Continuum Regression: Cross-Validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression

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.