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Applied Regression Analysis and Generalized Linear Models

Applied Regression Analysis and Generalized Linear Models

Third Edition

April 2015 | 816 pages | SAGE Publications, Inc
Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book. 

Accompanying website resources: An instructor website for the book is available at containing all answers to the end-of-chapter exercises. Answers to odd-numbered questions, as well as datasets and other student resources are available on the author's website at:

NEW! Bonus chapters available on the author's website at the URL above!
Chapter 25 on Bayesian Estimation of Regression Models, and
Chapter 26 on Causal Inferences from Observational Data: Directed Acyclic Graphs and Potential Outcomes

About the Author
1. Statistical Models and Social Science
1.1 Statistical Models and Social Reality

1.2 Observation and Experiment

1.3 Populations and Samples

2. What Is Regression Analysis?
2.1 Preliminaries

2.2 Naive Nonparametric Regression

2.3 Local Averaging

3. Examining Data
3.1 Univariate Displays

3.2 Plotting Bivariate Data

3.3 Plotting Multivariate Data

4. Transforming Data
4.1 The Family of Powers and Roots

4.2 Transforming Skewness

4.3 Transforming Nonlinearity

4.4 Transforming Nonconstant Spread

4.5 Transforming Proportions

4.6 Estimating Transformations as Parameters*

5. Linear Least-Squares Regression
5.1 Simple Regression

5.2 Multiple Regression

6. Statistical Inference for Regression
6.1 Simple Regression

6.2 Multiple Regression

6.3 Empirical Versus Structural Relations

6.4 Measurement Error in Explanatory Variables*

7. Dummy-Variable Regression
7.1 A Dichotomous Factor

7.2 Polytomous Factors

7.3 Modeling Interactions

8. Analysis of Variance
8.1 One-Way Analysis of Variance

8.2 Two-Way Analysis of Variance

8.3 Higher-Way Analysis of Variance

8.4 Analysis of Covariance

8.5 Linear Contrasts of Means

9. Statistical Theory for Linear Models*
9.1 Linear Models in Matrix Form

9.2 Least-Squares Fit

9.3 Properties of the Least-Squares Estimator

9.4 Statistical Inference for Linear Models

9.5 Multivariate Linear Models

9.6 Random Regressors

9.7 Specification Error

9.8 Instrumental Variables and Two-Stage Least Squares

10. The Vector Geometry of Linear Models*
10.1 Simple Regression

10.2 Multiple Regression

10.3 Estimating the Error Variance

10.4 Analysis-of-Variance Models

11. Unusual and Influential Data
11.1 Outliers, Leverage, and Influence

11.2 Assessing Leverage: Hat-Values

11.3 Detecting Outliers: Studentized Residuals

11.4 Measuring Influence

11.5 Numerical Cutoffs for Diagnostic Statistics

11.6 Joint Influence

11.7 Should Unusual Data Be Discarded?

11.8 Some Statistical Details*

12. Non-Normality, Nonconstant Error Variance, Nonlinearity
12.1 Non-Normally Distributed Errors

12.2 Nonconstant Error Variance

12.3 Nonlinearity

12.4 Discrete Data

12.5 Maximum-Likelihood Methods*

12.6 Structural Dimension

13. Collinearity and Its Purported Remedies
13.1 Detecting Collinearity

13.2 Coping With Collinearity: No Quick Fix

14. Logit and Probit Models for Categorical Response Variables
14.1 Models for Dichotomous Data

14.2 Models for Polytomous Data

14.3 Discrete Explanatory Variables and Contingency Tables

15. Generalized Linear Models
15.1 The Structure of Generalized Linear Models

15.2 Generalized Linear Models for Counts

15.3 Statistical Theory for Generalized Linear Models*

15.4 Diagnostics for Generalized Linear Models

15.5 Analyzing Data From Complex Sample Surveys

16. Time-Series Regression and Generalized Leasr Squares*
16.1 Generalized Least-Squares Estimation

16.2 Serially Correlated Errors

16.3 GLS Estimation With Autocorrelated Errors

16.4 Correcting OLS Inference for Autocorrelated Errors

16.5 Diagnosing Serially Correlated Errors

16.6 Concluding Remarks

17. Nonlinear Regression
17.1 Polynomial Regression

17.2 Piece-wise Polynomials and Regression Splines

17.3 Transformable Nonlinearity

17.4 Nonlinear Least Squares*

18. Nonparametric Regression
18.1 Nonparametric Simple Regression: Scatterplot Smoothing

18.2 Nonparametric Multiple Regression

18.3 Generalized Nonparametric Regression

19. Robust Regression*
19.1 M Estimation

19.2 Bounded-Influence Regression

19.3 Quantile Regression

19.4 Robust Estimation of Generalized Linear Models

19.5 Concluding Remarks

20. Missing Data in Regression Models
20.1 Missing Data Basics

20.2 Traditional Approaches to Missing Data

20.3 Maximum-Likelihood Estimation for Data Missing at Random*

20.4 Bayesian Multiple Imputation

20.5 Selection Bias and Censoring

21. Bootstrapping Regression Models
21.1 Bootstrapping Basics

21.2 Bootstrap Confidence Intervals

21.3 Bootstrapping Regression Models

21.4 Bootstrap Hypothesis Tests*

21.5 Bootstrapping Complex Sampling Designs

