Complete text of a book review that appeared in the journal Technometrics, May 1998 (Vol. 40, No. 2).

Applied Regression Analysis, Linear Models, and Related Methods, by John Fox, Thousand Oaks. CA: Sage Publications, 1997, ISBN 0-8039-4540-X, xxi + 597 pp., \$58.

As the title indicates, the author has taken on the challenging task of covering applied regression analysis, linear models, and related methods within the confines of a single book. Perhaps the best known book in this category is Applied Linear Statistical Models (ALSM). by Neter. Kutner, Nachtsheim, and Wasserman (1996), which is now in its fourth edition and is regarded by many as the comprehensive, authoritative source on the application of regression and linear models. The new book by Fox is not quite as encyclopedic in its coverage as ALSM, but it does cover its topics well and it is very much up-to-date in its treatment of regression and statistical graphics.

The book is divided into four major sections. Part I starts with a discussion of the role of statistics in social-science research. This is followed by a chapter introducing the regression concept via local averaging. Non-parametric regression and smoothing are introduced very early to help the reader understand the conditional mean interpretation of regression. Part I finishes with a chapter on modern graphical data displays and a chapter on data transformation. The author discusses the use of R-code (Cook and Weisberg 1994) and Lisp-Stat (Tierney 1990) for creating graphical displays. For example, the chapter on data transformation discusses the use of dynamic plots for choosing power transformations. There is also a good discussion of the need for data transformations.

Part II deals with linear models and least squares. Two chapters are devoted to the mechanics of least squares fitting and inference. They are followed by a good chapter on dummy variables in regression, which naturally leads into a chapter on analysis of variance and analysis of covariance (done from a linear model perspective). Part II concludes with two optional chapters on linear models, the first focusing on the basics and the second on the vector geometry associated with linear models. The first of these requires some background in mathematical statistics. (A brief review is given in one of the appendixes.) The geometrical diagrams and interpretations provided by the author are some of the best I have seen for pedagogical purposes.

Part III delves into the diagnosis and treatment of model and data problems. The first chapter is on influential data and regressions diagnostics, one of my areas of research. The author is obviously knowledgeable and current in this area. The second chapter covers nonlinearity, nonconstant error variance, and nonnormality of errors. "Collinearity and Its Purported Remedies" is the title of the third chapter, which contains a nice discussion of the collinearity problem and proposed treatments.

Part IV is a grand tour of several topics related to regression analysis including time series regression, generalized least squares regression, nonlinear regression, robust regression, nonparametric regression, logistic regression, generalized linear models, bootstrapping, and cross-validation. The depth of coverage of these topics is sufficient to introduce the reader to these ideas and, one hopes, whet his or her appetite to investigate these topics further. Suggested references are provided for this purpose.

I found the book to be extremely well written. From a pedagogical viewpoint, the author's explanations are lucid and well thought out. Well-timed placement of summary boxes throughout the text help to remind the reader of important points covered in the material just read. The summary section at the end of each chapter is a good review of the highlights of the chapter. The recommended reading lists could have been more thorough in some of the chapters.

The book could be used in a variety of ways. The author provides recommendations for using it in one-semester and two-semester courses based on his previous experiences with the book in both formats. There is enough material for a one-semester applied regression course that could also explore some of the basics of linear models and/or current topics such as nonparametric regression (smoothing) and bootstrapping. There is not enough material for a one-semester course in linear models [compared to the one-semester treatment by Myers and Milton (1991), for example], but the introductory material on linear models is very well done. I particularly liked the optional chapter on the vector geometry of the linear model. Although the book is primarily intended for students and researchers in the social sciences, the presentation is general enough to appeal to a wider audience. The book does not give superficial treatment to its topics. The reader should come prepared with some background in elementary calculus, basic matrix algebra, and vector geometry, in addition to basic statistical methods. A summary of much of the prerequisite background knowledge is provided in the appendixes. The book is certainly suitable for self-study by someone with the appropriate background.

J. Brian GRAY

University of Alabama

REFERENCES

Cook. R. D., and Weisberg, S. (1994), An Introduction to Regression Graphics, New York: Wiley.

Myers, R. H., and Milton. J. S. (1991), A First Course in the Theory of Linear Statistical Models. Boston: PWS-Kent.

Neter. J. Kutner, M.H., Nachtsheim, C.J. and Wasserman, W. (1996). Applied Linear Statistical Models (4th ed.) Chicago: Irwin.

Tierney. L. (1990). Lisp-Stat: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics, New York: Wiley.