Fitting of nonlinear regressions by orthogonalized power series
Milan Randić · Journal of Computational Chemistry · 1993
Abstract We outline a procedure that resolves ambiguities in fitting nonlinear data by power series. As is well known, the coefficients in the regression equations depend upon the truncation of the power series. We outline the procedure in which the coefficients of the regression using a power expansion are independent of the degree of the polynomials used. This is achieved by considering mutual regression of descriptors and using residuals as novel variables. The derived regression equations show unusual numerical stability, i.e., the coefficients of the regression equations are constant and independent of the truncation of the power series. The process is illustrated in an example to show all details and facilitate duplicating the process for interested readers. The method described here complements recently outlined procedures for construction of orthogonal descriptors for use in multivariate regression analysis. © 1993 John Wiley & Sons, Inc.