Question

Calculate the correlation coefficient for the following data.

X	5	10	5	11	12	4	3	2	7	1
Y	1	6	2	8	5	1	4	6	5	2

Answer 1

X	Y	x = `"X" - bar"X"` = X − 6	y = `"Y" - bar"Y"` = Y − 4	x2	y2	xy
5	1	− 1	− 3	1	9	3
10	6	4	2	16	4	8
5	2	− 1	− 2	1	4	2
11	8	5	4	25	16	20
12	5	6	1	36	1	6
4	1	− 2	− 3	4	9	6
3	4	− 3	0	9	0	0
2	6	− 4	2	16	4	− 8
7	5	1	1	1	1	1
1	2	− 5	− 2	25	4	10
60	40	0	0	134	52	48

N = 10, ∑X = 60, ∑Y = 40, ∑x² = 134, ∑y² = 52, ∑xy = 48, `bar"X" = (sum"X")/"N" = 60/10` = 6, `bar"Y" = (sum"Y")/"N" = 40/10` = 4.

Coefficient of correlation

r = `(sum"xy")/(sqrt(sum"x"^2 sum"y"^2))`, Where x = `"X" - bar"X"`, y = `"Y" - bar"Y"`

r = `48/sqrt (134 xx 52)`

r = 0.575