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प्रश्न
The regression equation of y on x is 2x – 5y + 60 = 0
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`
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उत्तर
The regression equation of y on x is 2x – 5y + 60 = 0.
Mean of x = 18
`2barx - 5bary + 60` = 0
`2 xx 8 - 5bary + 60` = 0
∴ `5 bary` = 36 + 60
∴ `5 bary` = 96
∴ `bary` = 19.2
`sigma_x : sigma_y` = 3 : 2
2x – 5y + 60 = 0 ⇒ y = 0.4x + 12
∴ byx = `2/5`
∴ byx = `("r"sigma_y)/sigma_`
∴ 0.4 = `"r"xx 2/3`
∴ r = `0.4 xx 3/2`
∴ r = 0.6
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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 = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
a. r = `square`
b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
