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3 - Multiple Linear Regression

Published online by Cambridge University Press:  11 May 2024

John H. Maindonald
Affiliation:
Statistics Research Associates, Wellington, New Zealand
W. John Braun
Affiliation:
University of British Columbia, Okanagan
Jeffrey L. Andrews
Affiliation:
University of British Columbia, Okanagan
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Summary

Multiple linear regression generalizes straight line regression to allow multiple explanatory (or predictor) variables, in this chapter under the normal errors assumption. The focus may be on accurate prediction. Or it may, alternatively or additionally, be on the regression coefficients themselves. Simplistic interpretations of coefficients can be grossly misleading. Later chapters elaborate on the ideas and methods developed in this chapter, applying them in new contexts. The attaching of causal interpretations to model coefficients must be justified both by reference to subject area knowledge and by careful checks to ensure that they are not artefacts of the correlation structure. There is attention to regression diagnostics, to assessment, and comparison of models. Variable selection strategies can readily over-fit. Hence the importance of training/test approaches and cross-validation. The potential is demonstrated for errors in x to seriously bias regression coefficients. Strong multicollinearity leads to large variance inflation factors.

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A Practical Guide to Data Analysis Using R
An Example-Based Approach
, pp. 144 - 207
Publisher: Cambridge University Press
Print publication year: 2024

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