Judging the significance of multiple linear regression models

It is common practice to calculate large numbers of molecular descriptors, apply variable selection procedures to reduce the numbers, and then construct multiple linear regression (MLR) models with biological activity. The significance of these models is judged using the usual statistical tests. Unfortunately, these tests are not appropriate under these circumstances since the MLR models suffer from "selection bias". Experiments with regression using random numbers have generated critical values (F-max) with which to assess significance.