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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, b_{xy} = `(1)/6` and b_{yx} = `(3)/2`
∴ r = `sqrt((1)/6 xx (3)/2`
= – 0.5
Given, Var (y) = 36, i.e., σ_{y}^{2} = 36
∴ σ_{y }= 6
Since b_{xy} = `"r" xx sigma_x/sigma_y`
`(1)/6 =  0.5 xx sigma_x/6`
∴ σ_{x }= `(6)/(6 xx 0.5)` = 2
∴ σ_{x}^{2} = Var (x) = 4
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