Question

Given two regression lines 5x+7y=22 and 6x+2y=20. Find mean values of x and y.​

Answer 1

Step-by-step explanation:

see the answer given above

Answer 2

$\large\underline{\sf{Solution-}}$

Two regression lines are as

• 5x + 7y = 22

• 6x + 2y = 20

We know that,

☆ The point of intersection of two regression lines gives the mean value of x and mean value of y.

☆ So, we solve these two equations using substitution method.

Consider,

$\rm :\longmapsto\:5x + 7y = 22 - - - - (1)$

and

$\rm :\longmapsto\:6x + 2y = 20$

can be rewritten as

$\rm :\longmapsto\:3x + y = 10$

$\bf\implies \:y = 10 - 3x - - - - (2)$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:5x + 7(10 - 3x) = 22$

$\rm :\longmapsto\:5x + 70 - 21x = 22$

$\rm :\longmapsto\: - 16x = 22 - 70$

$\rm :\longmapsto\: - 16x = -48$

$\bf\implies \:x = 3$

On substituting x = 3 in equation (2), we get

$\rm :\longmapsto\:y = 10 - 3 \times 3$

$\rm :\longmapsto\:y = 10 -9$

$\bf\implies \:y = 1$

Hence,

$\bf :\longmapsto\: \overline{x} = x = 3$

and

$\bf :\longmapsto\: \overline{y} = y = 3$

Additional Information :-

1. Regression coefficient are of same sign.

$\rm :\longmapsto\: {r}^{2} = b_{xy} \: \times \: b_{yx}$

$\rm :\longmapsto\:b_{xy} = r \: \dfrac{ \sigma_x}{\sigma_y}$

$\rm :\longmapsto\:b_{yx} = r \: \dfrac{ \sigma_y}{\sigma_x}$