Formula For Centered Coefficient of Determination

Question

I want to show that in the inhomogeneous regression model $y=\alpha+X\beta+u $ $$ R_*^2=max_{z\in \text{col}(X)}r_{x,y}^2, $$ where $r_{x,y}^2:=\frac{S_{xy}^2}{S_xS_y}$ is the squared empirical correlation coefficient, $R_*^2:=\frac{S_{\hat{y}}}{S_y}$ is the centered coefficient of determination and $\text{col}(X)$ the vectospace generated by the column vectors of $X$ . I could show a simpler version for the simple regression model but I don't see how it works for this more general case. I would be glad for any hints.