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Question
The equations of two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find variance of x if variance of y is 36
Solution
Here, bxy = `(-1)/6` and byx = `(-3)/2`
∴ r = `sqrt((-1)/6 xx (-3)/2`
= – 0.5
Given, Var (y) = 36, i.e., σy2 = 36
∴ σy = 6
Since bxy = `"r" xx sigma_x/sigma_y`
`(-1)/6 = - 0.5 xx sigma_x/6`
∴ σx = `(-6)/(-6 xx 0.5)` = 2
∴ σx2 = Var (x) = 4
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∴ Regression equation of y on x is `square`
The regression equation of y on x is 2x – 5y + 60 = 0
Mean of x = 18
`2 square - 5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `square`
bxy . byx = ______.
If byx > 1 then bxy is _______.
