For the following bivariate data obtain the equation of regression line of Y on X.X12345Y5791113

Q.6 (B) (i) For the following bivariate data obtain the equation of regression line of Y on X.

X	1	2	3	4	5
Y	5	7	9	11	13

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

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Answer: \(Y=2X+3\)

\(n=5,\ \bar{x}=\frac{15}{5}=3,\ \bar{y}=\frac{45}{5}=9\)

x	y	\(x-\bar{x}\)	\(y-\bar{y}\)	\((x-\bar{x})^2\)	\((x-\bar{x})(y-\bar{y})\)
1	5	-2	-4	4	8
2	7	-1	-2	1	2
3	9	0	0	0	0
4	11	1	2	1	2
5	13	2	4	4	8
15	45	0	0	10	20

\(b_{YX}=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{\Sigma(x-\bar{x})^2}=\frac{20}{10}=2\)

Regression line of Y on X: \(Y-\bar{y}=b_{YX}(X-\bar{x})\Rightarrow Y-9=2(X-3)\Rightarrow Y=2X+3\).

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

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