Question

If regression coefficient of y on x is $\frac{8}{5}$ and that of x on y is $\frac{2}{5}$and the acute angle between the two lines is $\alpha$, then the value of tan$\alpha$ is

• A. 9/25
• B. $9/2\sqrt{5}$
• C. 3/25
• D. 9/50

Answer 1

Answer: (D)

9/50

Answer 2

Here $b_{yx} = \frac{8}{5}$and $b_{xy} = \frac{2}{5}$

Hence $m_{1} = \frac{8}{5}$ and $m_{2} = \frac{1}{b_{xy}} = \frac{5}{2}$

⇒ $\tan\theta = \pm \left( \frac{m_{1} - m_{2}}{1 + m_{1}m_{2}} \right) = \pm \frac{\frac{8}{5} - \frac{5}{2}}{1 + \frac{8}{5} \times \frac{5}{2}} = \frac{9}{50}$.