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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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r = 0.5

byx = `square`

bxy = `square`

when x = 10,

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

∴ y = `square`


The regression equation of y on x is 2x – 5y + 60 = 0

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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`


x y xy x2 y2
6 9 54 36 81
2 11 22 4 121
10 5 50 100 25
4 8 32 16 64
8 7 `square` 64 49
Total = 30 Total = 40 Total = `square` Total = 220 Total = `square`

bxy = `square/square`

byx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`


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