State whether the following statement is True or False: If u = x – a and v = y – b then bxy = buv - Mathematics and Statistics

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MCQ
True or False

State whether the following statement is True or False: 

If u = x – a and v = y – b then bxy = buv 

Options

  • True

  • False

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Solution

True

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

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x y `x - barx` `y - bary` `(x - barx)(y - bary)` `(x - barx)^2` `(y - bary)^2`
1 5 – 2 – 4 8 4 16
2 7 – 1 – 2 `square` 1 4
3 9 0 0 0 0 0
4 11 1 2 2 4 4
5 13 2 4 8 1 16
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 = 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`


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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