Figure 1: The results of multiple linear regression depend on the correlation of the predictors, as measured here by the Pearson correlation coefficient r (ref. 2).

Multiple regression equations designed to explain or predict should be validated. This tutorial shows how recalculation of the coefficient of determination on hold-out sample data or new sample data ...

An algorithm is developed for the simultaneous optimization of several response functions that depend on the same set of controllable variables and are adequately represented by polynomial regression ...