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Regression Analysis by Example, 5th Edition

ISBN: 978-0-470-90584-5
424 pages
September 2012
Regression Analysis by Example, 5th Edition (0470905840) cover image

Praise for the Fourth Edition:

"This book is . . . an excellent source of examples for regression analysis. It has been and still is readily readable and understandable."

—Journal of the American Statistical Association Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgment. Regression Analysis by Example, Fifth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression.

The book now includes a new chapter on the detection and correction of multicollinearity, while also showcasing the use of the discussed methods on newly added data sets from the fields of engineering, medicine, and business. The Fifth Edition also explores additional topics, including:

  • Surrogate ridge regression
  • Fitting nonlinear models
  • Errors in variables
  • ANOVA for designed experiments

Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions, the required assumptions, and the evaluated success of each technique. Additionally, methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R.

Regression Analysis by Example, Fifth Edition is suitable for anyone with an understanding of elementary statistics.

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Preface xiv

1 Introduction 1

1.1 What Is Regression Analysis? 1

1.2 Publicly Available Data Sets 2

1.3 Selected Applications of Regression Analysis 3

1.4 Steps in Regression Analysis 13

1.5 Scope and Organization of the Book 21

Exercises 23

2 Simple Linear Regression 25

2.1 Introduction 25

2.2 Covariance and Correlation Coefficient 25

2.3 Example: Computer Repair Data 30

2.4 The Simple Linear Regression Model 32

2.5 Parameter Estimation 33

2.6 Tests of Hypotheses 36

2.7 Confidence Intervals 41

2.8 Predictions 41

2.9 Measuring the Quality of Fit 43

2.10 Regression Line Through the Origin 46

2.11 Trivial Regression Models 48

2.12 Bibliographic Notes 49

Exercises 49

3 Multiple Linear Regression 57

3.1 Introduction 57

3.2 Description of the Data and Model 57

3.3 Example: Supervisor Performance Data 58

3.4 Parameter Estimation 61

3.5 Interpretations of Regression Coefficients 62

3.6 Centering and Scaling 64

3.7 Properties of the Least Squares Estimators 67

3.8 Multiple Correlation Coefficient 68

3.9 Inference for Individual Regression Coefficients 69

3.10 Tests of Hypotheses in a Linear Model 71

3.11 Predictions 81

3.12 Summary 82

Exercises 82

Appendix: Multiple Regression in Matrix Notation 89

4 Regression Diagnostics: Detection of Model Violations 93

4.1 Introduction 93

4.2 The Standard Regression Assumptions 94

4.3 Various Types of Residuals 96

4.4 Graphical Methods 98

4.5 Graphs Before Fitting a Model 101

4.6 Graphs After Fitting a Model 105

4.7 Checking Linearity and Normality Assumptions 105

4.8 Leverage, Influence, and Outliers 106

4.9 Measures of Influence 111

4.10 The Potential-Residual Plot 115

4.11 What to Do with the Outliers? 116

4.12 Role of Variables in a Regression Equation 117

4.13 Effects of an Additional Predictor 122

4.14 Robust Regression 123

Exercises 123

5 Qualitative Variables as Predictors 129

5.1 Introduction 129

5.2 Salary Survey Data 130

5.3 Interaction Variables 133

5.4 Systems of Regression Equations 136

5.5 Other Applications of Indicator Variables 147

5.6 Seasonality 148

5.7 Stability of Regression Parameters Over Time 149

Exercises 151

6 Transformation of Variables 163

6.1 Introduction 163

6.2 Transformations to Achieve Linearity 165

6.3 Bacteria Deaths Due to XRay Radiation 167

6.4 Transformations to Stabilize Variance 171

6.5 Detection of Heteroscedastic Errors 176

6.6 Removal of Heteroscedasticity 178

6.7 Weighted Least Squares 179

6.8 Logarithmic Transformation of Data 180

6.9 Power Transformation 181

6.10 Summary 185

Exercises 186

7 Weighted Least Squares 191

7.1 Introduction 191

7.2 Heteroscedastic Models 192

7.3 Two-Stage Estimation 195

7.4 Education Expenditure Data 197

7.5 Fitting a Dose-Response Relationship Curve 206

Exercises 208

8 The Problem of Correlated Errors 209

8.1 Introduction: Autocorrelation 209

