Question

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

x	y
5	10.7
6	11.76
7	9.72
8	10.78
9	13.94
10	13.3
11	13.06
12	15.12
13	16.68
14	14.84
15	15.1
16	17.96

Answer 1

Solution:

X	Y	XY	X^2	Y^2
5	10.7	53.5	25	114.49
6	11.76	70.56	36	138.2976
7	9.72	68.04	49	94.4784
8	10.78	86.24	64	116.2084
9	13.94	125.46	81	194.3236
10	13.3	133	100	176.89
11	13.06	143.66	121	170.5636
12	15.12	181.44	144	228.6144
13	16.68	216.84	169	278.2224
14	14.84	207.76	196	220.2256
15	15.1	226.5	225	228.01
16	17.96	287.36	256	322.5616

n	12
sum(XY)	1800.36
sum(X)	126.00
sum(Y)	162.96
sum(X^2)	1466.00
sum(Y^2)	2282.89
Numerator	1071.36
Denominator	1199.65
r	0.8931
r square	0.7976
Xbar(mean)	10.5000
Ybar(mean)	13.5800
SD(X)	1.7078
SD(Y)	1.4915
b	0.6243
a	7.0245

r = 0.893