  We put forward an adaptive alpha (Type I Error) that decreases as the
information grows, for hypothesis tests in which nested linear models are
compared. A less elaborate adaptation was already presented in \citet{PP2014}
for comparing general i.i.d. models. In this article we present refined
versions to compare nested linear models. This calibration may be interpreted
as a Bayes-non-Bayes compromise, of a simple translations of a Bayes Factor on
frequentist terms that leads to statistical consistency, and most importantly,
it is a step towards statistics that promotes replicable scientific findings.
