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Choose the correct alternative: bxy and byx are ______ - Mathematics and Statistics

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Question

Choose the correct alternative:

bxy and byx are ______

Options

  • Independent of change of origin and scale

  • Independent of change of origin but not of scale

  • Independent of change of scale but not of origin

  • Affected by change of origin and scale

MCQ
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Solution

Independent of change of origin but not of scale

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

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For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.


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Choose the correct alternative:

If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______


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Mean of x = 53

Mean of y = 28

Regression coefficient of y on x = – 1.2

Regression coefficient of x on y = – 0.3

a. r = `square`

b. When x = 50,

`y - square = square (50 - square)`

∴ y = `square`

c. When y = 25,

`x - square = square (25 - square)`

∴ x = `square`


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Mean of x = 18

`2 square -  5 bary + 60` = 0

∴ `bary = square`

`sigma_x : sigma_y` = 3 : 2

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`


|bxy + byz| ≥ ______.


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