A General Procedure for Linear and Quadratic Regression Model Identification

A new regression procedure is developed for identification of linear and quadratic models. The new procedure uses indicators based on signal-to-noise ratio, as well as more traditional indicators, to validate the models. Various traditional stages in the modeling process, like stepwise regression, outlier detection and removal and variable transformations, are pursued, however the interdependence between these stages is accounted for to ensure detection of the best model (or subset of models).
Three examples are presented, where the proposed procedure is implemented. Some of the models identified have better goodness-of-fit than those reported in the literature. Furthermore, for two of the examples, complex quadratic models were identified that in fact model also the stochastic experimental error. While traditional indicators failed to signal the invalidity of these models, signal-to-noise ratio indicators, based on realistic noise estimates detected such over-fitting.