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Regression: Linear Models in Statistics

N. H. Bingham and John M. Fry
Publication Date: 
Number of Pages: 
Springer Undergraduate Mathematics Series
[Reviewed by
Susan D'Agostino
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As the authors state in their summary of the book, “linear regression is a branch of statistics in which a dependent variable of interest is modeled as a linear combination of one or more predictor variables, together with a random error.” A simple linear regression problem may be modeled in two dimensions whereas multiple linear regression problems may be modeled in three or more dimensions. Introductory undergraduate courses in statistics typically provide a brief introduction to regression analysis; the present book is intended for a second undergraduate or beginning graduate course in statistics providing further study of this single topic.

Regression: Linear Models in Statistics has numerous strengths. Complete, mathematically rigorous proofs are routinely provided for theorems. The fully-worked examples and solutions to the exercises are detailed. The conversational language that surrounds the technical details succeeds in making the text highly readable. In particular, the numerous “notes” that often follow the theorems, proofs and examples make the reader feel as if a helpful teacher who is interested in providing a context is standing close by. After addressing the requisite topics in regression analysis — linear regression, analysis of variance, multiple regression, analysis of covariance, linear hypotheses and models — the reader is treated to some additional topics, including nonparametric regression and experimental design.

Future editions of the text could be enhanced by additional problem sets with a larger number of problems in each set. The exercise sets are currently restricted to the end of each chapter, for a sum total of eight problem sets. Moreover, each problem set includes only ten to twelve problems. Also, while there are obvious advantages to the fully-worked solutions provided for every exercise, the addition of some problems without fully-worked solutions might encourage students to wrestle for just a little longer with those problems that present particular challenges.

Students from disciplines outside of mathematics who are interested in applying statistical methods to their own disciplines may find the text wanting because of the lack of numerous, real-data based examples, case studies and statistical software output files. On the other hand, Linear Regression: Linear Models in Statistics is highly suitable for a theoretical statistics course for advanced undergraduate math majors, beginning math graduate students or others interested in using the book for independent study.

Susan D’Agostino is an Assistant Professor of Mathematics at Southern New Hampshire University. She has written articles for The Chronicle of Higher Education, MAA Focus and Math Horizons. She is currently writing a book with mathematical themes intended for an audience of nonmathematicians.

Linear Regression.- The Analysis of Variance (ANOVA).- Multiple Regression.- Further Multilinear Regression.- Analysis of Covariance.- Linear Hypotheses.- Model Checking and Transformation of Data.- Generalized linear models.- Solutions.