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Linear Models and Design

  • Textbook
  • © 2022

Overview

Authors:
  1. Jay H. Beder

    1. University of Wisconsin–Milwaukee, Milwaukee, USA

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  • Guides students using a carefully paced exposition of the theory underlying linear models and experimental design
  • Provides a resource for researchers seeking a thorough mathematical treatment of the foundations of the subject
  • Offers a fresh perspective on the concepts, history and development of linear model theory and experimental design

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Linear Models

    • Jay H. Beder
    Pages 1-26

  3. Effects in a Factorial Experiment

    • Jay H. Beder
    Pages 27-60

  4. Estimation

    • Jay H. Beder
    Pages 61-78

  5. Testing

    • Jay H. Beder
    Pages 79-150

  6. Multifactor Designs

    • Jay H. Beder
    Pages 151-217

  7. Fractional Factorial Designs

    • Jay H. Beder
    Pages 219-289

  8. Back Matter

    Pages 291-343
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Keywords

About this book

This book is designed as a textbook for graduate students and as a resource for researchers seeking a thorough mathematical treatment of its subject. It develops the main results of regression and the analysis of variance, as well as the central results on confounded and fractional factorial experiments. Matrix theory is deemphasized; its role is taken instead by the theory of linear transformations between vector spaces.

The text gives a carefully paced and unified presentation of two topics, linear models and experimental design. Students are assumed to have a solid background in linear algebra, basic knowledge of regression and analysis of variance, and some exposure to experimental design, and should be comfortable with reading and constructing mathematical proofs.

The book leads students into the mathematical theory, including many examples both for motivation and for illustration. Over 130 exercises of varying difficulty are included. An extensive mathematical appendix and a detailed index make the text especially accessible.

Linear Models and Design can serve as a textbook for a year-long course in the topics covered, or for a one-semester course in either linear model theory or experimental design. It prepares students for more advanced topics in the field, and assists in developing a thoughtful approach to the existing literature. It includes a guide to terminology as well as discussion of the history and development of ideas, and offers a fresh perspective on the fundamental concepts and results of the subject.

Authors and Affiliations

  • University of Wisconsin–Milwaukee, Milwaukee, USA

    Jay H. Beder

About the author

​Jay H. Beder is Professor Emeritus in the Department of Mathematical Sciences at the University of Wisconsin – Milwaukee.  He has published papers in statistical design theory as well as on inference for Gaussian processes, with applications to evolutionary biology.  He has taught courses in linear models, design, and combinatorics for over 30 years, and is the recipient of teaching awards from his college and his university.

Bibliographic Information

  • Book Title: Linear Models and Design

  • Authors: Jay H. Beder

  • DOI: https://doi.org/10.1007/978-3-031-08176-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-08175-0Published: 16 November 2022

  • Softcover ISBN: 978-3-031-08178-1Published: 17 November 2023

  • eBook ISBN: 978-3-031-08176-7Published: 14 November 2022

  • Edition Number: 1

  • Number of Pages: XXI, 343

  • Number of Illustrations: 15 b/w illustrations

  • Topics: Statistical Theory and Methods, Biostatistics

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