Question

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.02α=0.02. You have the following bivariate data set.

x	y
67.7	89.8
52.3	93.4
62.3	62.7
61.3	66.5
52.1	64
51.1	16.3
59.9	44.2
49.1	83
53.6	50.3
58.8	65.4
42.8	77.4

What is the correlation coefficient for this data set?
r =

Answer 1

Solution =

X	Y	XY	X^2	Y^2
67.7	89.8	6079.46	4583.29	8064.04
52.3	93.4	4884.82	2735.29	8723.56
62.3	62.7	3906.21	3881.29	3931.29
61.3	66.5	4076.45	3757.69	4422.25
52.1	64	3334.4	2714.41	4096
51.1	16.3	832.93	2611.21	265.69
59.9	44.2	2647.58	3588.01	1953.64
49.1	83	4075.3	2410.81	6889
53.6	50.3	2696.08	2872.96	2530.09
58.8	65.4	3845.52	3457.44	4277.16
42.8	77.4	3312.72	1831.84	5990.76

n	11
sum(XY)	39691.47
sum(X)	611.00
sum(Y)	713.00
sum(X^2)	34444.24
sum(Y^2)	51143.48
Numerator	963.17
Denominator	17369.78
r	0.0555
r square	0.0031

The correlation coefficient is,

r =  0.0555

Answer :   The correlation coefficient r is 0.0555