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)Mean8590S.D.56Coefficient of correlation between X and Y is 0.6. Also estimate the production when de…

Q.5 (A) (ii) 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.

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: \(X=0.5Y+40\); estimated production = 90 when demand is 100.

\(\bar{x}=85,\ \bar{y}=90,\ \sigma_x=5,\ \sigma_y=6,\ r=0.6\)

\(b_{XY}=r\frac{\sigma_x}{\sigma_y}=0.6\times\frac{5}{6}=0.5\)

Regression line of X on Y: \(X-\bar{x}=b_{XY}(Y-\bar{y})\Rightarrow X-85=0.5(Y-90)\Rightarrow X=0.5Y+40\)

When \(Y=100\): \(X=0.5(100)+40=90\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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