Plane Answers to Complex Questions

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • Ronald Christensen

   Pages 1-15

3. Estimation

   • Ronald Christensen

   Pages 16-44

4. Testing Hypotheses

   • Ronald Christensen

   Pages 45-78

5. One-Way ANOVA

   • Ronald Christensen

   Pages 79-93

6. Multiple Comparison Techniques

   • Ronald Christensen

   Pages 94-109

7. Regression Analysis

   • Ronald Christensen

   Pages 110-142

8. Multifactor Analysis of Variance

   • Ronald Christensen

   Pages 143-182

9. Experimental Design Models

   • Ronald Christensen

   Pages 183-192

10. Analysis of Covariance

    • Ronald Christensen

    Pages 193-212

11. Estimation and Testing in General Gauss-Markov Models

    • Ronald Christensen

    Pages 213-236

12. Split Plot Models

    • Ronald Christensen

    Pages 237-261

13. Mixed Models and Variance Components

    • Ronald Christensen

    Pages 262-302

14. Checking Assumptions, Residuals, and Influential Observations

    • Ronald Christensen

    Pages 303-351

15. Variable Selection and Collinearity

    • Ronald Christensen

    Pages 352-373

16. Back Matter

    Pages 374-453

    PDF

The second edition of Plane Answers has many additions and a couple of deletions. New material includes additional illustrative examples in Ap­ pendices A and B and Chapters 2 and 3, as well as discussions of Bayesian estimation, near replicate lack of fit tests, testing the independence assump­ tion, testing variance components, the interblock analysis for balanced in­ complete block designs, nonestimable constraints, analysis of unreplicated experiments using normal plots, tensors, and properties of Kronecker prod­ ucts and Vee operators. The book contains an improved discussion of the relation between ANOVA and regression, and an improved presentation of general Gauss-Markov models. The primary material that has been deleted are the discussions of weighted means and of log-linear models. The mate­ rial on log-linear models was included in Christensen (1990b), so it became redundant here. Generally, I have tried to clean up the presentation of ideas wherever it seemed obscure to me. Much of the work on the second edition was done while on sabbatical at the University of Canterbury in Christchurch, New Zealand. I would par­ ticularly like to thank John Deely for arranging my sabbatical. Through their comments and criticisms, four people were particularly helpful in con­ structing this new edition. I would like to thank Wes Johnson, Snehalata Huzurbazar, Ron Butler, and Vance Berger.

• ANOVA
• Regression analysis
• analysis of variance
• data analysis
• linear model theory
• linear models
• textbook

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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