. (b) The number of predictors p is extremely large, and the number of observations n is small. (c) The relationship between the predictors and response is highly non-linear. (d) The variance of the error terms, i.e. σ 2 =Var(ɛ), is extremely high. 2. Explain whether each scenario is a classification or regression problem, and indicate whether we are most interested in inference or prediction. Finally, provide n and p. (a) We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary. (b) We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each product we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables. (c) We are interesting in predicting the % change in the US dollar in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the dollar, the % change in the US market, the % change in the British market, and the % change in the German market. 3. We now revisit the bias-variance decomposition. (a) Provide a sketch of typical (squared) bias, variance, training error, test error, and Bayes (or irreducible) error curves, on a single plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent
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Springer Texts in Statistics Gareth
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Gareth James • Daniela Witten •
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To our parents: Alison and Michael
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viii Preface disciplines who wish t
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x Contents 3 Linear Regression 59 3
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xii Contents 6.6 Lab 2: Ridge Regre
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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 119 Shel
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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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4.5 A Comparison of Classification
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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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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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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 211 C p 10000
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6.1 Subset Selection 213 will lead
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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 223 Mean Squa
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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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6.5 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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7 Moving Beyond Linearity So far in
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|| 7.1 Polynomial Regression 267 De
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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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304 8. Tree-Based Methods Years < 4
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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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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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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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10 Unsupervised Learning Most of th
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10.2 Principal Components Analysis
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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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10.5 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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