When stepwise regression fails: correlated variables some of which are redundant

Climatological data are presented which illustrate the counter‐intuitive phenomenon that Y can be almost uncorrelated with x 1 and with x 2, while at the same time the multiple correlation of Y with x 1 and x 2, considered jointly, is close to 1. Principal component theory is used to unearth the root of the problem. Stepwise regression can uncover the joint dependence of Yon x 1 and x 2 if it is started with the full model. However, in an expanded version of the example, this procedure is shown to select a model that is at odds with established climatological theory. These findings can be used to demonstrate the importance of both restricting multicollinearity and including subject‐matter theory in model building.