Multiple Linear Regression

Abstract Multiple regression analysis (MR) is a highly flexible system for examining the relationship of a collection of independent variables (or predictors) to a single dependent variable (or criterion). The independent variables may be quantitative (e.g., personality traits, family income) or categorical (e.g., ethnic group, treatment conditions in an experiment). The present chapter explores ordinary least‐squares regression with a continuous dependent variable. The chapter has two foci: (1) testing of theoretical predictions through multiple regression and (2) identification of problems with implementation of regression analysis, both from the perspectives of model specification and the data themselves. The structure of MR is described, including the regression equation, estimation of partial regression coefficients, measures of overall model fit, and the contribution of individual predictors and sets of predictors to prediction accuracy. The treatment of categorical predictors through effects, dummy, and contrast coding is explained. Polynomial regression for capturing curvilinear relationships is explored. The specification and testing of interactions between continuous variables and between a continuous and a categorical variable are explicated. Assumptions of MR and detection of violations are explained, as is the use of regression diagnostics to identify problematic cases. The chapter illustrates the interplay between theory and empirical findings in the specification, testing, and revision of regression models.