This paper presents an information criteria based model selection procedure (called FIC) for choosing the variables to be used in a linear regression. The penalty function is based on sums of critical values from particular F-distributions which are related to the small sample probabilities of incorrectly including additional regressors. Results from a Monte Carlo simulation study demonstrate that the performance of this new procedure is competitive with other asymptotically motivated procedures, while providing the practitioner with controls over the desired small sample probabilities of correct selection. An alternative, somewhat simpler selection criterion based on an asymptotic distribution is presented and compared to the finite sample criterion. Conditions for strong consistency of this variable selection procedure based on an approximate penalty function are presented.