Linear Models with R
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Summary
Books on regression and the analysis of variance abound-many are introductory, many are theoretical. While most of them do serve a purpose, the fact remains that data analysis cannot be properly learned without actually doing it, and this means using a statistical software package. There are many of these to choose from as well, all with their particular strengths and weaknesses. Lately, however, one such package has begun to rise above the others thanks to its free availability, its versatility as a programming language, and its interactivity. That software is R.
In the first book that directly uses R to teach data analysis, Linear Models with R focuses on the practice of regression and analysis of variance. It clearly demonstrates the different methods available and more importantly, in which situations each one applies. It covers all of the standard topics, from the basics of estimation to missing data, factorial designs, and block designs, but it also includes discussion on topics, such as model uncertainty, rarely addressed in books of this type. The presentation incorporates an abundance of examples that clarify both the use of each technique and the conclusions one can draw from the results. All of the data sets used in the book are available for download from http://www.stat.lsa.umich.edu/~faraway/LMR/.
The author assumes that readers know the essentials of statistical inference and have a basic knowledge of data analysis, linear algebra, and calculus. The treatment reflects his view of statistical theory and his belief that qualitative statistical concepts, while somewhat more difficult to learn, are just as important because they enable us to practice statistics rather than just talk about it.
Table of Contents
INTRODUCTION
Before b
Initial Data Analysis
When to Use Regression Analysis
History
ESTIMATION
Linear Model
Matrix Representation
Estimating b
Least b
Examples of Calculating
Gauss-Markov Theorem
Goodness of Fit
Example
Identifiability
INFERENCE
Hypothesis Tests to compare models
Testing Examples
Permutation tests
Confidence Intervals for b
Confidence Intervals for Predictions
Designed Experiments
Observational Data
Practical Difficulties
DIAGNOSTICS
Checking Error Assumptions
Finding Unusual Observations
Checking the Structure of the Model
PROBLEMS WITH THE PREDICTORS
Errors in Predictors
Changes of Scale
Collinearity
PROBLEMS WITH THE ERROR
Generalized Least Squares
Weighted Least Squares
Testing for Lack of Fit
Robust Regression
TRANSFORMATION
Transforming the Response
Transforming the Predictors
VARIABLE SELECTION
Hierarchical Models
Testing-based Procedures
Criterion-based procedures
Summary
SHRINKAGE METHODS
Principal Components
Partial Least Squares
Ridge Regression
STATISTICAL STRATEGY AND MODEL UNCERTAINTY
Strategy
An Experiment in Model Building
Discussion
CHICAGO INSURANCE REDLINING - A COMPLETE EXAMPLE
Ecological Correlation
Initial Data Analysis
Initial model and Diagnostics
Transformation and Variable Selection
Discussion
MISSING DATA
ANALYSIS OF COVARIANCE
A Two-Level Example
Coding Qualitative Predictors
A Multi-Level Factor Example
ONE-WAY ANOVA
The Model
An Example
Diagnostics
Pairwise Comparisons
FACTORIAL DESIGNS
Two-Way Anova
Two-Way Anova with One Observation per Cell
Two-Way Anova with more than One Observation per Cell
Larger Factorial Experiments
BLOCK DESIGNS
Randomized Block design
Latin Squares
Balanced Incomplete Block design
APPENDICES
R installation, Functions and Data
Quick Introduction to R
BIBLIOGRAPHY
INDEX
Editorial Reviews
"One danger with applied books such as this is that they become recipe lists of the kind 'press this key to get that result.' This is not so with Faraway's book. Throughout, it gives plenty of insight on what is going on, with comments that even the seasoned practitioner will appreciate. Interspersed with R code and the output that it produces one can find many little gems of what I think is sound statistical advice, well epitomized with the examples chosen…I read it with delight and think that the same will be true with anyone who is engaged in the use or teaching of linear models…I find this book a valuable buy for anyone who is involved with R and linear models, and it is essential in any university library where those topics are taught."
-Journal of the Royal Statistical Society
"Overall, Linear Models with R is well written and, given the increasing popularity of R, it is an important contribution."
-Technometrics, Vol. 47, No. 3, August 2005
"There are many books on regression and analysis of variance on the market, but this one is unique and has a novel approach to these statistical methods. The author uses R throughout the text to teach data analysis…The text also contains a wealth of references for the reader to pursue on related issues. This book is recommended for all who wish to use R for statistical investigations."
-Short Book Reviews of the International Statistical
Institute
"The book is very comprehensibly written and can therefore be recommended for beginners in linear models. It is clearly and simply explained how to use R and which packages are necessary to analyze linear models. …All in all, this book is recommendable as a textbook for computational linear regression courses and therefore for students and lecturers, but also for applied statisticians who want to get started on regression analysis using the software R."
-Biometrics
"…Dr. Faraway uses many examples and graphical procedures to illustrate the methods. This is a great strength of the book. … Linear Models with R is one of several books appearing to make R more accessible by bringing together functions from a number of packages and illustrating their use. From this perspective alone it is an important contribution. …I feel this book does a nice job of describing the methods available in linear modeling and illustrating the realistic implementation of these methods in a careful data analysis. …"
-Statistics in Medicine, 2006
