Plane Answers to Complex Questions

The Theory of Linear Models

  • Ronald Christensen
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

  • Ronald Christensen
    • 1
  1. 1., Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

Bibliographic information

  • 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
  • Print ISBN 978-1-4419-9815-6
  • Online ISBN 978-1-4419-9816-3
  • Series Print ISSN 1431-875X
  • About this book