Plane Answers to Complex Questions

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Ronald Christensen

   Pages 1-13

3. Estimation

   • Ronald Christensen

   Pages 14-28

4. Testing Hypotheses

   • Ronald Christensen

   Pages 29-56

5. One-Way ANOVA

   • Ronald Christensen

   Pages 57-69

6. Multiple Comparison Techniques

   • Ronald Christensen

   Pages 70-84

7. Regression Analysis

   • Ronald Christensen

   Pages 85-112

8. Multifactor Analysis of Variance

   • Ronald Christensen

   Pages 113-150

9. Experimental Design Models

   • Ronald Christensen

   Pages 151-159

10. Analysis of Covariance

    • Ronald Christensen

    Pages 160-178

11. Estimation and Testing in a General Gauss-Markov Model

    • Ronald Christensen

    Pages 179-200

12. Split Plot Models

    • Ronald Christensen

    Pages 201-222

13. Mixed Models and Variance Components

    • Ronald Christensen

    Pages 223-243

14. The Analysis of Residuals and Influential Observations in Regression

    • Ronald Christensen

    Pages 244-281

15. Additional Topics in Regression: Variable Selection and Collinearity

    • Ronald Christensen

    Pages 282-301

16. Maximum Likelihood Theory for Log-Linear Models

    • Ronald Christensen

    Pages 302-323

17. Back Matter

    Pages 324-380

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This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub­ spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems frequently become clearer when considered free of coordinate systems, my experience is that too many people never make the jump from coordinate free theory back to practical applications. I think that coordinate free theory is better tackled after mastering linear models from some other approach. In particular, I think it would be very easy to pick up the coordinate free approach after learning the material in this book. See Eaton (1983) for an excellent exposition of the coordinate free approach.

• Excel
• Likelihood
• data analysis
• linear model theory
• linear models

From the reviews of the third edition:

"This well-written and interesting book can serve as a textbook for a graduate-level course in linear model theory and its applications, and as a reference book for a wide range of definitions and results associated with particular linear models." Journal of the American Statistical Assoc.

"The following quotations are taken from the (same) reviewer's comments on the second edition (Short Book Reviews, Vol.17/1, April 1997, p.4): The book "retains its fairly mathematical character... The writing style is inviting... friendly and affable... The computing aspects of regression are de-emphasized and the text leans more towards well-prepared students." All are still true, and I once again recommend the book for the indicated target audience." ISI Short Book Reviews, Vol. 22/3, 2002

"This book with the unusual title has been quite popular because of its lucid treatment. What I like most about the book is that many important observations have been made in an entertaining manner. … In this edition the idea of identifiability has rightly been given more emphasis than estimability, which sets this book apart from most other books on linear models. … I have always regarded this book as a must-read for serious users of linear models. The third edition makes it even better.” (Debasis Sengupta, Sankhya, Vol. 65 (4), 2003)

"This is the third edition of a popular textbook in general linear models aimed at graduate students. … The appealing features of this book lie in its projection-based dogma and its thought-provoking conversational prose. It continues to serve as an authoritative, well-written, polished linear models text that is useful both as a reference and as a graduate course text." (Robert Lund, Journal of the American Statistical Association, Vol. 98 (463), September, 2003)

"The book ‘retains its fairly mathematical character. The writing style is inviting,friendly and affable. The computing aspects of regression are de-emphasized and the text leans more towards well-prepared students.’ All are still true, and I once again recommend the book for the indicated target audience." (N. R. Draper, Short Book Reviews, Vol. 22 (3), 2002)

"This 3rd edition, like the preceding editions, illustrates the practical applications of projective approach to linear models. … elegant treatment of identifiability and estimability and their connection. … Excellent examples are used to illustrate the effect of high leverage. … The intended audience for this book appears to be first-year graduate students. … I feel that Plane Answers to Complex Questions is a nice addition to the literature on linear models. … excellent references for practitioners." (Felix Famoye, Technometrics, Vol. 45 (2), May, 2003)

• Department of Mathematical Sciences, Montana State University, Bozeman, USA

  Ronald Christensen

Policies and ethics