Choose the correct alternative: If r = 0.5, σx = 3, σy2 = 16, then bxy = ______ - Mathematics and Statistics

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Choose the correct alternative:

If r = 0.5, σx = 3, σy2 = 16, then bxy = ______

Options

  • 0.375

  • 0.667

  • 2.667

  • 0.093

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Solution

0.375

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.1

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Total = 15 Total = 45 Total = 0 Total = 0 Total = `square` Total = 10 Total = 40

Mean of x = `barx = square`

Mean of y = `bary = square`

bxy = `square/square`

byx = `square/square`

Regression equation of x on y is `(x - barx) = "b"_(xy)  (y - bary)`

∴ Regression equation x on y is `square`

Regression equation of y on x is `(y - bary) = "b"_(yx)  (x - barx)`

∴ Regression equation of y on x is `square`


Mean of x = 25

Mean of y = 20

`sigma_x` = 4

`sigma_y` = 3

r = 0.5

byx = `square`

bxy = `square`

when x = 10,

`y - square = square (10 - square)`

∴ y = `square`


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