Question

x	10	8	13	9	11	14	6	4	12	7	5
y	9.14	8.13	8.75	8.76	9.26	8.09	6.13	3.11	9.13	7.26	4.73

b. Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

The linear correlation coefficient is r =?

Answer 1

Solution:

X	Y	XY	X^2	Y^2
10	9.14	91.4	100	83.5396
8	8.13	65.04	64	66.0969
13	8.75	113.75	169	76.5625
9	8.76	78.84	81	76.7376
11	9.26	101.86	121	85.7476
14	8.09	113.26	196	65.4481
6	6.13	36.78	36	37.5769
4	3.11	12.44	16	9.6721
12	9.13	109.56	144	83.3569
7	7.26	50.82	49	52.7076
5	4.73	23.65	25	22.3729

n	11
sum(XY)	797.40
sum(X)	99.00
sum(Y)	82.49
sum(X^2)	1001.00
sum(Y^2)	659.82
Numerator	604.89
Denominator	740.69
r	0.8167
r square	0.6669
Xbar(mean)	9.0000
Ybar(mean)	7.4991
SD(X)	2.1148
SD(Y)	0.4490
b	0.4999
a	2.9999

The linear correlation coefficient is r = 0.8167.