In a forest stand, the stem diameter \(X\) (measured \(1.3 \mathrm{~m}\) above ground) and the corresponding tree height \(Y\) have a bivariate normal distribution with joint density

\[f_{X, Y}(x, y)=\frac{1}{0.48 \pi} \exp \left\{-\frac{25}{18}\left(\frac{(x-0.3)^{2}}{\sigma_{x}^{2}}-2 ho \frac{(x-0.3)(y-30)}{0.4}+\frac{(y-30)^{2}}{25}\right)\right\}\]

Remark With this joint density, negative values of \(X\) and \(Y\) are extremely unlikely.

Determine

(1) the correlation coefficient \(ho=ho(X, Y)\), and

(2) the regression line \(\tilde{y}=\alpha x+\beta\).