Question

Find the coefficient of correlation for the following data:

X	35	40	60	79	83	95
Y	17	28	30	32	38	49

Answer 1

X	Y	dx = X − 65	dy = Y − 32	dx2	dy2	dxdy
35	17	− 30	− 15	900	225	450
40	28	− 25	− 4	625	16	100
60	30	− 5	− 2	25	4	10
79	32	14	0	196	0	0
83	38	18	6	324	36	108
95	49	30	17	900	289	510
392	194	2	2	2970	570	1178

${\displaystyle \overline{\text{X}}=\frac{392}{6}}$ = 65.33

${\displaystyle \overline{\text{Y}}=\frac{194}{6}}$ = 32.33

Coefficient of correlation

r(X, Y) = ${\displaystyle \frac{\text{N}\sum \text{dxdy}-(\sum \text{dx})(\sum \text{dy})}{\sqrt{\text{N}\sum {\text{dx}}^2-{(\sum \text{dx})}^2}\times \sqrt{\text{N}\sum {\text{dy}}^2-{(\sum \text{dy})}^2}}}$

= ${\displaystyle \frac{6\left(1178\right)-2\left(2\right)}{\sqrt{6\left(2970\right)-4}\times \sqrt{6\left(570\right)-4}}}$

= ${\displaystyle \frac{7064}{\sqrt{17816}\times \sqrt{3416}}}$

= ${\displaystyle \frac{7065}{\left(133.48\right)\left(58.45\right)}}$

= ${\displaystyle \frac{7064}{7801.91}}$

= 0.906