Question

Calculate the correlation coefficient for the following data.

X	25	18	21	24	27	30	36	39	42	48
Y	26	35	48	28	20	36	25	40	43	39

Answer 1

X	Y	x = `"X" - bar"X"`	y = `"Y" - bar"Y"`	x2	y2	xy
25	26	−6	−8	36	64	48
18	35	−13	1	169	1	−13
21	48	−10	14	100	196	−140
24	28	−7	−6	49	36	42
27	20	−4	−14	16	196	56
30	36	−1	2	1	4	−2
36	25	5	−9	25	81	−45
39	40	8	6	64	36	48
42	43	11	9	121	81	99
45	39	17	5	289	25	85
310	340	0	0	870	720	178

N = 10, ΣX = 310, ΣY = 340, Σx² = 870, Σy² = 720, Σxy = 178

`bar"X" = (sum"X")/"N" = 310/10` = 31

`bar"Y" = (sum"Y")/"N" = 340/10` = 34

Correlation coefficient

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

= `178/sqrt(870 xx 720)`

= `175/sqrt626400`

= `178/791.5`

= 0.225