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R squared when every observation appears twice

Question

An OLS regression yields R2=0.56R^2=0.56. If each observation is duplicated, so every point appears twice, and the regression is rerun, what is the new R2R^2? Enter −1-1 if it cannot be determined.

Short answer

0.560.56. The fitted line and the mean of yy are unchanged, so both the residual and total sums of squares exactly double, leaving their ratio and hence R2R^2 the same.

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