ABSTRACT
In Chapter 12, we introduced simple linear regression, which models a response variable as a straight line function of a single quantitative explanatory variable, or variate. In this chapter, we extend the concept to allow several variates in a multiple linear regression (MLR) model. This extension is analogous to the multi-factor model (Section 8.1) which investigates the simultaneous effects of several different qualitative variables, or factors, on the response. These extensions allow more realistic models, as usually several different explanatory variables might be associated with changes in the response, particularly in observational studies in which there is little or no control over the experimental conditions. In these circumstances, there can be strong correlation, or collinearity, between explanatory variates that can complicate the choice of which variates to include in a model. This chapter outlines the basic properties of MLR models and introduces methods for selection of explanatory variables.
