  We consider a new criterion-based approach to model selection in linear
regression. Properties of selection criteria based on p-values of a likelihood
ratio statistic are studied for families of linear regression models. We prove
that such procedures are consistent i.e. the minimal true model is chosen with
probability tending to 1 even when the number of models under consideration
slowly increases with a sample size. The simulation study indicates that
introduced methods perform promisingly when compared with Akaike and Bayesian
Information Criteria.
