For the following bivariate data obtain equation of regression line \(Y\) on \(X\):\(X\)12345\(Y\)5791113

Q.6 (A) (ii) For the following bivariate data obtain equation of regression line \(Y\) on \(X\):

\(X\)	1	2	3	4	5
\(Y\)	5	7	9	11	13

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

1 answer

Best answer

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

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

\(x\)	\(y\)	\(x-\bar x\)	\(y-\bar y\)	\((x-\bar x)^2\)	\((x-\bar x)(y-\bar y)\)
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

\(b_{yx}=\frac{\sum(x-\bar x)(y-\bar y)}{\sum(x-\bar x)^2}=\frac{20}{10}=2\).

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

Was this answer helpful?