Question

From the following data, calculate coefficient correlation between the variables X and Y using Karl Pearson's method:

X	10	6	9	10	12	13	11	9
Y	9	4	6	9	11	13	8	4

Answer 1

X	Y	X2	Y2	XY
10 6 9 10 12 13 11 9	9 4 6 9 11 13 8 4	100 36 81 100 144 169 121 81	81 16 36 81 121 169 64 16	90 24 54 90 132 169 88 36
$\sum X=80$	$\sum Y=64$	$\sum X^2=832$	$\sum Y^2=584$	$\sum XY=683$

N = 8

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2\sqrt{N\Sigma {\mathrm{Y}}^2-{\left(\Sigma Y\right)}^2}}} \\ \mathrm{or},r=\frac{8\times 683-80\times 64}{\sqrt{8\times 832-{\left(80\right)}^2}\sqrt{8\times 584-{\left(64\right)}^2}} \\ \mathrm{or},r=\frac{344}{16\times 24} \\ \Rightarrow r=0.895 \end{gathered}$$

Thus, the coefficient of correlation between the variables X and Y is 0.895.