Question

If slopes of two regression lines are $1.5$ and $0.8$, and $\theta$ is the angle between the two regression lines, then $\tan \theta$ is :

• A. $0.31$
• B. $0.20$
• C. $0.18$
• D. $0.9$

Answer 1

The correct option is A $0.31$

Given, slopes of two regression lines are $1.5$ and $0.8$

Let $m_1=1.5$ and $m_2=0.8$

We know that,

$\tan \theta =\frac{m_1-m_2}{1+m_1{m}_2}$

$=\frac{1.5-0.8}{1+\left(1.5\right)\left(0.8\right)}$

$=\frac{0.7}{1+1.2}$

$=\frac{0.7}{2.2}$

Thus $\tan \theta =0.31$