# Given the following information about the production and demand of a commodity. Obtain the two regression lines: Production(X) Demand(Y) Mean 85 90 Variance 25 36 Coefficient of correlation between - Mathematics and Statistics

Sum

Given the following information about the production and demand of a commodity.

Obtain the two regression lines:

 Production(X) Demand(Y) Mean 85 90 Variance 25 36

Coefficient of correlation between X and Y is 0.6. Also estimate the demand when the production is 100 units.

#### Solution

Given, bar(x) = 85, bar(y) = 90, sigma_x^2 = 25, sigma_y^2 = 36, r = 0.6

∴ sigma_x = 5, sigma_y = 6

byx = "r" sigma_y/sigma_x = 0.6 xx 6/5 = 0.72

bxy = "r" sigma_x/sigma_y = 0.6 xx 5/6 = 0.5

The regression equation of Y on X is given by ("Y" - bary) = "b"_(xy)  ("X" - barx)

(Y – 90) = 0.72(X – 85)

Y – 90 = 0.72X – 61.2

Y = 0.72X – 61.2 + 90

Y = 28.8 + 0.72X     ......(i)

The regression equation of X on Y is given by ("X" - barx) = "b"_(xy)  ("Y" - bary)

(X – 85) = 0.5(Y – 90)

X – 85 = 0.5Y – 45

X = 0.5Y – 45 + 85

X = 40 + 05Y     ......(ii)

For X = 100, from equation (i) we get

Y = 28.8 + 0.72(100)

= 28.8 + 72

= 100.8

∴ The production is 90 when demand is 100.

Concept: Properties of Regression Coefficients
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Chapter 2.3: Linear Regression - Q.4
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