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प्रश्न
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient
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उत्तर
r = `+- sqrt("b"_(xy) * "b"_(yx))`
= `+- sqrt((-1)/6 xx (-3)/2)`
= `+- 1/2`
= `+- 0.5`
Since the values of bxy and byx are negative,
r is also negative.
∴ r = – 0.5
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bxy = `square/square`
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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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`
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`2 square - 5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `square`
