I know that the r^2 value for the data is 0.9832. Is there a way to use that value to find the percent variation in Y is explained by X? Or do I need to use the data given to me?
$\endgroup$ 31 Answer
$\begingroup$$r^2*100$ is the percentage of variance explained by $X$.
When you regress $Y$ on $X$ you get $\hat{Y}=a+r\frac{s_y}{s_x}X$
And $Var(\hat{Y})=r^2Var(Y)$ from the above equation.
So $\frac{Var(\hat{Y})}{Var(Y)}*100=r^2*100$ is the percentage of variance explained by x.
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