Standard Article

Multiple Linear Regression

  1. David E. Matthews

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a09033

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Matthews, D. E. 2005. Multiple Linear Regression. Encyclopedia of Biostatistics. 5.

Author Information

  1. University of Waterloo, Waterloo, Ontario, Canada

Publication History

  1. Published Online: 15 JUL 2005


Multiple linear regression involves finding the best-fitting surface of a suitable functional form that relates the values of explanatory variables, X1, …, Xk, and the mean value of a response variable, Y, given values of X1, …, Xk. The objectives of regression modeling are to determine whether Y and one or more of the explanatory variables are associated in some systematic way, and to estimate or predict the value of Y, or its mean, corresponding to known values of a selected subset of X1, …, Xk. We describe methods of estimation, variable selection, statistical inference, and diagnostic checking of the assumed model and any associated unknown parameters, giving due importance to their statistical and scientific interpretations. An example concerning the relationship between oxygen uptake and age, weight, sex, the time required to run 1.5 miles, and various pulse rates for participants in a physical fitness workshop illustrates these concepts concretely. Finally, we outline the close connection between ordinary and weighted linear regression.


  • least squares estimation;
  • multiple linear regression model;
  • weighted regression