Goodness-of-Fit Tests for Continuous Regression

A family of transformations of the processes of accumulated residues of linear models is used to construct tests of fit of the models, consistent for any alternative, and focused on alternatives in the direction selected by the user. The resulting tests are asymptotically distribution free, both under the null hypothesis of fit, and under the selected alternatives. An interesting feature is that this distributions do not depend on (possible) parameter estimations.