Criterion Mixing Lack of Fit and Multicolinearity for Variable Selection in Regression.

We describe in this paper a method allowing to order submodels in linear regression. A real function is attached to each submodel, allowing to graphically compare and order them. Our procedure defines an objective function depending on two factors (lack of fit and multicolinearity) with the property that the minimum of this function over subsets of the regressors determines the "best" such subset of variables. The latter will be found by systematically examining all possible subsets having at least two regressors. The method is built in such a way that it allows a graphical inspection of the submodels. Although it is presented here only in the framework of linear regression with a single, continuous, response variable, the procedure may be extended in a natural way to more general regression models. Simulation and implementation on various data sets gave very satisfying results