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

`bar"X" = 392/6` = 65.33

`bar"Y" = 194/6` = 32.33

Coefficient of correlation

r(X, Y) = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/(sqrt("N"sum"dx"^2 - (sum"dx")^2) xx sqrt("N"sum"dy"^2 - (sum"dy")^2))`

= `(6(1178) - 2(2))/(sqrt(6(2970) - 4) xx sqrt(6(570) - 4))`

= `7064/(sqrt17816 xx sqrt3416)`

= `7065/((133.48) (58.45))`

= `7064/7801.91`

= 0.906