Question

The regression coefficient of y on x is $\frac{2}{3}$ and of x on y is $\frac{4}{3}$. If the acute angle between the regression line is $\theta$, then $\tan\theta =$

• A. $\frac{1}{18}$
• B. $\frac{1}{9}$
• C. $\frac{2}{9}$
• D. None of these

Answer 1

Answer: (A)

$\frac{1}{18}$

Answer 2

$b_{yx} = \frac{2}{3},b_{xy} = \frac{4}{3}$. Therefore, $\tan\theta = \left| \frac{b_{xy} - \frac{1}{b_{yx}}}{1 + \frac{b_{xy}}{b_{yx}}} \right|$ =

$\left| \frac{\frac{4}{3} - \frac{3}{2}}{1 + \frac{4/3}{2/3}} \right| = \frac{1}{18}$.