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

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प्रश्न

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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उत्तर

Given:

`bar x = 53`,

`bar y = 28`,

byx = −1.2,

bxy = −0.3.

Correlation coefficient between x and y:

r = `+-sqrt("b"_"xy" * "b"_"yx")`

`= +- sqrt((-0.3)(-1.2))`

= `+- sqrt 0.36` 

= ± 0.6          ...[∵ byx and bxy are negative]

Since byx and bxy both are negative,

r is also negative.

∴ r = −0.6

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Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 3 Linear Regression
Exercise 3.2 | Q 1.1 | पृष्ठ ४७

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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`

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

∴ y = `square`

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`x - square = square (25 - 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`


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`

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byx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`


|bxy + byz| ≥ ______.


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