The Racing Car Problem

An approach to teaching linear regression with unbalanced data is outlined that emphasizes its role as a method of adjustment for associated regressors. The method is introduced via direct standardization, a simple form of regression for categorical regressors. Properties of regression in the presence of association and interaction are emphasized. Least squares is introduced as a more efficient way of calculating adjusted effects for which exact decompositions of the variance are possible. Interval-scaled regressors are initially grouped and treated as categorical; polynomial regression and analysis of covariance can be introduced later as alternative methods.