Question

If "$\theta$" be the angle between two regression lines and regression coefficients are $b_{xx}=1.6$ and $b_{xy}=4,$ then find the value of $\tan \theta$.

Answer 1

$\tan \theta =\frac{b_{xy}{b}_{yx}-1}{b_{yx}+b_{xy}}$
where $b_{xy}=0.4,b_{yx}=1.6$
$\therefore \tan \theta =\frac{0.4\times 1.6-1}{1.6+0.4}=\frac{0.64-1}{2}$
$\tan \theta =\frac{-0.36}{2}=-0.18$.