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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 = □ b. When x = 50, y-□=□(50-□) ∴ y = □ c. When y = 25, x-□=□(25-□) ∴ x = □ - Mathematics and Statistics

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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`

Fill in the Blanks
Sum
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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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Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.5

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