You are here

Regression Diagnostics

Regression Diagnostics
An Introduction

Second Edition

December 2019 | 168 pages | SAGE Publications, Inc

Regression diagnostics are methods for determining whether a regression model that has been fit to data adequately represents the structure of the data. For example, if the model assumes a linear (straight-line) relationship between the response and an explanatory variable, is the assumption of linearity warranted? Regression diagnostics not only reveal deficiencies in a regression model that has been fit to data but in many instances may suggest how the model can be improved. The Second Edition of this bestselling volume by John Fox considers two important classes of regression models: the normal linear regression model (LM), in which the response variable is quantitative and assumed to have a normal distribution conditional on the values of the explanatory variables; and generalized linear models (GLMs) in which the conditional distribution of the response variable is a member of an exponential family. R code and data sets for examples within the text can be found on an accompanying website at

Series Editors Introduction
About the Author
Chapter 1. Introduction
Chapter 2. The Linear Regression Model: Review
The Normal Linear Regression Models

Least-Squares Estimation

Statistical Inference for Regression Coefficients

The Linear Regression Model in Matrix Forms

Chapter 3. Examining and Transforming Regression Data
Univariate Displays

Transformations for Symmetry

Transformations for Linearity

Transforming Nonconstant Variation

Interpreting Results When Variables are Transformed

Chapter 4. Unusual data
Measuring Leverage: Hatvalues

Detecting Outliers: Studentized Residuals

Measuring Influence: Cook’s Distance and Other Case-Deletion Diagnostics

Numerical Cutoffs for Noteworthy Case Diagnostics

Jointly Influential Cases: Added-Variable Plots

Should Unusual Data Be Discarded?

Unusual Data: Details

Chapter 5. Non-Normality and Nonconstant Error Variance
Detecting and Correcting Non-Normality

Detecting and Dealing With Nonconstant Error Variance

Robust Coefficient Standard Errors


Weighted Least Squares

Robust Standard Errors and Weighted Least Squares: Details

Chapter 6. Nonlinearity
Component-Plus-Residual Plots

Marginal Model Plots

Testing for Nonlinearity

Modeling Nonlinear Relationships with Regression Splines

Chapter 7. Collinearity
Collinearity and Variance Inflation

Visualizing Collinearity

Generalized Variance Inflation

Dealing With Collinearity

*Collinearity: Some Details

Chapter 8. Diagnostics for Generalized Linear Models
Generalized Linear Models: Review

Detecting Unusual Data in GLMs

Nonlinearity Diagnostics for GLMs

Diagnosing Collinearity in GLMs

Quasi-Likelihood Estimation of GLMs

*GLMs: Further Background

Chapter 9. Concluding Remarks
Complementary Reading


The work of a master who knows how to make regression come alive with engaging language and catchy graphics.

Helmut Norpoth
Stony Brook University

This monograph provides very clear and quite comprehensive treatment of many tools and strategies for dealing with the various issues and situations that might arise to compromise the extent to which a regression model accurately represents the structure that exists within a dataset. As such, I would recommend this work to both beginners and experienced researchers in the social sciences. 

William G. Jacoby
Professor Emeritus, Michigan State University

John Fox has substantially updated his authoritative, compact, and accessible presentation on diagnosing and correcting problems in regression models. New sections on graphical inspection and transformation prior to analysis, and on diagnostics for generalized linear models enhance its utility. I recommend it strongly to instructors and practitioners alike.

Peter Marsden
Harvard University

Sample Materials & Chapters

Chapter 1. Introduction

John David Fox

John Fox received a BA from the City College of New York and a PhD from the University of Michigan, both in Sociology. He is Professor Emeritus of Sociology at McMaster University in Hamilton, Ontario, Canada, where he was previously the Senator William McMaster Professor of Social Statistics. Prior to coming to McMaster, he was Professor of Sociology, Professor of Mathematics and Statistics, and Coordinator of the Statistical Consulting Service at York University in Toronto. Professor Fox is the author of many articles and books on applied statistics, including \emph{Applied Regression Analysis and Generalized Linear Models, Third Edition... More About Author

Purchasing options

Please select a format:

ISBN: 9781544375229

SAGE Research Methods is a research methods tool created to help researchers, faculty and students with their research projects. SAGE Research Methods links over 175,000 pages of SAGE’s renowned book, journal and reference content with truly advanced search and discovery tools. Researchers can explore methods concepts to help them design research projects, understand particular methods or identify a new method, conduct their research, and write up their findings. Since SAGE Research Methods focuses on methodology rather than disciplines, it can be used across the social sciences, health sciences, and more.