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Question
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`
Solution
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 = `+- sqrt("b"_(xy)*"b"_(yx))`
= `+- sqrt((-0.3)(-1.2))`
= `+- 0.6`
Since bYX and bXY both are – negative,
r is also negative.
∴ r = – 0.6
b. When x = 50,
`(y - bary) = "b"_(yx) (x- barx)`
∴ `(y - 28) = - 1.2 (50 - 53)`
∴ y = 28 – 60 + 63.6
∴ y = 31.6
c. When y = 25,
`(x - 53) = - 0.3 (25 - 28)`
∴ X = 53 – 7.5 + 8.4
∴ X = 53.9
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