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If u = x-ac and v = y-bd, then bxy = ______ - Mathematics and Statistics

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Question

If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______ 

Fill in the Blanks

Solution

`"c"/"d"` buv 

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Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.3

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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`

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byx = `square/square`

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∴ 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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