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1 Downloaded by [University of Toronto] at 16:20 23 May 2014. CHAPMAN & HALL/CRC. Texts in Statistical Science Series Series Editors Chris Chatfield, University of Bath, UK. Martin Tanner, Northwestern University, USA. Jim Zidek, University of British Columbia, Canada Downloaded by [University of Toronto] at 16:20 23 May 2014. Analysis of Failure and Survival Data Peter The Analysis and Interpretation of Multivariate Data for Social Scientists David , Fiona Steele, Irini Moustaki, and Jane Galbraith The Analysis of Time Series An Introduction, Sixth Edition Chris Chatfield Applied Bayesian Forecasting and Time Series Analysis , and Applied Nonparametric Statistical Methods, Third Edition and Applied Statistics Handbook of GENSTAT Analysis and Applied Statistics Principles and Examples and Bayes and Empirical Bayes Methods for Data Analysis, Second Edition Bradley and Thomas Bayesian Data Analysis, Second Edition Andrew Gelman, John , Hal , and Donald Beyond ANOVA Basics of Applied Statistics , Jr.

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4 Statistics for Accountants Statistics for Epidemiology Nicholas Statistics for Technology A Course in Applied Statistics, Third Edition Statistics in Engineering A Practical Approach Statistics in Research and Development, Second Edition Survival Analysis Using S Analysis of Time-to-Event Data Mara Tableman and Jong Sung Kim The Theory of Linear Models rgensen Linear Models with R. Julian Texts in Statistical Science Linear Models with R. Downloaded by [University of Toronto] at 16:20 23 May 2014. Julian CHAPMAN & HALL/CRC. A CRC Press Company Boca Raton London NewYork Washington, This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge's collection of thousands of eBooks please go to Library of Congress Cataloging-in-Publication Data Faraway, Julian James.

5 Linear models with R/Julian p. cm. (Chapman & Hall/CRC texts in statistical science series; v. 63). Includes bibliographical references and index. ISBN 1-58488-425-8 (alk. paper). Downloaded by [University of Toronto] at 16:20 23 May 2014. 1. Analysis of variance. 2. Regression analysis. I. Title. II. Texts in statistical science;. v. 63. 2004. '38 dc22 2004051916. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher.

6 The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC. Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at 2005 by Chapman & Hall/CRC. No claim to original Government works ISBN 0-203-50727-4 Master e-book ISBN. ISBN 0-203-59454-1 (Adobe ebook Reader Format). International Standard Book Number 1-58488-425-8. Library of Congress Card Number 2004051916. Contents Preface xi 1 Introduction 1. Before You Start 1. Downloaded by [University of Toronto] at 16:20 23 May 2014.

7 Initial Data Analysis 2. When to Use Regression Analysis 7. History 7. 2 estimation 12. Linear Model 12. Matrix Representation 13. Estimating ! 13. Least Squares estimation 14. Examples of Calculating 16. Gauss Markov Theorem 17. Goodness of Fit 18. Example 20. Identifiability 23. 3 Inference 28. Hypothesis Tests to Compare Models 28. Testing Examples 30. Permutation Tests 36. Confidence Intervals for ! 38. Confidence Intervals for Predictions 41. Designed Experiments 44. Observational Data 48. Practical Difficulties 53. 4 Diagnostics 58. Checking Error Assumptions 58. Finding Unusual Observations 69. Checking the Structure of the Model 78. viii Contents 5 Problems with the Predictors 83. Errors in the Predictors 83. Changes of Scale 88. Collinearity 89. 6 Problems with the Error 96. Generalized Least Squares 96. weighted Least Squares 99.

8 Downloaded by [University of Toronto] at 16:20 23 May 2014. Testing for Lack of Fit 102. Robust Regression 106. 7 Transformation 117. Transforming the Response 117. Transforming the Predictors 120. 8 Variable Selection 130. Hierarchical Models 130. Testing-Based Procedures 131. Criterion-Based Procedures 134. Summary 139. 9 Shrinkage Methods 142. Principal Components 142. Partial Least Squares 150. Ridge Regression 152. 10 Statistical Strategy and Model Uncertainty 157. Strategy 157. An Experiment in Model Building 158. Discussion 159. 11 Insurance Redlining A Complete Example 161. Ecological Correlation 161. Initial Data Analysis 163. Initial Model and Diagnostics 165. Transformation and Variable Selection 168. Discussion 171. 12 missing Data 173. Contents ix 13 Analysis of Covariance 177. A Two-Level Example 178. Coding Qualitative Predictors 182.

9 A Multilevel Factor Example 184. 14 One-Way Analysis of Variance 191. The Model 191. An Example 192. Diagnostics 195. Downloaded by [University of Toronto] at 16:20 23 May 2014. Pairwise Comparisons 196. 15 Factorial Designs 199. Two-Way ANOVA 199. Two-Way ANOVA with One Observation per Cell 200. Two-Way ANOVA with More than One Observation per Cell 203. Larger Factorial Experiments 207. 16 Block Designs 213. Randomized Block Design 213. Latin Squares 218. Balanced Incomplete Block Design 222. A R Installation, Functions and Data 227. B Quick Introduction to R 229. Reading the Data In 229. Numerical Summaries 229. Graphical Summaries 230. Selecting Subsets of the Data 231. Learning More about R 232. Bibliography 233. Index 237. Downloaded by [University of Toronto] at 16:20 23 May 2014. Preface There are many books on regression and analysis of variance.

10 These books expect different levels of preparedness and place different emphases on the material. This book is not introductory. It presumes some knowledge of basic statistical theory and practice. Readers are expected to know the essentials of statistical inference such as estimation , hypothesis testing and confidence intervals. A basic knowledge of data analysis is presumed. Some linear algebra and calculus are also required. The emphasis of this text is on the practice of regression and analysis of variance. The Downloaded by [University of Toronto] at 16:20 23 May 2014. objective is to learn what methods are available and more importantly, when they should be applied. Many examples are presented to clarify the use of the techniques and to demonstrate what conclusions can be made. There is relatively less emphasis on mathematical theory, partly because some prior knowledge is assumed and partly because the issues are better tackled elsewhere.