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Regression Analysis: Statistical Modeling of a Response Variable

Rudolf J. Freund, William J. Wilson, and Ping Sa
Academic Press
Publication Date: 
Number of Pages: 
Hardcover with CDROM
[Reviewed by
Huizhen Guo
, on

This book arrived when I was thinking of offering a course named "Applied Regression Model." While I went through the book, I kept in mind a question: would I use it as a text if I taught the course?

When I started reading, I decided I would not recommend it as a textbook. It doesn't say what prerequisites are needed for using this text. It seems students need to take "Mathematical Statistics" before taking this course (see the χ2 distribution on page 7).

After finishing Chapter one, I began to like the way the materials are presented (e.g., inferences on populations means are presented using sampling distribution and using a linear model as well). I decided I would recommended it as a reference book , since I felt it might be hard for students to read. (See the last line of page 10 and the first line of page 11.)

After reading the first three chapters and skimming rest of the chapters, I decided that I do like the book in general, and would like to try it as a text for my "Applied Regression Model" course.

The book consists of three parts. Part I covers the basic theory of simple and multiple linear regression models, assuming the data fit the model well. I especially like the sections on "Uses and Misuses of Regression" and "Inverse Predictions". Part II provides remedies for all kinds of problems that can happen when situations are not ideal. The good thing about this part is that the topics are classified as either problems with the data or problems with the model. Part III is an extension of regression models, dealing with problems which can be solved by regression. The structure makes both teaching and learning easier. I assume it is a text for one semester course. If there is not enough time to cover all the topics in part III, the instructors may choose some topics, or it can be used as references for both teachers and students.

At last I would like to mention some minor things:

  • The book is well manufactured; I don't need to worry about pages falling out.
  • The statistical software package SAS is used to perform the computations, and a reference for it is suggested.
  • I like the paragraph on page 10 which reviews the mechanism of hypothesis testing and the paragraph on page 11 which explains the variance of the error term in the linear model.
  • The space between words is too small at some points (see line 4 and 5 on page 66), making the text less legible, and too large at other points (line 6 on page 66).
  • What is the purpose of leaving a large margin on the left?
  • For upper level courses, I always prefer to use upper case letters for random variables and lower case ones for observed values. For example, X represents a random variable and x a fixed value. When the distinction is not made in text, it is harder to explain and to understand.
  • What is the purpose of mentioning "maximum likelihood" in chapter 1 (page 5 and page 9)? The usual s2 is not a maximum likelihood estimator of σ2, but we use it.
  • The central limit theorem is not needed to make inference on β1 (page 42) if we assume a normal distribution (page 37).
  • Variance is a statistical term and represents a fixed unknown value; how can it be minimized (line 14 and 34 on page 12)?
  • The graph doesn't match the description on page 107. (Typos are unavoidable in any publication, I guess. But this one jumps out.)

Huizhen Guo taught mathematics in a college in China for many years, taught "Elementary Statistics" as a graduate student, and taught "Elementary Statistics", "General Statistics", "Survey of Statistics", and "Mathematical Statistics" as a professor. These three teaching experiences were quite different, she says, so teaching is still a challenge. She is looking for good textbooks for the courses she is teaching now and will teach later.

 1. The Analysis of Means: A Review of Basics and an
Introduction to Linear Models
2. Simple Linear Regression:Linear Regression with
One Independent Variable
3. Multiple Regression
4. Problems with Observations
5. Multicollinearity
6. Problems with the Model
7. Curve Fitting
8. Introduction to Nonlinear Models
9. Indicator Variables
10. Categorical Response Variables
11. Generalized Linear Models
Appendix A: Statistical Tables
Appendix B: A Brief Introduction to Matrices
Appendix C: Estimation Procedures