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Fitting of nonlinear regressions by orthogonalized power series
Author(s) -
Randić Milan
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540140311
Subject(s) - series (stratigraphy) , truncation (statistics) , mathematics , power series , nonlinear regression , multivariate statistics , nonlinear system , polynomial regression , regression analysis , linear regression , regression , bayesian multivariate linear regression , statistics , mathematical analysis , paleontology , physics , quantum mechanics , biology
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.