I am doing a regression project on some medical data using SAS. I used forward selection, backward selection, stepwise selection, and the LASSO, and all procedures gave me the same subset of variables.
However, when I run the reduced model, for some reason I have a higher MSRes and a lower adjusted $R^2$ than I had for the full model.
Assumptions have been met and there is no multicollinearity.
Is this normal? It seems a bit weird to me.