# 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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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

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.5
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