# Regression analysis question on model selection and reduced model

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.

Thanks!