Question

The two lines of regression are $2x - 7y + 6 = 0$and $7x - 2y + 1 = 0$. The correlation coefficient between x and y is

• A. – 2/7
• B. 2/7
• C. 4/49
• D. None

Answer 1

Answer: (B)

2/7

Answer 2

The two lines of regression are $2x - 7y + 6 = 0$ .....(i) and $7x - 2y + 1 = 0$ ......(ii)

If (i) is regression equation of y on x, then (ii) is regression equation of x on y.

We write these as $y = \frac{2}{7}x + \frac{6}{7}$ and $x = \frac{2}{7}y - \frac{1}{7}$

$\therefore$ $b_{yx} = \frac{2}{7}$, $b_{xy} = \frac{2}{7}$; $\therefore$ $b_{yx}.b_{xy} = \frac{4}{49} < 1$, So our choice is valid.

$\therefore$ $r^{2} = \frac{4}{49}$ ⇒ $r = \frac{2}{7}$. [$\because b_{yx} > 0,b_{xy} > 0$]