A graph approach to generate all possible subset regression models

A regression graph which can be employed to enumerate and evaluate all possible subset regression models is introduced. The graph can be seen as a generalization of a previously introduced regression tree. Specifically, the regression tree describes a non-unique shortest path for traversing the graph. Furthermore, all the subtrees of the graph containing all the nodes are equivalent in the sense that they provide all subset models with the same minimum computational complexity. Complexity measures of generating all sub-models by traversing the regression graph are presented. The relationship between the regression graph and the regression trees is investigated. That is, it shows how the various minimum spanning (regression) trees can be obtained from the regression graph. The merits of the derived regression trees are discussed. A branch-and-bound strategy that computes the best subset models without traversing the whole graph is described