Non-linear least-squares fitting with microsoft excel solver and related routines in HPLC modelling of retention |
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Authors: | P Nikitas A Pappa-Louisi |
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Institution: | (1) Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece |
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Abstract: | Summary 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. |
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Keywords: | Column liquid chromatography Non-linear least squares routines Standard errors in fitting parameters Jacknife technique Monte Carlo simulations |
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