Multiple Regression
We saw in Chapter 1 how the model $${y}_{i} = a + b{x}_{i} + {\epsilon }_{i},\qquad {\epsilon }_{i}\quad \mbox{ iid}\quad N(0,{\sigma }^{2})$$for simple linear regression occurs. We saw also that we may need to consider two or more regressors. We dealt wi
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N.H. Bingham
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John M. Fry
Regression Linear Models in Statistics
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N.H. Bingham Imperial College, London UK [email protected]
John M. Fry University of East London UK [email protected]
Springer Undergraduate Mathematics Series ISSN 1615-2085 ISBN 978-1-84882-968-8 e-ISBN 978-1-84882-969-5 DOI 10.1007/978-1-84882-969-5 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010935297 Mathematics Subject Classification (2010): 62J05, 62J10, 62J12, 97K70 c Springer-Verlag London Limited 2010 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: Deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To James, Ruth and Tom Nick
To my parents Ingrid Fry and Martyn Fry John
Preface
The subject of regression, or of the linear model, is central to the subject of statistics. It concerns what can be said about some quantity of interest, which we may not be able to measure, starting from information about one or more other quantities, in which we may not be interested but which we can measure. We model our variable of interest as a linear combination of these variables (called covariates), together with some error. It turns out that this simple prescription is very flexible, very powerful and useful. If only because regression is inherently a subject in two or more dimensions, it is not the first topic one studies in statistics. So this book should not be the first book in statistics that the student uses. That said, the statistical prerequisites we assume are modest, and will be covered by any first course on the subject: ideas of sample, population, variation and randomness; the basics of parameter estimation, hypothesis testing, p–values, confidence intervals etc.; the standard distributions and their uses (normal, Student t, Fisher F and chisquare – though we develop what we need of F and chi-s
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