Modern Regression Methods

ISBN-13: 9780470081860 / Angielski / Twarda / 2008 / 672 str.

Thomas P. Ryan

Opis

"Over the years, I have had the opportunity to teach several regression courses, and I cannot think of a better undergraduate text than this one." (The American Statistician) "The book is well written and has many exercises. It can serve as a very good textbook for scientists and engineers, with only basic statistics as a prerequisite. I also highly recommend it to practitioners who want to solve real-life prediction problems." (Computing Reviews) Modern Regression Methods, Second Edition maintains the accessible organization, breadth of coverage, and cutting-edge appeal that earned its predecessor the title of being one of the top five books for statisticians by an Amstat News book editor in 2003. This new edition has been updated and enhanced to include all-new information on the latest advances and research in the evolving field of regression analysis. The book provides a unique treatment of fundamental regression methods, such as diagnostics, transformations, robust regression, and ridge regression. Unifying key concepts and procedures, this new edition emphasizes applications to provide a more hands-on and comprehensive understanding of regression diagnostics. New features of the Second Edition include:

• A revised chapter on logistic regression, including improved methods of parameter estimation
• A new chapter focusing on additional topics of study in regression, including quantile regression, semiparametric regression, and Poisson regression
• A wealth of new and updated exercises with worked solutions
• An extensive FTP site complete with Minitab macros, which allow the reader to compute analyses, and specialized procedures
• Updated references at the end of each chapter that direct the reader to the appropriate resources for further study

An accessible guide to state-of-the-art regression techniques, Modern Regression Methods, Second Edition is an excellent book for courses in regression analysis at the upper-undergraduate and graduate levels. It is also a valuable reference for practicing statisticians, engineers, and physical scientists.

Recenzje

"The book is to be praised in that it makes the reader aware of a large number of approaches to regression situations, and also to their possible pitfalls. It is thus an excellent basis for an experienced instructor to teach regression at different levels." ( Springer, August 2010)

"This book, at the undergraduate level and even at the graduate level, will be rewarding reading for anyone interested in learning the nuances of regression analysis." ( Mathmatical Reviews, January 2010)

"The exercises are interesting and thought–provoking throughout. If you liked the first edition, you will be pleased with this revision also." (International Statistical Review, August 2009)

"The book is well written and has many exercises. It can serve as a very good textbook for scientists and engineers, with only basic statistics as a prerequisite. I also highly recommend it to practitioners who want to solve real–life prediction problems." (Computing Reviews, July 2009)

"In this second edition, Ryan (author, editor, and educator) provides substantial updates and revisions of his popular text for statisticians to include new information on the most current advances and research in regression analysis" (SciTech Reviews, March 2009)

"One would be hard–pressed to find another text that rivals this one in terms of coverage of the regression literature." (The American Statistician, 2009)

"I strongly recommend the book as a reference for anyone teaching or using regression." (MAA Reviews, 2009)

"Highly recommended for those already trained in mathematics and statistics who want a good guide to current practice and issues in multiple regression techniques." (Journal of Biopharmaceutical Statistics, 2009)

Spis treści

Preface.

1. Introduction.

1.1 Simple Linear Regression Model.

1.2 Uses of Regression Models.

1.3 Graph the Data!

1.4 Estimation of ß₀ and ß₁.

1.5 Inferences from Regression Equations.

1.6 Regression Through the Origin.

1.7 Additional Examples.

1.8 Correlation.

1.9 Miscellaneous Uses of Regression.

1.10 Fixed Versus Random Regressors.

1.11 Missing Data.

1.12 Spurious Relationships.

1.13 Software.

1.14 Summary.

Appendix.

References.

Exercises.

2. Diagnostics and Remedial Measures.

2.1 Assumptions.

2.2 Residual Plots.

2.3 Transformations.

2.4 Influential Observations.

2.5 Outliers.

2.6 Measurement Error.

2.7 Software.

2.8 Summary.

Appendix.

References.

Exercises.

3. Regression with Matrix Algebra.

3.1 Introduction to Matrix Algebra.

3.2 Matrix Algebra Applied to Regression.

3.3 Summary.

Appendix.

References.

Exercises.

