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

Question

Sum

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_y² = 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_x² = Var (x) = 4

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Properties of Regression Coefficients

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Chapter 2.3: Linear Regression - Q.4

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SCERT Maharashtra Mathematics and Statistics (Commerce) [English] Standard 12 Maharashtra State Board

Chapter 2.3 Linear Regression
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