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© 2011

Plane Answers to Complex Questions

The Theory of Linear Models

  • Updated version of a classic textbook in Statistics

  • Focus on Fisherian inference, rather than the previous blend of Fisherian and Neyman–Pearson inference

  • Illustrates the practical application of the projective approach to linear models

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Ronald Christensen
    Pages 1-16
  3. Ronald Christensen
    Pages 17-48
  4. Ronald Christensen
    Pages 49-90
  5. Ronald Christensen
    Pages 91-103
  6. Ronald Christensen
    Pages 105-119
  7. Ronald Christensen
    Pages 121-161
  8. Ronald Christensen
    Pages 163-201
  9. Ronald Christensen
    Pages 203-214
  10. Ronald Christensen
    Pages 215-236
  11. Ronald Christensen
    Pages 237-266
  12. Ronald Christensen
    Pages 267-290
  13. Ronald Christensen
    Pages 291-331
  14. Ronald Christensen
    Pages 333-379
  15. Ronald Christensen
    Pages 381-390
  16. Ronald Christensen
    Pages 391-409
  17. Back Matter
    Pages 411-494

About this book

Introduction

This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill’s generalization of Tukey’s one degree of freedom for nonadditivity test.

Keywords

data analysis linear model theory linear models textbook

Authors and affiliations

  1. 1., Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

About the authors

Ronald Christensen is Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, and former Chair of the ASA Section on Bayesian Statistical Science.

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
  • DOI https://doi.org/10.1007/978-1-4419-9816-3
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-9815-6
  • Softcover ISBN 978-1-4614-2885-5
  • eBook ISBN 978-1-4419-9816-3
  • Series ISSN 1431-875X
  • Edition Number 4
  • Number of Pages XXII, 494
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Statistical Theory and Methods
  • Buy this book on publisher's site
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Reviews

From the reviews of the fourth edition:

“Researchers and students interested in linear statistical models. … I admire Christensen’s very personal and somehow easy-going writing style. … All in all, Christensen’s fourth edition is an excellent course and reference book … .”­­­ (Simo Puntanen, International Statistical Review, Vol. 79 (3), 2011)