How to choose between two regression models when one has a higher adjusted R^2 and the other has a lower BIC?

#1
I have two regression models with different number of covariates/predictors.

After performing a subset selection, the remaining two choices are

Model 1, which has 7 covariates and a lower BIC.
Model 2, which has 11 covariates and a higher adjusted R^2.

Using the BIC criteria, you select the model with the lowest value.
Using the adjusted R^2, you select the model with the highest value.

So in this case, which model selection criteria would take precedence?
 

noetsi

Fortran must die
#3
Personally I am not a great fan of R squared or even adjusted R square (which is a lot better). Spurious regression, if the data occurs over time, is a real possibility.

I would always prefer BIC to it. I don't think I have read an article that suggested r square as a selection criteria.