Introduction

This chapter introduces the concept of multiple regression, which in many ways is similar to bivariate regression. Both methods produce conditional predictions, though multiple regression employs more than one independent X variable to predict the value of the Y variable. Just as before, the predicted value of the dependent variable is expressed in a simple equation, and in the case of least squares regression the RMSE summarizes the likely size of the residual and the R2 statistic measures the fraction of total variation, which is explained by the regression. Once again, the OLS regression coefficients are those that minimize the SSR.

Multiple regression introduces some new issues, however. Some of the complications are purely mathematical. Although it is relatively easy to move back and forth between the algebraic expression and the pictorial (geometric) representation of the regression line in the bivariate case, most people have difficulty translating the algebraic formulation for a multiple regression into its geometric representation as a plane (in trivariate regression) or hyperplane (when there are more than two independent variables). Furthermore, the formulas for the OLS regression coefficients become very unwieldy (we discuss them in the appendix of this chapter).