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Choose the correct alternative: If byx < 0 and bxy < 0, then r is ______

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Question

Choose the correct alternative:

If byx < 0 and bxy < 0, then r is ______

Options

  • < 0

  • > 0

  • c = 0

  • > 1

MCQ
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Solution

< 0

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

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If r = 0.6, Estimate x when y = 16 and y when x = 10


x y `x - barx` `y - bary` `(x - barx)(y - bary)` `(x - barx)^2` `(y - bary)^2`
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3 9 0 0 0 0 0
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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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`2 square -  5 bary + 60` = 0

∴ `bary = square`

`sigma_x : sigma_y` = 3 : 2

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`


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`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

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  2. bxy
  3. Correlation coefficient between x and y.

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