Question

Calculate product moment correlation between the values of X and Y.

X	2	3	1	5	6	4
Y	4	5	3	4	6	2

Answer 1

X	Y	X2	Y2	XY
2 3 1 5 6 4	4 5 3 4 6 2	4 9 1 25 36 16	16 25 9 16 36 4	8 15 3 20 36 8
$\mathit{\Sigma }\mathit{X}$=21	$\mathit{\Sigma }\mathit{Y}$=24	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=91	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=106	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=90

N = 6

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma \mathrm{Y}}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{6\times 90-24\times 21}{\sqrt{6\times 91-{\left(21\right)}^2}\sqrt{6\times 106-{\left(24\right)}^2}} \\ \mathrm{or},r=\frac{36}{10.24\times 7.74} \\ \Rightarrow r=0.454 \end{gathered}$$

Hence, product moment correlation = 0.454