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|bxy + byx| ≥ ______

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Question

|bxy + byx| ≥ ______

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Solution

2|r| 

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

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For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.


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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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bxy and byx are ______


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If r = 0.5, σx = 3, σy2 = 16, then bxy = ______


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If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent


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Corr(x, x) = 0


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If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90 , Σxy = 76 Find Covariance (x,y) 


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 = 25

Mean of y = 20

`sigma_x` = 4

`sigma_y` = 3

r = 0.5

byx = `square`

bxy = `square`

when x = 10,

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

∴ y = `square`


The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

  x y
Mean 53 142
Variance 130 165

`sum(x_i - barx)(y_i - bary)` = 1170


|bxy + byz| ≥ ______.


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