Question

If the regression line of x on y is, 9x + 3y − 46 = 0 and y on x is, 3x + 12y − 7 = 0, then the correlation coefficient ‘r’ is equal to:

पर्याय

• ${\displaystyle \frac{-1}{12}}$

• ${\displaystyle \frac{1}{12}}$

• ${\displaystyle \frac{-1}{2\sqrt{3}}}$

• ${\displaystyle \frac{1}{2\sqrt{3}}}$

Answer 1

${\displaystyle \frac{-1}{2\sqrt{3}}}$

Explanation:

Given lines of regression are:

9x + 3y − 46 = 0  ....(x on y)

9x = − 3y + 46

⇒ x = ${\displaystyle \frac{-3}{9}\text{y}+\frac{46}{9}}$

⇒ x = ${\displaystyle \frac{-1}{3}\text{y}+\frac{46}{9}}$

∴ b_xy = ${\displaystyle \frac{-1}{3}}$

and 3x + 12y − 7 = 0 ........(y on x)

⇒ 12y = − 3x + 7

⇒ y = ${\displaystyle \frac{-3}{12}\text{x}+\frac{7}{12}}$

⇒ y = ${\displaystyle \frac{-1}{4}\text{x}+\frac{7}{12}}$

∴ b_yx = ${\displaystyle \frac{-1}{4}}$

Now, r = ${\displaystyle \sqrt{{\text{b}}_{\text{xy}}.{\text{b}}_{\text{yx}}}}$

= ${\displaystyle \sqrt{\left(\frac{-1}{3}\right)\left(\frac{-1}{4}\right)}}$

= ${\displaystyle \frac{1}{\sqrt{12}}}$

⇒ r = ${\displaystyle \frac{1}{2\sqrt{3}}}$

∴ r = ${\displaystyle \frac{-1}{2\sqrt{3}}}$ ......(Since b_xy and b_yx are negative ∴ r is negative)