You are given the following model to estimate.

Question

Yi=αo+α1X1+α2X2+ α3X3+µi.
However,in your estimation one variable say X3 was dropped.What effect would this have
on the adjustedR-square? What about R-square?

Answer 1

The effect on the adjusted R-square would be a decrease, since the adjusted R-square takes into account the number of variables used in the model. The R-square, however, would remain unchanged since it does not take into account the number of variables used in the model.