Question

Calculate coefficient of correlation from the following data:

X	30	36	42	48	54	60	72	82
Y	50	50	54	54	62	66	70	82

Answer 1

X	Y	X2	Y2	XY
30 36 42 48 54 60 72 82	50 50 54 54 62 66 70 82	900 1296 1764 2304 2916 3600 5184 6724	2500 2500 2916 2916 3844 4356 4900 6724	1500 1800 2268 2592 3348 3960 5040 6724
$\mathit{\Sigma }\mathit{X}$=424	$\mathit{\Sigma }\mathit{Y}$=488	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=24688	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=30656	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=27232

N = 8

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\mathrm{\Sigma }Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma \mathrm{Y}\right)}^2}} \\ \mathrm{or},r=\frac{8\times 27232-424\times 488}{\sqrt{8\times 24688-{\left(424\right)}^2}\sqrt{8\times 30656-{\left(488\right)}^2}} \\ \mathrm{or},r=\frac{10944}{133.14\times 84.28} \\ \Rightarrow r=0.9753 \end{gathered}$$

Hence, coefficient of correlation= 0.9753