Question

Find the coefficient of correlation for the following:

X	78	89	96	69	59	79	68	62
Y	121	72	88	60	81	87	123	92

Answer 1

X	Y	dx = X − 75	dy = Y − 90	dx2	dy2	dxdy
78	121	3	31	9	961	93
89	72	14	− 18	196	324	− 252
96	88	21	− 2	441	4	− 42
69	60	− 6	− 30	36	900	180
59	81	− 16	− 9	256	81	144
79	87	4	− 3	16	9	− 12
68	123	− 7	33	49	1089	− 231
62	92	− 13	2	169	4	− 26
600	724	0	4	1172	3372	− 146

N = 8, ΣX = 600, ΣY = 724, Σdx² = 1172, Σdy² = 3372, Σdxdy = − 146

Correlation coefficient

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

= `(8(-146) - 0(4))/(sqrt(8 xx 1172 - 0) sqrt(8 xx 3372 - 16))`

= `(-1168)/(96.83 xx 164.2)`

= − 0.0735