I have tried equaling $\displaystyle R^2$ and $\displaystyle r^2$ and it comes out that $\displaystyle s_{\hat{y}\hat{y}}$ is equal to $\displaystyle s_{y\hat{y}}$. But then if I insert the $\displaystyle s_{y\hat{y}}$ into the $\displaystyle R^2$ and try to show that it equals to firstly defined $\displaystyle R^2$ I get hooked up. Probably the approach is not correct.