Question

If $\theta$ is the angle between two regression lines with correlation coefficient $\gamma$, then

• A. $\sin \theta \ge 1-{\gamma }^2$
• B. $\sin \theta \le 1-{\gamma }^2$
• C. $\sin \theta \le {\gamma }^2+1$
• D. $\sin \theta \le {\gamma }^2-1$

Answer 1

The correct option is B

$\sin \theta \le 1-{\gamma }^2$

Explanation for the correct option.

If angle between two regression lines is $\theta$, and the correlation coefficient is $\gamma$ then

$\sin \theta \le 1-{\gamma }^2$

Hence, option (B) is correct.