Iterative regression strategy

The scheme of interpolation followed in the iterative regression strategy explained above is not very simple from a practical point of view. The method of triangles requires at least four different equations, one for each established subspace. The use of a single equation to describe the retention behavior of a solute, in the whole variable space, seems to be more convenient to predict the retention of a solute in any mobile phase, with a minimum effort. Table 8.1 shows some of the models (equations) that have been considered, where the logarithm (eqs. 8.15-8.22), or the reciprocal of the retention factor (eqs. 8.23-8.30) are related to micelle concentration and volume fraction of organic modifier. 

The process of research in chemical systems is one of developing and testing different models for process behavior. Whether empirical or mechanistic models are involved, the discipline of statistics provides data-based tools for discrimination between competing possible models, parameter estimation, and model verification for use in this enterprise. In the case where empirical models are used, techniques associated with linear regression (linear least squares) are used, whereas in mechanistic modeling contexts nonlinear regression (nonlinear least squares) techniques most often are needed. In either case, the statistical tools are applied most fruitfully in iterative strategies. 

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