8.2 Consumer Expenditure and Money Stock 210

8.3 Durbin-Watson Statistic 212

8.4 Removal of Autocorrelation by Transformation 214

8.5 Iterative Estimation With Autocorrelated Errors 216

8.6 Autocorrelation and Missing Variables 217

8.7 Analysis of Housing Starts 218

8.8 Limitations of Durbin-Watson Statistic 222

8.9 Indicator Variables to Remove Seasonality 223

8.10 Regressing Two Time Series 226

Exercises 228

9 Analysis of Collinear Data 233

9.1 Introduction 233

9.2 Effects of Collinearity on Inference 234

9.3 Effects of Collinearity on Forecasting 240

9.4 Detection of Collinearity 245

Exercises 254

10 Working With Collinear Data 259

10.1 Introduction 259

10.2 Principal Components 259

10.3 Computations Using Principal Components 263

10.4 Imposing Constraints 263

10.5 Searching for Linear Functions of the β’s 267

10.6 Biased Estimation of Regression Coefficients 272

10.7 Principal Components Regression 272

10.8 Reduction of Collinearity in the Estimation Data 274

10.9 Constraints on the Regression Coefficients 276

10.10 Principal Components Regression: A Caution 277

10.11 Ridge Regression 280

10.12 Estimation by the Ridge Method 281

10.13 Ridge Regression: Some Remarks 285

10.14 Summary 287

10.15 Bibliographic Notes 288

Exercises 288

Appendix 10.A: Principal Components 291

Appendix 10.B: Ridge Regression 294

Appendix 10.C: Surrogate Ridge Regression 297

11 Variable Selection Procedures 299

11.1 Introduction 299

11.2 Formulation of the Problem 300

11.3 Consequences of Variables Deletion 300

11.4 Uses of Regression Equations 302

11.5 Criteria for Evaluating Equations 303

11.6 Collinearity and Variable Selection 306

11.7 Evaluating All Possible Equations 306

11.8 Variable Selection Procedures 307

11.9 General Remarks on Variable Selection Methods 309

11.10 A Study of Supervisor Performance 310

11.11 Variable Selection With Collinear Data 314

11.12 The Homicide Data 314

11.13 Variable Selection Using Ridge Regression 317

11.14 Selection of Variables in an Air Pollution Study 318

11.15 A Possible Strategy for Fitting Regression Models 326

11.16 Bibliographic Notes 327

Exercises 328

Appendix: Effects of Incorrect Model Specifications 332

12 Logistic Regression 335

12.1 Introduction 335

12.2 Modeling Qualitative Data 336

12.3 The Logit Model 336

12.4 Example: Estimating Probability of Bankruptcies 338

12.5 Logistic Regression Diagnostics 341

12.6 Determination of Variables to Retain 342

12.7 Judging the Fit of a Logistic Regression 345

12.8 The Multinomial Logit Model 347

12.8.1 Multinomial Logistic Regression 347

12.9 Classification Problem: Another Approach 354

Exercises 355

13 Further Topics 359

13.1 Introduction 359

13.2 Generalized Linear Model 359

13.3 Poisson Regression Model 360

13.4 Introduction of New Drugs 361

13.5 Robust Regression 363

13.6 Fitting a Quadratic Model 364

13.7 Distribution of PCB in U.S. Bays 366

Exercises 370

Appendix A: Statistical Tables 371

References 381

Index 389

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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 Kazhakstan and Mongolia. He is the coauthor of Sensitivity Analysis in Linear Regression and A Casebook for a First Course in Statistics and Data Analysis, both published by Wiley.

ALI S. HADI, PhD, is a Distinguished University Professor and former vice provost at the American University in Cairo (AUC). He is the founding Director of the Actuarial Science Program at AUC. He is also a Stephen H. Weiss Presidential Fellow and Professor Emeritus at Cornell University. Dr. Hadi is the author of four other books, a Fellow of the American Statistical Association, and an elected Member of the International Statistical Institute.

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 “The text is suitable for anyone with an understanding of elementary statistics.”  (Zentralblatt MATH, 1 July 2013)

“All in all, here we have a nice and valuable up-to-date book showing examples how the famous ever-lasting regression analysis works with the data. No doubt, this book will continue to be frequently used in statistics classrooms.”  (International Statistical Review, 15 February 2013)



 

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