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An R Companion to Applied Regression

An R Companion to Applied Regression

Third Edition

September 2018 | 608 pages | SAGE Publications, Inc
An R Companion to Applied Regression is a broad introduction to the R statistical computing environment in the context of applied regression analysis. John Fox and Sanford Weisberg provide a step-by-step guide to using the free statistical software R, an emphasis on integrating statistical computing in R with the practice of data analysis, coverage of generalized linear models, and substantial web-based support materials.

The Third Edition has been reorganized and includes a new chapter on mixed-effects models, new and updated data sets, and a de-emphasis on statistical programming, while retaining a general introduction to basic R programming. The authors have substantially updated both the car and effects packages for R for this edition, introducing additional capabilities and making the software more consistent and easier to use. They also advocate an everyday data-analysis workflow that encourages reproducible research. To this end, they provide coverage of RStudio, an interactive development environment for R that allows readers to organize and document their work in a simple and intuitive fashion, and then easily share their results with others. Also included is coverage of R Markdown, showing how to create documents that mix R commands with explanatory text. 

An R Companion to Applied Regression continues to provide the most comprehensive and user-friendly guide to estimating, interpreting, and presenting results from regression models in R.”

–Christopher Hare, University of California, Davis

1. Getting Started with R and RStudio
Projects in RStudio

R Basics

Fixing Errors and Getting Help

Organizing Your Work in R and RStudio

An Extended Illustration

R Functions for Basic Statistics

Generic Functions and Their Methods*

2. Reading and Manipulating Data
Data Input

Managing Data

Working With Data Frames

Matrices, Arrays, and Lists

Dates and Times

Character Data

Large Data Sets in R*

Complementary Reading and References

3. Exploring and Transforming Data
Examining Distributions

Examining Relationships

Examining Multivariate Data

Transforming Data

Point Labeling and Identication

Scatterplot Smoothing

Complementary Reading and References

4. Fitting Linear Models
The Linear Model

Linear Least-Squares Regression

Predictor Effect Plots

Polynomial Regression and Regression Splines

Factors in Linear Models

Linear Models with Interactions

More on Factors

Too Many Regressors*

The Arguments of the lm Function

Complementary Reading and References

5. Standard Errors, Confidence Intervals, Tests
Coefficient Standard Errors

Confidence Intervals

Testing Hypotheses About Regression Coefficients

Complementary Reading and References

6. Fitting Generalized Linear Models
The Structure of GLMs

The glm() Function in R

GLMs for Binary-Response Data

Binomial Data

Poisson GLMs for Count Data

Loglinear Models for Contingency Tables

Multinomial Response Data

Nested Dichotomies

The Proportional-Odds Model


Arguments to glm()

Fitting GLMs by Iterated Weighted Least-Squares*

Complementary Reading and References

7. Fitting Mixed-Effects Models
Background: The Linear Model Revisited

Linear Mixed-Effects Models

Generalized Linear Mixed Models

Complementary Reading

8. Regression Diagnostics

Basic Diagnostic Plots

Unusual Data

Transformations After Fitting a Regression Model

Non-Constant Error Variance

Diagnostics for Generalized Linear Models

Diagnostics for Mixed-Effects Models

Collinearity and Variance-Inflation Factors

Additional Regression Diagnostics

Complementary Reading and References

9. Drawing Graphs
A General Approach to R Graphics

Putting It Together: Local Linear Regression

Other R Graphics Packages

Complementary Reading and References

10. An Introduction to R Programming
Why Learn to Program in R?

Defining Functions: Preliminary Examples

Working With Matrices*

Conditionals, Loops, and Recursion

Avoiding Loops

Optimization Problems*

Monte-Carlo Simulations*

Debugging R Code*

Object-Oriented Programming in R*

Writing Statistical-Modeling Functions in R*

Organizing Code for R Functions

Complementary Reading and References



Student Study Site

An accompanying website for the book found at provides:

  • R scripts for examples by chapter
  • Data files used in the book
  • The car package (Companion to Applied Regression), an accompanying software for regression diagnostics and other regression-related tasks
  • Other resources to help students get the most out of the text

An R Companion to Applied Regression continues to provide the most comprehensive and user-friendly guide to estimating, interpreting, and presenting results from regression models in R.”

Christopher Hare
University of California, Davis

“This is the best book I’ve read for teaching the modern practice of regression. By going deeply into both R and applied regression, it manages to use each topic to motivate and illustrate the other. The whole is much greater than sum of the parts because each thread so effectively reinforces the other. There are many nice surprises in this new edition.  R Studio and markdown are used to encourage a reproducible workflow. There’s an excellent and accessible chapter on mixed and longitudinal data that expands the reach of regression methods to the much more complex data structures typical of current practice. Like its predecessors, this edition is a model of clear, thoughtful exposition. It’s an outstanding contribution to the teaching and practice of regression.”

Georges Monette
York University

“This is an impressive update to a book I have long admired. The authors have brought the description of how to do data analysis and plots of Applied Regression related data to a modern and more comprehensive level.”

Michael Friendly
York University

Made a good supplement with a heavy emphasis on R.

Mike Minnotte
Mathematics Dept, University Of North Dakota
February 11, 2022
Key features


  • New coverage of linear and generalized linear mixed-effects models and a new section in the existing chapter on model diagnostics.
  • Increased emphasis on interpreting the results of fitting statistical models to data along with integrated discussion of predictor effect plots as a means of visualizing regression models, particularly models that are difficult to interpret directly from coefficient estimates.
  • A new emphasis on work-flow of data analysis and an explanation on how to use dynamic R Markdown documents in the RStudio interactive development environment to facilitate the process of data analysis and to make it easily reproducible.
  • Focused coverage of R programming is emphasized for performing the tasks that readers are likely to encounter in the process of analyzing data while still providing an introduction to statistical programming.
  • Newer and superior tools that have become available, such as in the treatment of data input and manipulation, are used throughout.


  • Detailed, worked-out examples introduce various facilities of R.
  • The book focuses on how to use R in everyday data analysis.
  • More demanding material is marked with an asterisk so that it may be skipped without loss of continuity.
  • A companion website includes several appendices for various extensions of regression analysis that are not covered in the text, downloadable scripts for all of the examples in the text, and more.

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