Q. The regression coefficient of y on $x$ is 2/3 and that of $x$ on y is 4/3 .The acute angle between the two regression lines is $\tan^{- 1}{k,\ }$where k is equal to
A) 1/9
B) 2/9
C) 1/18
D) 1/3
Explanation
(c)
$\theta = \tan^{- 1}\left\{ \frac{\frac{2}{3} \times \frac{4}{3} - 1}{\frac{2}{3} + \frac{4}{3}} \right\}$
$\Rightarrow \theta = \tan^{- 1}{\left\{ - \frac{\frac{1}{9}}{2} \right\} = \tan^{- 1}{\left\{ - \frac{1}{18} \right\}\ }}$
$\therefore Angle\ is\ acute\ angle.$
$\therefore\$k=$\frac{1}{18}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.