Question

Find Karl Pearson's coefficient of correlation between the values of X and Y given data:

X	128	129	130	140	132	135	125	130	132	135
Y	80	89	90	95	96	94	80	100	96	100

Answer 1

X	Y	X2	Y2	XY
128 129 130 140 132 135 125 130 132 135	80 89 90 95 96 94 80 100 96 100	16384 16641 16900 19600 17424 18225 15625 16900 17424 18225	6400 7921 8100 9025 9261 8836 6400 10000 9216 10000	10240 11481 11700 13300 12672 12690 10000 13000 12672 13500
$\mathit{\Sigma }\mathit{X}$=1316	$\mathit{\Sigma }\mathit{Y}$=920	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=173348	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=85159	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=121255

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{\mathit{}N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{10\times 121255-1316\times 920}{\sqrt{10\times 173348-{\left(1316\right)}^2}\sqrt{10\times 85159-{\left(920\right)}^2}} \\ \mathrm{or},r=\frac{1830}{40.29\times 72.04} \\ \Rightarrow r=0.63 \end{gathered}$$

Thus, the correlation coefficient between the values of X and Y is 0.63.