Modelling and graphic interpretation of response surface in chemical analysis

The complicated effects of several factors on an analytical signal can be studied comprehensively only by an experimental design in which the additive and non-additive effects of these factors are included in one experimental run, with simultaneous variation of the values of all factors. From the law of mass action, it is shown that systems in which the analytical signal is produced by a species formed during a chemical reaction (i.e., for spectrophotometry) can be described by a model based on quasi-linear regressions with squares and products of variables. The regression coefficients can be evaluated by means of factorial designs at three levels. Interpretation of results in the case of two or three independent variables is simplified by using a graphic method in which the complex effects of factors on the dependent variable are represented as an empirical response surface. In the case of regression with three independent variables, the response surface is four-dimensional; its dimensionality is reduced to three by several three-dimensional representations. The shapes of the response surfaces described by the response functions and the adequacy of the models are discussed.