Given that the overall F-test of a multiple regression model has an F distribution, which depends on the number of predictors in the model, I understand why you cannot compare the F-statistics from models with different number of predictors.
However, the p-value of the F-statistics always has a uniform distribution between 0 and 1, and represents the probability that at least one βj ≠ 0 under the null hypothesis.
Can I compare the F-statistics p-value from models with different number of predictors? If not, what are good alternatives? (R-squared?; adjusted R-squared?)