Question

Calculate Karl Pearson’s coefficient of correlation between x and y for the following data and interpret the result: 
(1, 6), (2, 5), (3, 7), (4, 9), (5, 8), (6, 10), (7, 11), (8, 13), (9, 12)

Answer 1

Here n = 9, `barx = (45)/(9) = 5, bary = (81)/(9) = 9`

x	y	`x - barx`	`y - bary`	`(x - barx)^2`	`(y - bary)^2`	`(x - barx) (y - bary`
1	6	- 4	- 3	16	9	12
2	5	- 3	- 4	9	16	12
3	7	- 2	- 2	4	4	4
4	9	- 1	0	1	0	0
5	8	0	- 1	0	1	0
6	10	1	1	1	1	1
7	11	2	2	4	4	4
8	13	3	3	9	16	12
9	12	4	4	16	9	12
∑x = 45	∑y = 81			∑`(x -barx)^2` = 60	∑`(y -bary)^2` = 60	∑`(x -barx) (y -bary)` = 57

 

r = `(∑(x - barx) (y - bary))/(sqrt(∑(x - barx)^2)  sqrt(∑(y -bary)^2)) = 57/(sqrt60 sqrt60) =  (57)/(60) = 0.95`

x	y	u = x - 17	v = y - 19	u2	v2	uv
20	17	3	- 2	9	4	- 6
13	12	- 4	- 7	16	49	28
18	23	1	4	1	16	4
21	25	4	6	16	36	24
11	14	- 6	- 5	36	25	30
12	8	- 5	- 11	25	121	55
17	19	0	0	0	0	0
14	21	- 3	2	9	4	- 6
19	22	2	3	4	9	6
15	19	- 2	0	4	0	0
		∑u = -10	∑v = -10	∑u2 = 120	∑v2 = 264	∑uv = 135