Linear Regression

  • David J.¬†Olive

Table of contents

  1. Front Matter
    Pages i-xiv
  2. David J. Olive
    Pages 1-15
  3. David J. Olive
    Pages 17-83
  4. David J. Olive
    Pages 85-162
  5. David J. Olive
    Pages 163-173
  6. David J. Olive
    Pages 175-211
  7. David J. Olive
    Pages 213-225
  8. David J. Olive
    Pages 227-244
  9. David J. Olive
    Pages 245-282
  10. David J. Olive
    Pages 283-297
  11. David J. Olive
    Pages 299-312
  12. David J. Olive
    Pages 313-342
  13. David J. Olive
    Pages 343-387
  14. David J. Olive
    Pages 389-458
  15. David J. Olive
    Pages 459-471
  16. Back Matter
    Pages 473-494

About this book

Introduction

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models.

This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics. 

Keywords

Regression Prediction Interval Bootstrap Confidence Region Experimental Design Variable Selection Multivariate Regression Response Transformation Generalized Linear Model

Authors and affiliations

  • David J.¬†Olive
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-55252-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-55250-7
  • Online ISBN 978-3-319-55252-1
  • About this book
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