Question

Find the coefficient of correlation for the following:

Cost (₹)	14	19	24	21	26	22	15	20	19
Sales (₹)	31	36	48	37	50	45	33	41	39

Answer 1

X	Y	x = `"X" - bar"X"` = X − 20	y = `"Y" - bar"Y"` = Y − 40	x2	y2	xy
14	31	− 6	− 9	36	81	54
19	36	− 1	− 4	1	16	4
24	48	4	8	16	64	32
21	37	1	− 3	1	9	− 3
26	50	6	10	36	100	60
22	45	2	5	4	25	10
15	33	− 5	− 7	25	49	35
20	41	0	1	0	1	0
19	39	− 1	− 1	1	1	1
180	360	0	0	120	346	193

N = 9, ∑X = 180, ∑Y = 360, ∑x² = 120, ∑y² = 346, ∑xy = 193, `bar"X" = (sum"X")/"N" = 180/9` = 20, `bar"Y" = (sum"Y")/"N" = 360/9` = 40.

Correlation coefficient (r) = `(sum"xy")/(sqrt(sum"x"^2 sum"y"^2))`

r = `193/sqrt (120 xx 346)`

r = 0.947