Question

If the lines of regression of y on x and x on y make angles $30^{o}$ and $60^{o}$ respectively with the positive direction of X-axis, then the correlation coefficient between x and y is

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{3}$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{3}}$

Answer 2

Slope of regression line of y on x = $b_{yx} = \tan 30^{o} = \frac{1}{\sqrt{3}}$

Slope of regression line of x on y = $\frac{1}{b_{xy}} = \tan 60^{o} = \sqrt{3}$

⇒ $b_{xy} = \frac{1}{\sqrt{3}}$. Hence, $r = \sqrt{b_{xy}.b_{yx}} = \sqrt{\left( \frac{1}{\sqrt{3}} \right)\left( \frac{1}{\sqrt{3}} \right)} = \frac{1}{\sqrt{3}}$.