4. Introduction to Multiple Linear Regression.

4.1 An Example of Multiple Linear Regression.

4.2 Centering And Scaling.

4.3 Interpreting Multiple Regression Coefficients.

4.4 Indicator Variables.

4.5 Separation or Not?

4.6 Alternatives to Multiple Regression.

4.7 Software.

4.8 Summary.

References.

Exercises.

5. Plots in Multiple Regression.

5.1 Beyond Standardized Residual Plots.

5.2 Some Examples.

5.3 Which Plot?

5.4 Recommendations.

5.5 Partial Regression Plots.

5.6 Other Plots For Detecting Influential Observations.

5.7 Recent Contributions to Plots in Multiple Regression.

5.8 Lurking Variables.

5.9 Explanation of Two Data Sets Relative to R².

5.10 Software.

5.11 Summary.

References.

Exercises.

6. Transformations in Multiple Regression.

6.1 Transforming Regressors.

6.2 Transforming Y.

6.3 Further Comments on the Normality Issue.

6.4 Box–Cox Transformation.

6.5 Box–Tidwell Revisited.

6.6 Combined Box–Cox and Box–Tidwell Approach.

6.7 Other Transformation Methods.

6.8 Transformation Diagnostics.

6.9 Software.

6.10 Summary.

References.

Exercises.

7. Selection of Regressors.

7.1 Forward Selection.

7.2 Backward Elimination.

7.3 Stepwise Regression.

7.4 All Possible Regressions.

7.5 Newer Methods.

7.6 Examples.

7.7 Variable Selection for Nonlinear Terms.

7.8 Must We Use a Subset?

7.9 Model Validation.

7.10 Software.

7.11 Summary.

Appendix.

References.

Exercises.

8. Polynomial and Trigonometric Terms.

8.1 Polynomial Terms.

8.2 Polynomial–Trigonometric Regression.

8.3 Software.

8.4 Summary.

References.

Exercises.

9. Logistic Regression.

9.1 Introduction.

9.2 One Regressor.

9.3 A Simulated Example.

9.4 Detecting Complete Separation, Quasicomplete Separation and Near Separation.

9.5 Measuring the Worth of the Model.

9.6 Determining the Worth of the Individual Regressors.

9.7 Confidence Intervals.

9.8 Exact Prediction.

9.9 An Example With Real Data.

9.10 An Example of Multiple Logistic Regression.

9.11 Multicollinearity in Multiple Logistic Regression.

9.12 Osteogenic Sarcoma Data Set.

9.13 Missing Data.

9.14 Sample Size Determination.

9.15 Polytomous Logistic Regression.

9.16 Logistic Regression Variations.

9.17 Alternatives to Logistic Regression.

9.18 Software for Logistic Regression.

9.19 Summary.

Appendix.

References.

Exercises.

10. Nonparametric Regression.

10.1 Relaxing Regression Assumptions.

10.2 Monotone Regression.

10.3 Smoothers.

10.4 Variable Selection.

10.5 Important Considerations in Smoothing.

10.6 Sliced Inverse Regression.

10.7 Projection Pursuit Regression.

10.8 Software.

10.9 Summary.

Appendix.

References.

Exercises.

11. Robust Regression.

11.1 The Need for Robust Regression.

11.2 Types of Outliers.

11.3 Historical Development of Robust Regression.

11.4 Goals of Robust Regression.

11.5 Proposed High Breakdown Point Estimators.

11.6 Approximating HBP Estimator Solutions.

11.7 Other Methods for Detecting Multiple Outliers.

11.8 Bounded Influence Estimators.

11.9 Multistage Procedures.

11.10 Other Robust Regression Estimators.

11.11 Applications.

11.12 Software for Robust Regression.

11.13 Summary.

References.

Exercises.

12. Ridge Regression.

12.1 Introduction.

12.2 How Do We Determine K?

12.3 An Example.

12.4 Ridge Regression for Prediction.

12.5 Generalized Ridge Regression.

12.6 Inferences in Ridge Regression.

12.7 Some Practical Considerations.

12.8 Robust Ridge Regression?

12.9 Recent Developments in Ridge Regression.

12.10 Other Biased Estimators.

12.11 Software.

12.12 Summary.

Appendix.

References.

Exercises.

