Multiple regression equation of $$X_{1}$$ on $$X_{2}$$ and $$X_{3}$$ is $$\left(X_{1} -\overline{X}_{1}\right) = b_{12.3}\left(X_{2} -\overline{X}_{2}\right) + b_{13.2}\left(X_{3} -\overline{X}_{3}\right)$$ where $$ b_{13.2}$$ is:

$$\frac{\sigma_{1}}{\sigma_{2}}\left(\frac{r_{12} -r_{23}r_{13}}{1-\left(r_{23}\right)^{2}}\right)$$

$$\frac{\sigma_{1}}{\sigma_{3}}\left(\frac{r_{13} - r_{23}r_{13}}{1-\left(r_{23}\right)^{2}}\right)$$

$$\frac{\sigma_{3}}{\sigma_{1}}\left(\frac{r_{13} -r_{23}r_{13}}{1-\left(r_{23}\right)^{2}}\right)$$

$$\frac{\sigma_{2}}{\sigma_{1}}\left(\frac{r_{12} - r_{23}r_{13}}{1-\left(r_{23}\right)^{2}}\right)$$