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.

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.

Zusammenfassung

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 xiii

Preface to the First Edition xvii

Part I The Multiple Linear Regression Model

1 Multiple Linear Regression 3

1.1 Introduction 3

1.2 Concepts and Background Material 4

1.2.1 The Linear Regression Model 4

1.2.2 Estimation Using Least Squares 5

1.2.3 Assumptions 8

1.3 Methodology 9

1.3.1 Interpreting Regression Coefficients 9

1.3.2 Measuring the Strength of the Regression Relationship 11

1.3.3 Hypothesis Tests and Confidence Intervals for _ 12

1.3.4 Fitted Values and Predictions 14

1.3.5 Checking Assumptions Using Residual Plots 15

1.4 Example Estimating Home Prices 16

1.5 Summary 19

2 Model Building 23

2.1 Introduction 23

2.2 Concepts and Background Material 24

2.2.1 Using Hypothesis Tests to Compare Models 24

2.2.2 Collinearity 26

2.3 Methodology 29

2.3.1 Model Selection 29

2.3.2 ExampleEstimating Home Prices (continued) 31

2.4 Indicator Variables and Modeling Interactions 39

2.4.1 ExampleElectronic Voting and the 2004 Presidential Election 41

2.5 Summary 46

Part II Addressing Violations of Assumptions

3 Diagnostics for Unusual Observations 53

3.1 Introduction 53

3.2 Concepts and Background Material 54

3.3 Methodology 56

3.3.1 Residuals and Outliers 56

3.3.2 Leverage Points 57

3.3.3 Influential Points and Cook's Distance 58

3.4 Example Estimating Home Prices (continued) 60

3.5 Summary 64

4 Transformations and Linearizable Models 67

4.1 Introduction 67

4.2 Concepts and Background Material: The Log-Log Model 69

4.3 Concepts and Background Material: Semilog Models 69

4.3.1 Logged Response Variable 70

4.3.2 Logged Predictor Variable 70

4.4 Example Predicting Movie Grosses After One Week 71

4.5 Summary 78

5 Time Series Data and Autocorrelation 81

5.1 Introduction 81

5.2 Concepts and Background Material 83

5.3 Methodology: Identifying Autocorrelation 85

5.3.1 The Durbin-Watson Statistic 86

5.3.2 The Autocorrelation Function (ACF) 87

5.3.3 Residual Plots and the Runs Test 87

5.4 Methodology: Addressing Autocorrelation 88

5.4.1 Detrending and Deseasonalizing 88

5.4.2 Example e-Commerce Retail Sales 89

5.4.3 Lagging and Differencing 95

5.4.4 Example Stock Indexes 96

5.4.5 Generalized Least Squares (GLS): The Cochrane- Orcutt Procedure 102

5.4.6 Example Time Intervals Between Old Faithful Geyser Eruptions 104

5.5 Summary 107

Part III Categorical Predictors

6 Analysis of Variance 113

6.1 Introduction 113

6.2 Concepts and Background Material 114

6.2.1 One-Way ANOVA 114

6.2.2 Two-Way ANOVA 115

6.3 Methodology 117

6.3.1 Codings for Categorical Predictors 117

6.3.2 Multiple Comparisons 122

6.3.3 Levene's Test and Weighted Least Squares 124

6.3.4 Membership in Multiple Groups 127

6.4 Example DVD Sales of Movies 129

6.5 Higher-Way ANOVA 134

6.6 Summary 136

7 Analysis of Covariance 139

7.1 Introduction 139