Chapter: Linear Regression· Mathematics & Statistics (Commerce) Part 2

Following are given information about advertising expenditure and sales.Advertisement expenditure (₹ in lakh) (X)Sales (₹ in lakh) (Y)Arithmetic mean1090Standard deviation312Correlation coefficient between \(X\) and \(Y\) is 0.8(a) Obtain the regress…

Q.5 (A) (ii) Following are given information about advertising expenditure and sales.

	Advertisement expenditure (₹ in lakh) (X)	Sales (₹ in lakh) (Y)
Arithmetic mean	10	90
Standard deviation	3	12

Correlation coefficient between \(X\) and \(Y\) is 0.8
(a) Obtain the regression of \(Y\) on \(X\)
(b) What is the likely sales when the advertising budget is ₹15 lakh?

Doubtly Asked 29 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: (a) \(Y=3.2X+58\); (b) ₹ 106 lakh

\(\bar{x}=10,\ \bar{y}=90,\ \sigma_x=3,\ \sigma_y=12,\ r=0.8\).

(a) \(b_{yx}=r\frac{\sigma_y}{\sigma_x}=0.8\times\frac{12}{3}=3.2\).
Regression of \(Y\) on \(X\): \(Y-\bar{y}=b_{yx}(X-\bar{x})\)
\(Y-90=3.2(X-10)\Rightarrow Y=3.2X+58\).

(b) When \(X=15\): \(Y=3.2(15)+58=48+58=106\). Likely sales are ₹ 106 lakh.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

Was this answer helpful?

Following are given information about advertising expenditure and sales.Advertisement expenditure (₹ in lakh) (X)Sales (₹ in lakh) (Y)Arithmetic mean1090Standard deviation312Correlation coefficient between \(X\) and \(Y\) is 0.8(a) Obtain the regress…

1 answer

Your answer