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:

Options

• `(-1)/12`

• `1/12`

• `(-1)/(2sqrt3)`

• `1/(2sqrt3)`

Answer 1

`(-1)/(2sqrt3)`

Explanation:

Given lines of regression are:

9x + 3y − 46 = 0  ....(x on y)

9x = − 3y + 46

⇒ x = `(-3)/9"y" + 46/9`

⇒ x = `(-1)/3"y" + 46/9`

∴ b_xy = `(-1)/3`

and 3x + 12y − 7 = 0 ........(y on x)

⇒ 12y = − 3x + 7

⇒ y = `(-3)/12"x" + 7/12`

⇒ y = `(-1)/4"x" + 7/12`

∴ b_yx = `(-1)/4`

Now, r = `sqrt("b"_"xy". "b"_"yx")`

= `sqrt(((-1)/3)((-1)/4))`

= `1/sqrt12`

⇒ r = `1/(2sqrt3)`

∴ r = `(-1)/(2sqrt3)` ......(Since b_xy and b_yx are negative ∴ r is negative)