3. Multiple Linear Regression

  1. Bee Choo Tai1 and
  2. David Machin2

Published Online: 11 OCT 2013

DOI: 10.1002/9781118721957.ch3

Regression Methods for Medical Research

Regression Methods for Medical Research

How to Cite

Tai, B. C. and Machin, D. (2013) Multiple Linear Regression, in Regression Methods for Medical Research, John Wiley & Sons Ltd, Oxford. doi: 10.1002/9781118721957.ch3

Author Information

  1. 1

    Saw Swee Hock School of Public Health, National University of Singapore and National University Health System; Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore

  2. 2

    Medical Statistics Unit, School of Health and Related Sciences, University of Sheffield; Cancer Studies, Faculty of Medicine, University of Leicester, Leicester, UK

Publication History

  1. Published Online: 11 OCT 2013
  2. Published Print: 29 NOV 2013

ISBN Information

Print ISBN: 9781444331448

Online ISBN: 9781118721957



  • 2-covariate model;
  • collinearity;
  • covariates;
  • multiple linear regression;
  • parsimonious model;
  • quadratic models


This chapter extends the simple linear regression model to the situation where two or more covariates are necessary to describe the study design and the consequent analysis. In particular the authors depict models that may be appropriate for non-linear situations and those that allow for the possible influence of the interaction between two covariates. The chapter describes how these models are fitted and whether they may or may not be regarded as providing an adequate description of the data. It stresses the desirability of using parsimonious (those with few covariates and a simple structure) models to describe the essence of the study results. The authors emphasize that simple models can best be compared with more complex ones if they are nested within them. Problems associated with collinearity of covariates are detailed.