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 - Mathematics and Statistics

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Sum

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 

∴ σ= 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

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.4

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