# For the Given Lines of Regression, 3x – 2y = 5 and X – 4y = 7, Find: (A) Regression Coefficients Byx and Bxy (B) Coefficient of Correlation R (X, Y) - Mathematics

Sum

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

#### Solution

(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)

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

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

y = (1)/(4) x -(7)/(4)

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

Hence, the value of bxy  = (2)/(3) and byx =(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)

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Is there an error in this question or solution?