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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

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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)

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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?
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