# Plane Answers to Complex Questions

## The Theory of Linear Models

• RonaldÂ Christensen
Book

Part of the Springer Texts in Statistics book series (STS)

1. Front Matter
Pages i-xiv
2. Ronald Christensen
Pages 1-13
3. Ronald Christensen
Pages 14-28
4. Ronald Christensen
Pages 29-56
5. Ronald Christensen
Pages 57-69
6. Ronald Christensen
Pages 70-84
7. Ronald Christensen
Pages 85-112
8. Ronald Christensen
Pages 113-150
9. Ronald Christensen
Pages 151-159
10. Ronald Christensen
Pages 160-178
11. Ronald Christensen
Pages 179-200
12. Ronald Christensen
Pages 201-222
13. Ronald Christensen
Pages 223-243
14. Ronald Christensen
Pages 244-281
15. Ronald Christensen
Pages 282-301
16. Ronald Christensen
Pages 302-323
17. Back Matter
Pages 324-380

### Introduction

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 subÂ­ 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.

### Keywords

Excel Likelihood data analysis linear model theory linear models

#### Authors and affiliations

• RonaldÂ Christensen
• 1
1. 1.Department of Mathematical SciencesMontana State UniversityBozemanUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-1951-2
• Copyright Information Springer-Verlag New York 1987
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-1953-6
• Online ISBN 978-1-4757-1951-2
• Series Print ISSN 1431-875X