Question

Given the following information about the production (X) and demand (Y) of a commodity, obtain the regression line of X on Y.

	Production (X)	Demand (Y)
Mean	85	90
S.D.	5	6

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

Answer 1

Given

Mean of Production `barX` = 85

Mean of Demand `barY` = 90

S.D. of Production σ_X = 5 

S.D. of Demand σ_Y = 6

Correlation coefficient r = 0.6

Required

Regression line of X on Y

Estimate X when Y = 100

Step 1: Find the regression coefficient b_XY

`b_(XY) = r = ((σ_X)/(σ_Y))`

`b_(XY) = 0.6(5/6)`

= 0.6 × 0.8333 

= 0.5

Step 2: Write the regression equation of X on Y

X − `barX= b_(XY)​(Y − barY)`

X − 85 = 0.5(Y − 90)

X − 85 = 0.5Y − 45

X = 0.5Y + 40

Regression line of X on Y:

X = 0.5Y + 40

Step 3: Estimate production when demand is 100.

Put Y = 100 in X

= 0.5Y + 40

X = 0.5(100) + 40

= 50 + 40 = 90

Estimated production when demand is 100

X = 90