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SUMMARY The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable ‘parameters’ controlling the procedure: ‘alpha’, in the continuum 0, 1, and ‘omega’, the number of regressors finally accepted. These control parameters are chosen by cross-validation. The method is illustrated by a range of examples of its application.
Stone et al. (Mon,) studied this question.