A Brief Introduction
This book deals with a class of models that pertain to data consisting of the values of p + 1 variables y, x1, x2, …, xp taken on each of n “observational units.” We refer to y as the response variable (regardless of whether it actually makes sense to thi
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Linear Model Theory
With Examples and Exercises
Linear Model Theory
Dale L. Zimmerman
Linear Model Theory With Examples and Exercises
Dale L. Zimmerman Department of Statistics and Actuarial Science University of Iowa Iowa City, IA, USA
ISBN 978-3-030-52062-5 ISBN 978-3-030-52063-2 (eBook) https://doi.org/10.1007/978-3-030-52063-2 Mathematics Subject Classification: 62J05, 62J10, 62F03, 62F10, 62F25 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my wife, Bridget, and our children, Nathan, Joshua, Bethany, Anna, and Abby
Preface
Several excellent books exist on the theory of linear models (I won’t list them here, for fear of omitting someone’s favorite!). So why did I write another one? Primarily for two reasons. First, while the existing books do a fine job (imho) of presenting a broad range of appropriate content, they tend to be too light on examples and exercises for many students to become proficient at obtaining concrete results for specific linear models. For example, a student who has taken a linear models course using an existing book undoubtedly can tell you that the best linear unbiased estimator (BLUE) of an estimable function cT β, under a linear model y = Xβ + e ˆ where βˆ is any solution to with Gauss–Markov assumptions on the errors, is cT β, T T the equations X Xβ = X y; but in my experience, that student will often struggle to use that knowledge to obtain a simplified expression for, say, the BLUE of a factor-level difference in a two-way main effects model. Second, it has long been my view [see, for example, Zimmerman (2014)] that existing linear models texts give relatively too much attention to estimation and hypothes
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