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Plane Answers to Complex Questions

The Theory of Linear Models

  • Ronald Christensen
Textbook
  • 1.2k Downloads

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

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Ronald Christensen
    Pages 1-20
  3. Ronald Christensen
    Pages 21-60
  4. Ronald Christensen
    Pages 61-105
  5. Ronald Christensen
    Pages 107-121
  6. Ronald Christensen
    Pages 123-143
  7. Ronald Christensen
    Pages 145-195
  8. Ronald Christensen
    Pages 197-240
  9. Ronald Christensen
    Pages 241-254
  10. Ronald Christensen
    Pages 255-279
  11. Ronald Christensen
    Pages 281-311
  12. Ronald Christensen
    Pages 313-339
  13. Ronald Christensen
    Pages 341-391
  14. Ronald Christensen
    Pages 393-417
  15. Ronald Christensen
    Pages 419-446
  16. Back Matter
    Pages 447-529

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: estimation including biased and Bayesian estimation, significance testing, ANOVA, 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: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.

Keywords

data analysis linear model theory linear models textbook estimation Bayes ANOVA regression analysis Gauss-Markov fifth edition heteroscedasticity

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-32097-3
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-32096-6
  • Online ISBN 978-3-030-32097-3
  • Series Print ISSN 1431-875X
  • Series Online ISSN 2197-4136
  • Buy this book on publisher's site