# If $b_{yx} = \large\frac{1}{2}$ and $b_{xy} = \large\frac{2}{3}$ and $\theta$ is the acute angle between the two regression lines then $\tan \theta$ =

$\begin {array} {1 1} (A)\;\large\frac{2}{7} & \quad (B)\;\large\frac{4}{7} \\ (C)\;\large\frac{6}{7} & \quad (D)\;None \: of \: these \end {array}$

$\tan \theta \begin{vmatrix} \large\frac{b_{yx}b_{xy}-1}{b_{yx}+b_{xy}} \end{vmatrix}$
$= \begin{vmatrix} \large\frac{\large\frac{1}{2}.\large\frac{2}{3}-1}{\large\frac{1}{2}+\large\frac{2}{3}} \end{vmatrix}$
$= \large\frac{4}{7}$
Ans : (B)
answered Feb 1, 2014