Variance explained by a regression

MediumStatistics Linear Algebra~4m

In a simple linear regression of $Y$ on $X$ you measure $\operatorname{Cov}(X,Y)=3$ , $\operatorname{Var}(X)=4$ , and $\operatorname{Var}(Y)=9$ . What fraction of the variance of $Y$ does the fitted line explain (the $R^2$ )? (to 2 decimals)

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R^2 equals the squared correlation, rho^2 = Cov(X,Y)^2 / (Var(X) Var(Y)).
Do not stop at the slope Cov/Var(X); square the correlation.

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0.25 (± 0.01)

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Variance explained by a regression

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