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An introduction to computational statistics. Regression analysis. (English) Zbl 0833.62058

Englewood Cliffs, NJ: Prentice Hall. xvi, 364 p. (1995).
This interesting and useful book on regression is intended to provide a fully integrated development of the computational aspects of data analysis and traditional regression theory. The theme of this book is set in Chapter I where an overview of a typical regression program, the PROC REG program in the SAS system, is presented in detail. The author also includes in this chapter two other statistical systems, SPSS and BMDP, and points out the similarities between these well-known software systems. However, it is the SAS system used extensively in examples and exercises throughout each of the 9 chapters. An attractive feature of this book is to include in it diagnostic techniques to reveal inadequacies in the assumed regression model and possible departures of the collected data from the statistical assumptions made about it.
The simple linear regression model and its basic statistical properties are discussed in Chapter 2. It includes topics such as obtaining least squares estimates of the unknown parameters, prediction intervals, testing hypotheses and confidence intervals under assumptions on errors. Some potential problems in applying regression are also pointed out. In the next chapter the author addresses the problem of formulating an appropriate regression model for a given set of data, and presents numerous considerations useful in data analysis. These include the use of some mathematical transformations to linearize an assumed model, weighted regression, residual analysis, correlated errors, and a variety of remedial procedures to assess departures from assumptions. To extend a simple linear regression model to a multiple linear regression model is done in Chapter 4 which also includes a discussion of collinearity, leverage, and influence.
Chapter 5 is devoted to model building by using stepwise and best subset regression methods. It also includes a discussion of some criteria for evaluating the models produced. However, the author cautions the reader not to turn over blindly the model building task to the computer. In chapter 6 the mathematical theory of the General Linear Model is developed by using projections and finite dimensional vector spaces. The next chapter is concerned with analysis of variance and analysis of covariance procedures viewed as natural extensions of the regression theory. In this connection some material on transformations and model diagnostics is also presented.
Chapter 8 is set aside exclusively for a discussion on nonlinear regression models. After presenting an overview of a nonlinear regression program, the author takes up nonlinear least squares fitting. A specific algorithm, called Gauss-Newton algorithm, is detailed for producing nonlinear least squares estimates and the statistical properties of such estimates. Some of the problems encountered in fitting nonlinear models are illustrated by using growth curves. The last chapter 9 is concerned with robust estimation and maximum likelihood analysis, both using iteratively reweighted least squares. Also considered here in some detail are the log-linear models, exponential and generalized linear models.
A list of references is provided in appendix C, partial answers to selected problems in appendix B, and statistical tables in appendix A. There is also a symbol index, and a subject index. The background material needed is a strong and sound introductory statistics course with some knowledge of linear algebra. A salient feature of this book is the inclusion of several illustrative examples providing a good understanding of the problems faced in regression analysis. Every chapter ends with a set of useful problems for students and researchers to work on.
Computers are being extensively used in complex data analysis and are mostly within the reach of researchers and students alike. Modern statistical software is easy to understand and use. In view of this a substantial effort is devoted here to clarify the basic theory and concepts of regression analysis and much less to computing techniques. Furthermore, the use of computers is blended directly into the presentation and a discussion on how to use specific software forms an integral part of this book. As stated by the author, “…the reader …will appreciate the ubiquity of regression in statistical analysis and have an understanding of the theoretical and software tools needed to apply this very useful methodology.”
In the opinion of this reviewer, the author has succeeded in his mission. There are some minor errors in the book which can be easily detected and corrected. The material is presented in an easy-to-understand style, and the book should prove useful to researchers and students alike. It provides a clear view and good understanding of the problems faced by a researcher working with regression procedures. It is a welcome addition to the statistical literature, and highly recommended for all academic libraries serving students and researchers interested in data analysis.

MSC:

62Jxx Linear inference, regression
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
65C99 Probabilistic methods, stochastic differential equations
62-04 Software, source code, etc. for problems pertaining to statistics
62-07 Data analysis (statistics) (MSC2010)

Software:

SPSS; SAS; PROC REG; BMDP
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