Linear Regression

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • David J. Olive

   Pages 1-15

3. Multiple Linear Regression

   • David J. Olive

   Pages 17-83

4. Building an MLR Model

   • David J. Olive

   Pages 85-162

5. WLS and Generalized Least Squares

   • David J. Olive

   Pages 163-173

6. One Way Anova

   • David J. Olive

   Pages 175-211

7. The K Way Anova Model

   • David J. Olive

   Pages 213-225

8. Block Designs

   • David J. Olive

   Pages 227-244

9. Orthogonal Designs

   • David J. Olive

   Pages 245-282

10. More on Experimental Designs

    • David J. Olive

    Pages 283-297

11. Multivariate Models

    • David J. Olive

    Pages 299-312

12. Theory for Linear Models

    • David J. Olive

    Pages 313-342

13. Multivariate Linear Regression

    • David J. Olive

    Pages 343-387

14. GLMs and GAMs

    • David J. Olive

    Pages 389-458

15. Stuff for Students

    • David J. Olive

    Pages 459-471

16. Back Matter

    Pages 473-494

    PDF

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.

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

“Very nice features of the book are the many practical hints and discussion on how to do model building, the various rules of thumb, the summaries and exercises. … I think that the book will turn out helpful in particular for people interested in modeling aspects of linear regression with some mathematical background.” (Alexander Lindner, zbMath 1417.62002, 2019)

• Department of Mathematics, Southern Illinois University, Carbondale, USA

  David J. Olive

David Olive is a Professor at Southern Illinois University, Carbondale, IL, USA.  His research interests include the development of computationally practical robust multivariate location and dispersion estimators, robust multiple linear regression estimators, and resistant dimension reduction estimators.

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