13. Nonlinear Regression.

13.1 Introduction.

13.2 Linear Versus Nonlinear Regression.

13.3 A Simple Nonlinear Example.

13.4 Relative Offset Convergence Criterion.

13.5 Adequacy of the Estimation Approach.

13.6 Computational Considerations.

13.7 Determining Model Adequacy.

13.7.1 Lack–of–Fit Test.

13.8 Inferences.

13.9 An Application.

13.10 Rational Functions.

13.11 Robust Nonlinear Regression.

13.12 Applications.

13.13 Teaching Tools.

13.14 Recent Developments.

13.15 Software.

13.16 Summary.

Appendix.

References.

Exercises.

14. Experimental Designs for Regression.

14.1 Objectives for Experimental Designs.

14.2 Equal Leverage Points.

14.3 Other Desirable Properties of Experimental Designs.

14.4 Model Misspecification.

14.5 Range of Regressors.

14.6 Algorithms for Design Construction.

14.7 Designs for Polynomial Regression.

14.8 Designs for Logistic Regression.

14.9 Designs for Nonlinear Regression.

14.10 Software.

14.11 Summary.

References.

Exercises.

15. Miscellaneous Topics in Regression.

15.1 Piecewise Regression and Alternatives.

15.2 Semiparametric Regression.

15.3 Quantile Regression.

15.4 Poisson Regression.

15.5 Negative Binomial Regression.

15.6 Cox Regression.

15.7 Probit Regression.

15.8 Censored Regression and Truncated Regression.

15.8.1 Tobit Regression.

15.9 Constrained Regression.

15.10 Interval Regression.

15.11 Random Coefficient Regression.

15.12 Partial Least Squares Regression.

15.13 Errors–in–Variables Regression.

15.14 Regression with Life Data.

15.15 Use of Regression in Survey Sampling.

15.16 Bayesian Regression.

15.17 Instrumental Variables Regression.

15.18 Shrinkage Estimators.

15.19 Meta–Regression.

15.20 Classification and Regression Trees (CART).

15.21 Multivariate Regression.

References.

Exercises.

16. Analysis of Real Data Sets.

16.1 Analyzing Buchanan s Presidential Vote in Palm Beach County in 2000.

16.2 Water Quality Data.

16.3 Predicting Lifespan?

16.4 Scottish Hill Races Data.

16.5 Leukemia Data.

16.6 Dosage Response Data.

16.7 A Strategy for Analyzing Regression Data.

16.8 Summary.

References.

Answers to Selected Exercises.

Statistical Tables.

Author Index.

Subject Index.

O autorze

Thomas P. Ryan, PhD, served on the Editorial Review Board of the Journal of Quality Technology from 1990 2006, including three years as the book review editor. He is the author of four books, all of which are published by Wiley, and he is also an elected Fellow of the American Statistical Association, the American Society for Quality, and the Royal Statistical Society. A former consultant to Cytel Software Corporation, Dr. Ryan currently teaches advanced courses at statistics.com on the design of experiments, statistical process control, and engineering statistics.

Blurb

Praise for the First Edition

". . . provides a very thorough treatment of regression approaches, including techniques not covered in many books . . ."
Technometrics

". . . an excellent book . . . worthwhile for anyone who uses regression techniques to obtain their own copy of this book . . ."
Australian & New Zealand Journal of Statistics

Modern Regression Methods, Second Edition maintains the accessible organization, breadth of coverage, and cutting–edge appeal that earned its predecessor the title of being one of the top five books for statisticians by an Amstat News book editor in 2003. This new edition has been updated and enhanced to include all–new information on the latest advances and research in the evolving field of regression analysis.

The book provides a unique treatment of fundamental regression methods, such as diagnostics, transformations, robust regression, and ridge regression. Unifying key concepts and procedures, this new edition emphasizes applications to provide a more hands–on and comprehensive understanding of regression diagnostics. New features of the Second Edition include:

• A revised chapter on logistic regression, including improved methods of parameter estimation

• A new chapter focusing on additional topics of study in regression, including quantile regression, semiparametric regression, and Poisson regression

• A wealth of new and updated exercises with worked solutions

• An extensive FTP site complete with Minitab® macros, which allow the reader to compute analyses, and specialized procedures

• Updated references at the end of each chapter that direct the reader to the appropriate resources for further study

An accessible guide to state–of–the–art regression techniques, Modern Regression Methods, Second Edition is an excellent book for courses in regression analysis at the upper–undergraduate and graduate levels. It is also a valuable reference for practicing statisticians, engineers, and physical scientists.