Question

Calculate product moment correlation between age of cars and annual maintenance cost and comment.

Age of cars (years)	:	2	4	6	7	8	10	12
Annual maintenance ​Cost (in ₹)	:	1600	1500	1800	1900	1700	2100	2000

Answer 1

Age of Cars (X)	Maintenance (Y)	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ x	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ y	x2	y2	xy
2	1600	−5	−200	25	40000	1000
4	1500	−3	−30	9	90000	900
6	1800	−1	0	1	0	0
7	1900	0	100	0	10000	0
8	1700	1	−100	1	10000	−100
10	2100	3	300	9	90000	900
12	2000	5	200	25	40000	1000
ƩX = 49	ƩY =12600			Ʃx2 =70	Ʃy2 =280000	Ʃxy =3700

N = 7

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{49}{7}=7 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{12600}{7}=1800 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ =\frac{3700}{\sqrt{70}\times \sqrt{280000}} \\ =\frac{3700}{8.36\times 529.15} \\ =0.836 \end{gathered}$$
Thus, there exists high positive correlation between age of car and maintenance cost.