Plane Answers to Complex Questions
The Theory of Linear Models
Authors: Christensen, Ronald
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 About this Textbook

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.
 Reviews

From the reviews of the third edition:
"This wellwritten and interesting book can serve as a textbook for a graduatelevel 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 deemphasized and the text leans more towards wellprepared 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 mustread 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 projectionbased dogma and its thoughtprovoking conversational prose. It continues to serve as an authoritative, wellwritten, 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 deemphasized and the text leans more towards wellprepared 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 firstyear 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)
 Table of contents (14 chapters)


Introduction
Pages 117

Estimation
Pages 1849

Testing Hypotheses
Pages 5090

OneWay ANOVA
Pages 91105

Multiple Comparison Techniques
Pages 106121

Table of contents (14 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Plane Answers to Complex Questions
 Book Subtitle
 The Theory of Linear Models
 Authors

 Ronald Christensen
 Series Title
 Springer Texts in Statistics
 Copyright
 2002
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9780387215440
 DOI
 10.1007/9780387215440
 Softcover ISBN
 9781441929716
 Series ISSN
 1431875X
 Edition Number
 3
 Number of Pages
 XIX, 476
 Number of Illustrations
 1 b/w illustrations
 Topics