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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
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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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