Question

The equations of the two regression lines are 3x + 2y − 26 = 0 and 6x + y − 31 = 0. Obtain the correlation coefficient between x and y.

Solution: To find correlation coefficient, we have to find the regression coefficients b_yx and b_xy.

Let 3x + 2y = 26 be equation of the line of regression of y on x.

This gives y = `square` + x + 13

∴ b_yx = `-3/2`

Now, consider 6x + y = 31 as equation of the line of regression of x on y.

This can be written as x = `square y + 31/6`

∴ b_yx = `-1/6`

Now, `r^2 = square = 0.25`

As both b_yx and b_xy are negative,

∴ r = `square`

Answer 1

To find correlation coefficient, we have to find the regression coefficients b_yx and b_xy.

Let 3x + 2y = 26 be equation of the line of regression of y on x.

This gives y = \[\boxed{-\frac{3}{2}}\] + x + 13

∴ b_yx = `-3/2`

Now, consider 6x + y = 31 as equation of the line of regression of x on y.

This can be written as x = \[\boxed{-\frac{1}{6}}\] y + `31/6`

∴ b_yx = `-1/6`

Now, r² = \[\boxed{b_(yx) . b_(xy)}\] = `(-3/2)(-1/6)` = 0.25

As both b_yx and b_xy are negative,

∴ r = \[\boxed{-0.5}\]