Question

Based on the data shown below, calculate the correlation coefficient (rounded to three decimal places)

x	y
1	8.32
2	12.24
3	11.46
4	15.78
5	20.2
6	20.42
7	23.94
8	27.96
9	27.48
10	31.5
11	33.82
12	38.24

Answer 1

Solution:

X	Y	XY	X^2	Y^2
1	8.32	8.32	1	69.2224
2	12.24	24.48	4	149.8176
3	11.46	34.38	9	131.3316
4	15.78	63.12	16	249.0084
5	20.2	101	25	408.04
6	20.42	122.52	36	416.9764
7	23.94	167.58	49	573.1236
8	27.96	223.68	64	781.7616
9	27.48	247.32	81	755.1504
10	31.5	315	100	992.25
11	33.82	372.02	121	1143.7924
12	38.24	458.88	144	1462.2976

n	12
sum(XY)	2138.30
sum(X)	78.00
sum(Y)	271.36
sum(X^2)	650.00
sum(Y^2)	7132.77
Numerator	4493.52
Denominator	4529.71
r	0.9920
r square	0.9841
Xbar(mean)	6.5000
Ybar(mean)	22.6133
SD(X)	1.7078
SD(Y)	4.4978
b	2.6186
a	5.5924

r = 0.992