Question

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.

Answer 1

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

∴ `sigma_x` = 5, `sigma_y` = 6

b_yx = `"r" sigma_y/sigma_x = 0.6 xx 6/5` = 0.72

b_xy = `"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.