The use of relative residues in non-linear regression

Abstract

A non-linear curve-fitting model is presented which minimizes the sum of squares of relative residues, and expressions are derived for the fit parameters and their respective errors. A detailed comparison is made between the new general relative least squares model (GRLS) and other non-linear regression models available in the literature, using two sets of data representing fluid mechanics problems encountered in many engineering applications. The results showed that GRLS was the best model for fitting non-linear functions in the case of experimental data spanning several orders of magnitude, indicating its potential as a tool for data analysis.