From CFAI :
Suppose that you deleted several of the observations that had small residual values. If you re-estimated the regression equation using this reduced sample, what would likely happen to the standard error of the estimate and the R-squared?
The answer is:
SE Increases and R-Square Dec
SE = (xi - x)/ n-1 so if n decreases SE will increase were as R-Square is 1- Unexplained/Total Variance… would decrease in observation reduce Total variance and the ratio of Unexplained /Total increase there by reducing R-Square?