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If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______ - Mathematics and Statistics

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Question

If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______

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Solution

negative

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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`


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
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Total = 30 Total = 40 Total = `square` Total = 220 Total = `square`

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byx = `square/square`

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∴ Regression equation of y on x is `square`


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For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

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

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