Non-linear least-squares fitting with microsoft excel solver and related routines in HPLC modelling of retention

Abstract

Two problems related to non-linear regression, the evaluation of the best set of fitting parameters and the reliability of the methods used for the estimation of the standard errors of these parameters, are examined. It is shown that a non-linear curve fitting routine, like the Microsoft Excel Solver, may give more than one solution for the same data set and a simple Monte Carlo routine is described for the evaluation of the bestfit. For standard errors, the reliability of two procedures based on the conventional curvature matrix method, four Jackknife techniques and the bootstrap method are examined by comparing their results to those obtained from a Monte Carlo simulation of the experimental data. It is shown that a fitting parameter may follow a nonnormal distribution when the equation to be fitted is complicated, even if the errors on the data are normally distributed. In this case only Monte Carlo methods of data simulation can give accurate information about the standard errors and the confidence intervals of these parameters.