21.6 Concluding Remarks

22. Model Selection, Averaging, and Validation
22.1 Model Selection

22.2 Model Averaging*

22.3 Model Validation

23. Linear Mixed-Effects Models for Hierarchical and Longitudinal Data
23.1 Hierarchical and Longitudinal Data

23.2 The Linear Mixed-Effects Model

23.3 Modeling Hierarchical Data

23.4 Modeling Longitudinal Data

23.5 Wald Tests for Fixed Effects

23.6 Likelihood-Ratio Tests of Variance and Covariance Components

23.7 Centering Explanatory Variables, Contextual Effects, and Fixed-Effects Models

23.8 BLUPs

23.9 Statistical Details*

24. Generalized Linear and Nonlinear Mixed-Effects Models
24.1 Generalized Linear Mixed Models

24.2 Nonlinear Mixed Models

Appendix A
Author Index
Subject Index
Data Set Index


Companion Website
The companion website features data sets, data analysis exercises, Appendixes B,C,D, and errata.

The strength of this text is the unified presentation of several regression topics that provides the student with a global perspective on regression analysis.  The student is well served with this unified approach as it facilitates deeper research on any one topic with more advanced texts.

E. C. Hedberg, Arizona State University

This text is a one-stop shop for me for my first year stats sequence for students in our program. Those wanting the technical detail will be satisfied; those wanting an excellent explanation of these methods using real-world examples and approachable language will also be satisfied.

Corey S. Sparks, The University of Texas at San Antonio

I have enjoyed using previous editions of this text and look forward to using this edition. It covers all key topics, and quite a few advanced ones, in one well-written text.

Michael S. Lynch, University of Georgia


In summary, this is an excellent text on regression applications and methods, written with authority, lucidity, and eloquence. The second edition provides substantive and topical updates, and makes the book suitable for courses designed to emphasize both the classical and the modern aspects of regression.

Journal of the American Statistical Association (review of the second edition)


Even though the book is written with social scientists as the target audience, the depth of material and how it is conveyed give it far broader appeal. Indeed, I recommend it as a useful learning text and resource for researchers and students in any field that applies regression or linear models (that is, most everyone), including courses for undergraduate statistics majors…. The author is to be commended for giving us this book, which I trust will find a wide and enduring readership.

Journal of the American Statistical Association (review of the first edition)


[T]his wonderfully comprehensive book focuses on regression analysis and linear models… We enthusiastically recommend this book—having used it in class, we know that it is thorough and well-liked by students.

Chance (review of the first edition)

I loved it and students did too (well, as much as they will!)

Dr Erin M Hodgess
Computer Mathematical Sci Dept, Univ Of Houston-Downtown
May 10, 2016

The book covers regression only and not all the topics in regression. I need a book that covers both regression methods and design of experiments methods.

Mr Ahmed Almaskut
Human Kinetics, University Of Ottawa
June 25, 2015
Key features


  • A new Part IV on mixed-effects models for hierarchical and longitudinal data with chapters on linear mixed-effects models (Chapter 23) and nonlinear and generalized linear mixed-effects models (Chapter 24) provides readers with a basis for applying these models in practice, as well as for reading more extensive treatments of the subject.
  • A revised presentation of analysis-of-variance models includes a simplified treatment that allows readers to skip the more complex aspects of the topic if they wish.
  • An introduction to instrumental-variables estimation and two-stage least-squares regression has been added.
  • The book now includes a brief introduction to design-based inference for regression models fit to data from complex survey samples.
  • References have been updated.


  • The book is a valuable resource for graduate students and researchers in the social sciences (particularly sociology, political science, and psychology) and other disciplines that employ linear, generalized-linear, and related models for data analysis.
  • Each chapter ends with a summary and exercises.
  • An extensive website includes: appendices with background information on matrices, linear algebra, vector geometry, calculus, probability and estimation; datasets used in the book and for data-analytic exercises; and the data-analytic exercises themselves. 

Sample Materials & Chapters

Chapter 7

Chapter 21

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