R-squared when you duplicate every point

EasyStatistics~3m

You run OLS on a dataset and get $R^2 = 0.56$ . You then duplicate every data point (so each $(x_i, y_i)$ now appears twice) and rerun the regression. What is the new $R^2$ ?

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How do the sums $\sum(x-\bar x)^2$ , $\text{SSR}$ , $\text{SST}$ change when every point is duplicated?
They all double, so their ratio $R^2$ is unchanged.

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0.56

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Asked at: DRW, Two Sigma

R-squared when you duplicate every point

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