Inverse Polynomials, a Useful Group of Multi-Factor Response Functions

Abstract

If x1, X2, . . . , xk represent the levels of k experimental factors, and y''the yield, then inverse polynomials are defined by the relation [image] Polynomial in (x1; x2, . . .,xk). Methods are given for fitting inverse polynomial surfaces with and without unknown origins for the x1. For the latter case fitting is shown to be as easy as for ordinary polynomials, over which inverse polynomials are shown to have theoretical and empirical advantages.