Plane Answers to Complex Questions

1. Front Matter

   Pages i-xix

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2. Introduction

   • Ronald Christensen

   Pages 1-17

3. Estimation

   • Ronald Christensen

   Pages 18-49

4. Testing Hypotheses

   • Ronald Christensen

   Pages 50-90

5. One-Way ANOVA

   • Ronald Christensen

   Pages 91-105

6. Multiple Comparison Techniques

   • Ronald Christensen

   Pages 106-121

7. Regression Analysis

   • Ronald Christensen

   Pages 122-155

8. Multifactor Analysis of Variance

   • Ronald Christensen

   Pages 156-195

9. Experimental Design Models

   • Ronald Christensen

   Pages 196-208

10. Analysis of Covariance

    • Ronald Christensen

    Pages 209-229

11. Estimation and Testing in General Gauss-Markov Models

    • Ronald Christensen

    Pages 230-253

12. Split Plot Models

    • Ronald Christensen

    Pages 254-278

13. Mixed Models and Variance Components

    • Ronald Christensen

    Pages 279-319

14. Checking Assumptions, Residuals, and Influential Observations

    • Ronald Christensen

    Pages 320-368

15. Variable Selection and Collinearity

    • Ronald Christensen

    Pages 369-390

16. Back Matter

    Pages 391-476

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The third edition of Plane Answers includes fundamental changes in how some aspects of the theory are handled. Chapter 1 includes a new section that introduces generalized linear models. Primarily, this provides a defini­ tion so as to allow comments on how aspects of linear model theory extend to generalized linear models. For years I have been unhappy with the concept of estimability. Just because you cannot get a linear unbiased estimate of something does not mean you cannot estimate it. For example, it is obvious how to estimate the ratio of two contrasts in an ANOVA, just estimate each one and take their ratio. The real issue is that if the model matrix X is not of full rank, the parameters are not identifiable. Section 2.1 now introduces the concept of identifiability and treats estimability as a special case of identifiability. This change also resulted in some minor changes in Section 2.2. In the second edition, Appendix F presented an alternative approach to dealing with linear parametric constraints. In this edition I have used the new approach in Section 3.3. I think that both the new approach and the old approach have virtues, so I have left a fair amount of the old approach intact. Chapter 8 contains a new section with a theoretical discussion of models for factorial treatment structures and the introduction of special models for homologous factors. This is closely related to the changes in Section 3.3.

• ANOVA
• Analysis
• Analysis of variance
• Factor analysis
• Regression analysis
• best fit
• mathematical statistics

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 Mathematics and Statistics, University of New Mexico, Albuquerque, USA

  Ronald Christensen

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