21] Regression analysis, experimental error, and statistical criteria in the design and analysis of experiments for discrimination between rival kinetic models

Abstract

The fitting of rate equations to kinetic data in enzymology is an application of the treatment of experimental data in general and the use of mathematical models for quantitative description. By using statistical methods, a certain degree of objectivity is ascertained insofar as all investigators should get the same analytical results once they have agreed on the techniques to use. Certain statistical fitting procedures also provide quantitative measures of goodness of fit and of the reliability of the kinetic constants estimated, facilitating evaluation of the results and testing of hypotheses. This is the case for nonlinear regression analysis based on the principle of least squares. In this chapter, it is assumed that a mathematical model (rate equation) should be fitted by nonlinear regression analysis to a set of experimental data. Most procedures use the principle of least squares. While discrimination between rival mathematical models, two questions arise: do the models adequately describe the data? Is one model better than the other is? The first question may be answered by evaluating the results of the regression by the criteria for goodness of fit. If both models are adequate and fit the data equally well, the simplest model is chosen. However, independent information obtained by additional kinetic studies or by completely different experimental methods should be included in the discrimination procedure.