Assuming we have three random variables $X$, $Y$, and $Z$, and we want to estimate a least squares regression plane of the form $Z = a + bX + cY$. We do not know the individual observations, but we know all the means $\mu_X$,$\mu_Y$,$\mu_Z$, variances $\sigma_X^2$,$\sigma_Y^2$,$\sigma_Z^2$ covariances $\sigma_{XY}$,$\sigma_{XZ}$,$\sigma_{YZ}$ and correlations $\rho_{XY}$,$\rho_{XZ}$,$\rho_{YZ}$. Suppose we have estimated $a$, $b$, and $c$. How can we calculate the $R^2$ value given only this information?



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