Does dropping observations near the regression lines reduces R squared

Question

I saw a pretty interesting claim:

Suppose you estimate a regression with only dummy's and a intercept as explanatory variables (sample size is 288):

$\hat{y_{i}} = \hat{\beta_{1}} + \hat{\beta_{2}}D_{1i} + ... + \hat{\beta_{11}}{D_{11i}}$

Some of the $\hat\beta$'s are individually significant, others not. The claim in question is the next:

If you drop 10 observations, that you know their present low values of residuals, the $R^{2}$ decreases.

Is the calim true? Why?

Now suddenly comes another question to my mind, does the variance of the estimators decreases or increases?

Thanks