Question

The two regression equations : the regression equation of X on Y is 10x – 2y = 4 and regression equation of Y on X is 2y – 5x = 8 Find x̄, ȳ and γxy.

Answer 1

Consider regression equation of x on y:

10x – 2y = 4; 10x = 2y + 4

Regression equation of y on x : 2y – 5x = 8 2y = 5x + 8

Solving the two regression equations

10x – 2y = 4

2y – 5x = 8

i.e. 10x – 2y = 4

2y – 5x = 8

i.e. 10x – 2y = 4

(+) -5x + 2y = 8

5x = 12,x = 12/5⇒ x̄ = 2.4

put x̄ = 2.4 in 2y – 5x = 8

2y – 5(2.4) = 8

2y = 8 +12.0

y = 20/2 = 10 ⇒ ȳ = 10.