Question

For the given lines of regression, 3x – 2y = 5 and x – 4y = 7, find:
(a) regression coefficients b_yx and b_xy
(b) coefficient of correlation r (x, y)

Answer 1

(a) The two regression lines are 
3x - 2y = 5                                               ...(i)
and     x - 4y = 7                                     ...(ii)
from equation (i),   3x -2y = 5
⇒     3x = 2y + 5

x = `(2)/(3) y + (5)/(3)`

∴ b_xy = `(2)/(3)`                    ...( Regression of x on y)

From equation (ii), 
x - 4y = 7
⇒  4y = x - 7

 y = `(1)/(4) x -(7)/(4)`

b_yx  = `(1)/(4)`                     ...( Regression of y on x)

Hence, the value of b_xy  = `(2)/(3)` and b_yx =`(1)/(4)` 

(b) Coefficient of correlation r(x, y) = | r |

= `sqrt(b_(xy) . b_(yx))`

= `sqrt(2/3 xx 1/4)`

= `sqrt(1/6)`

= `1/sqrt(6)`