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E-raamat: Handbook of Regression Analysis With Applications in R

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"Building on the Handbook of Regression Analysis and Regression Analysis by Example, the authors' thorough treatments of "classic" regression analysis, this book covers two important and more advanced topics of time-to-event survival data and longitudinal and clustered data. Further, methods that have become prominent in the last 15-30 years that are designed for analyses on often-large data sets and can take advantage of exibility in modeling were not covered, including smoothing, tree- based, and regularization methods, all of which are increasingly becoming part of the data analysis toolkit. Examples are drawn from a wide variety of application areas using real data sets and all of the R code is provided. The book will be of interest to data scientists as well as in regression analysis courses at the graduate and undergraduate level. Regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables -- that is, the average value of the dependent variable when the independent variables are fixed. Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning"--

Handbook and reference guide for students and practitioners of statistical regression-based analyses in R 

Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors’ thorough treatment of “classical” regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data.  

The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include: 

  • Regularization methods 
  • Smoothing methods 
  • Tree-based methods 

In the new edition of the Handbook, the data analyst’s toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website. 

Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians. 

Preface to the Second Edition xv
Preface to the First Edition xix
PART I THE MULTIPLE LINEAR REGRESSION MODEL
1 Multiple Linear Regression
3(20)
1.1 Introduction
3(1)
1.2 Concepts and Background Material
4(5)
1.2.1 The Linear Regression Model
4(1)
1.2.2 Estimation Using Least Squares
5(3)
1.2.3 Assumptions
8(1)
1.3 Methodology
9(6)
1.3.1 Interpreting Regression Coefficients
9(1)
1.3.2 Measuring the Strength of the Regression Relationship
10(2)
1.3.3 Hypothesis Tests and Confidence Intervals for β
12(1)
1.3.4 Fitted Values and Predictions
13(1)
1.3.5 Checking Assumptions Using Residual Plots
14(1)
1.4 Example --- Estimating Home Prices
15(4)
1.5 Summary
19(4)
2 Model Building
23(30)
2.1 Introduction
23(1)
2.2 Concepts and Background Material
24(5)
2.2.1 Using Hypothesis Tests to Compare Models
24(2)
2.2.2 Collinearity
26(3)
2.3 Methodology
29(9)
2.3.1 Model Selection
29(2)
2.3.2 Example --- Estimating Home Prices
31(7)
2.4 Indicator Variables and Modeling Interactions
38(8)
2.4.1 Example --- Electronic Voting and the 2004 Presidential Election
40(6)
2.5 Summary
46(7)
PART II ADDRESSING VIOLATIONS OF ASSUMPTIONS
3 Diagnostics For Unusual Observations
53(14)
3.1 Introduction
53(1)
3.2 Concepts and Background Material
54(2)
3.3 Methodology
56(4)
3.3.1 Residuals and Outliers
56(1)
3.3.2 Leverage Points
57(1)
3.3.3 Influential Points and Cook's Distance
58(2)
3.4 Example --- Estimating Home Prices (continued)
60(3)
3.5 Summary
63(4)
4 Transformations And Linearizable Models
67(12)
4.1 Introduction
67(2)
4.2 Concepts and Background Material: The Log-Log Model
69(1)
4.3 Concepts and Background Material: Semilog Models
69(2)
4.3.1 Logged Response Variable
70(1)
4.3.2 Logged Predictor Variable
70(1)
4.4 Example --- Predicting Movie Grosses After One Week
71(6)
4.5 Summary
77(2)
5 Time Series Data And Autocorrelation
79(30)
5.1 Introduction
79(2)
5.2 Concepts and Background Material
81(2)
5.3 Methodology: Identifying Autocorrelation
