ABSTRACT
This chapter examines least squares estimation of multiple-variable prediction equations. Estimation of model parameters and summarization of the adequacy of the fit are discussed. Although computers are generally used to perform the calculations that are needed for multiple-variable regression analyses, it is instructive to examine the algebraic derivation and properties of the statistics that are used in the analyses. The benefits are twofold: the data analyst must understand the operations that the computer is undertaking and the output that it provides; and theoretical properties of the estimators and prediction equations are easily described with algebraic expressions. Regression analyses that utilize several predictor variables in the specification of a prediction equation are simultaneously more flexible and more complicated than those that incorporate a single predictor variable. Flexibility is introduced into the analysis by the investigator's ability to assess the influence on the response variable of several predictor variables, several different specifications of one predictor variable, or a combination of both.
