Question

Find the coefficient of correlation between X and Y series from the data:

X	10	12	8	15	20	25	40
Y	15	10	6	25	16	12	8

Answer 1

X	Y	X2	Y2	XY
10 12 8 15 20 25 40	15 10 6 25 16 12 8	100 144 64 225 400 625 1600	225 100 36 625 256 144 64	150 120 48 375 320 300 320
$\mathit{\Sigma }\mathit{X}$=130	$\mathit{\Sigma }\mathit{Y}$=92	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=3158	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=1450	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=1633

N = 7

$$\begin{gathered} r=\frac{N\mathrm{\Sigma }XY-\mathrm{\Sigma }X\mathrm{\Sigma }Y}{\sqrt{N\mathrm{\Sigma }{X}^{\mathit{2}}-{\left(\mathrm{\Sigma }X\right)}^2}\sqrt{\mathit{}N\mathrm{\Sigma }{Y}^2-{\left(\mathrm{\Sigma }Y\right)}^2}} \\ \mathrm{or},r=\frac{7\times 1633-130\times 92}{\sqrt{7\times 3158-{\left(130\right)}^2}\sqrt{7\times 1450-{\left(92\right)}^2}} \\ \mathrm{or},r=\frac{11431-11960}{\sqrt{22106-16900}\sqrt{10150-8464}} \\ \mathrm{or},r=\frac{-529}{72.15\times 41.06} \\ \mathrm{or},r=-\frac{529}{2962.47} \\ \Rightarrow r=-0.178 \end{gathered}$$

Thus, coefficient of correlation is 0.178.