83(3)
5.3.1 The Durbin-Watson Statistic
83(1)
5.3.2 The Autocorrelation Function (ACF)
84(1)
5.3.3 Residual Plots and the Runs Test
85(1)
5.4 Methodology: Addressing Autocorrelation
86(18)
5.4.1 Detrending and Deseasonalizing
86(1)
5.4.2 Example --- e-Commerce Retail Sales
87(6)
5.4.3 Lagging and Differencing
93(1)
5.4.4 Example --- Stock Indexes
94(5)
5.4.5 Generalized Least Squares (GLS): The Cochrane-Orcutt Procedure
99(1)
5.4.6 Example --- Time Intervals Between Old Faithful Geyser Eruptions
100(4)
5.5 Summary
104(5)
PART III CATEGORICAL PREDICTORS
6 Analysis Of Variance
109(26)
6.1 Introduction
109(1)
6.2 Concepts and Background Material
110(3)
6.2.1 One-Way ANOVA
110(1)
6.2.2 Two-Way ANOVA
111(2)
6.3 Methodology
113(12)
6.3.1 Codings for Categorical Predictors
113(5)
6.3.2 Multiple Comparisons
118(2)
6.3.3 Levene's Test and Weighted Least Squares
120(3)
6.3.4 Membership in Multiple Groups
123(2)
6.4 Example --- DVD Sales of Movies
125(5)
6.5 Higher-Way ANOVA
130(2)
6.6 Summary
132(3)
7 Analysis Of Covariance
135(10)
7.1 Introduction
135(1)
7.2 Methodology
136(1)
7.2.1 Constant Shift Models
136(1)
7.2.2 Varying Slope Models
137(1)
7.3 Example --- International Grosses of Movies
137(5)
7.4 Summary
142(3)
PART IV NON-GAUSSIAN REGRESSION MODELS
8 Logistic Regression
145(28)
8.1 Introduction
145(2)
8.2 Concepts and Background Material
147(5)
8.2.1 The Logit Response Function
148(1)
8.2.2 Bernoulli and Binomial Random Variables
149(1)
8.2.3 Prospective and Retrospective Designs
149(3)
8.3 Methodology
152(7)
8.3.1 Maximum Likelihood Estimation
152(1)
8.3.2 Inference, Model Comparison, and Model Selection
153(2)
8.3.3 Goodness-of-Fit
155(2)
8.3.4 Measures of Association and Classification Accuracy
157(2)
8.3.5 Diagnostics
159(1)
8.4 Example --- Smoking and Mortality
159(4)
8.5 Example --- Modeling Bankruptcy
163(5)
8.6 Summary
168(5)
9 Multinomial Regression
173(14)
9.1 Introduction
173(1)
9.2 Concepts and Background Material
174(4)
9.1.1 Nominal Response Variable
174(2)
9.2.2 Ordinal Response Variable
176(2)
9.3 Methodology
178(2)
9.3.1 Estimation
178(1)
9.3.2 Inference, Model Comparisons, and Strength of Fit
178(2)
9.3.3 Lack of Fit and Violations of Assumptions
180(1)
9.4 Example --- City Bond Ratings
180(4)
9.5 Summary
184(3)
10 Count Regression
187(22)
10.1 Introduction
187(1)
10.2 Concepts and Background Material
188(2)
10.2.1 The Poisson Random Variable
188(1)
10.2.2 Generalized Linear Models
189(1)
10.3 Methodology
190(2)
10.3.1 Estimation and Inference
190(1)
10.3.2 Offsets
191(1)
10.4 Overdispersion and Negative Binomial Regression
192(2)
10.4.1 Quasi-likelihood
192(1)
10.4.2 Negative Binomial Regression
193(1)
10.5 Example --- Unprovoked Shark Attacks in Florida
194(7)
10.6 Other Count Regression Models
201(4)
10.7 Poisson Regression and Weighted Least Squares
205(1)
10.7.1 Example --- International Grosses of Movies (continued)
204(2)
10.8 Summary
206(3)
11 Models For Time-To-Event (Survival) Data
209(34)
11.1 Introduction
210(1)
11.2 Concepts and Background Material
211(3)
11.2.1 The Nature of Survival Data
211(1)
11.2.2 Accelerated Failure Time Models
212(2)
11.2.3 The Proportional Hazards Model
214(1)
11.3 Methodology
214(9)
11.3.1 The Kaplan-Meier Estimator and the Log-Rank Test
214(5)
11.3.2 Parametric (Likelihood) Estimation
219(2)
11.3.3 Semiparametric (Partial Likelihood) Estimation
221(2)
11.3.4 The Buckley-James Estimator
223(1)
11.4 Example --- The Survival of Broadway Shows (continued)
223(7)
11.5 Left-Truncated/Right-Censored Data and Time-Varying Covariates
230(8)
11.5.1 Left-Truncated/Right-Censored Data
230(3)
11.5.2 Example --- The Survival of Broadway Shows (continued)
233(1)
11.5.3 Time-Varying Covariates
233(2)
11.5.4 Example --- Female Heads of Government
235(3)
