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Question
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)`
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