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State whether the following statement is True or False: If byx = 1.5 and bxy = 13 then r = 12, the given data is consistent - Mathematics and Statistics

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Question

State whether the following statement is True or False:

If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent

Options

  • True

  • False

MCQ
True or False
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Solution

False

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Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.2

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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`


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

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