11.6 Summary
238(5)
PART V OTHER REGRESSION MODELS
12 Nonlinear Regression
243(12)
12.1 Introduction
243(1)
12.2 Concepts and Background Material
244(2)
12.3 Methodology
246(2)
12.3.1 Nonlinear Least Squares Estimation
246(1)
12.3.2 Inference for Nonlinear Regression Models
247(1)
12.4 Example --- Michaelis-Menten Enzyme Kinetics
248(4)
12.5 Summary
252(3)
13 Models For Longitudinal And Nested Data
255(22)
13.1 Introduction
257(1)
13.2 Concepts and Background Material
257(3)
13.2.1 Nested Data and ANOVA
257(1)
13.2.2 Longitudinal Data and Time Series
258(1)
13.2.3 Fixed Effects Versus Random Effects
259(1)
13.3 Methodology
260(4)
13.3.1 The Linear Mixed Effects Model
260(2)
13.3.2 The Generalized Linear Mixed Effects Model
262(1)
13.3.3 Generalized Estimating Equations
262(1)
13.3.4 Nonlinear Mixed Effects Models
263(1)
13.4 Example --- Tumor Growth in a Cancer Study
264(5)
13.5 Example --- Unprovoked Shark Attacks in the United States
269(6)
13.6 Summary
275(2)
14 Regularization Method's And Sparse Models
277(18)
14.1 Introduction
277(1)
14.2 Concepts and Background Material
278(2)
14.2.1 The Bias-Variance Tradeoff
278(1)
14.2.2 Large Numbers of Predictors and Sparsity
279(1)
14.3 Methodology
280(7)
14.3.1 Forward Stepwise Regression
280(1)
14.3.2 Ridge Regression
281(1)
14.3.3 The Lasso
281(2)
14.3.4 Other Regularization Methods
283(1)
14.3.5 Choosing the Regularization Parameter(s)
284(1)
14.3.6 More Structured Regression Problems
285(1)
14.3.7 Cautions About Regularization Methods
286(1)
14.4 Example --- Human Development Index
287(2)
14.5 Summary
289(6)
PART VI NONPARAMETRIC AND SEMIPARAMETRIC MODELS
15 Smoothing And Additive Models
295(18)
15.1 Introduction
296(1)
15.2 Concepts and Background Material
296(2)
15.2.1 The Bias-Variance Tradeoff
296(1)
15.2.2 Smoothing and Local Regression
297(1)
15.3 Methodology
298(3)
15.3.1 Local Polynomial Regression
298(1)
15.3.2 Choosing the Bandwidth
298(1)
15.3.3 Smoothing Splines
299(1)
15.3.4 Multiple Predictors, the Curse of Dimensionality, and Additive Models
300(1)
15.4 Example --- Prices of German Used Automobiles
301(3)
15.5 Local and Penalized Likelihood Regression
304(3)
15.5.1 Example --- The Bechdel Rule and Hollywood Movies
305(2)
15.6 Using Smoothing to Identify Interactions
307(3)
15.6.1 Example --- Estimating Home Prices (continued)
308(2)
15.7 Summary
310(3)
16 Tree-Based Models
313(24)
16.1 Introduction
314(1)
16.2 Concepts and Background Material
314(4)
16.2.1 Recursive Partitioning
314(3)
16.2.2 Types of Trees
317(1)
16.3 Methodology
318(3)
16.3.1 CART
318(1)
16.3.2 Conditional Inference Trees
319(1)
16.3.3 Ensemble Methods
320(1)
16.4 Examples
321(206)
16.4.1 Estimating Home Prices (continued)
321(1)
16.4.2 Example --- Courtesy in Airplane Travel
322(5)
16.5 Trees for Other Types of Data
327(1)
16.5.1 Trees for Nested and Longitudinal Data
327(1)
16.5.2 Survival Trees
328(4)
16.6 Summary
332(5)
Bibliography 337(6)
Index 343
Samprit Chatterjee, PhD, is Professor Emeritus of Statistics at New York University. A Fellow of the American Statistical Association, Dr. Chatterjee has been a Fulbright scholar in both Kazakhstan and Mongolia. He is the coauthor of multiple editions of Regression Analysis By Example, Sensitivity Analysis in Linear Regression, A Casebook for a First Course in Statistics and Data Analysis, and the first edition of Handbook of Regression Analysis, all published by Wiley.

Jeffrey S. Simonoff, PhD, is Professor of Statistics at the Leonard N. Stern School of Business of New York University. He is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He has authored, coauthored, or coedited more than one hundred articles and seven books on the theory and applications of statistics.
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