Question

Here is a bivariate data set.

x	y
77.2	35
84	32.8
68.1	34.9
81	27.8
91.3	25.6
79.9	30.1
80.9	30
90.3	27.1
69.3	29.3
73.3	34.3
86	31

Find the correlation coefficient and report it accurate to three decimal places.
r =

Answer 1

Solution:

X	Y	XY	X^2	Y^2
77.2	35	2702	5959.84	1225
84	32.8	2755.2	7056	1075.84
68.1	34.9	2376.69	4637.61	1218.01
81	27.8	2251.8	6561	772.84
91.3	25.6	2337.28	8335.69	655.36
79.9	30.1	2404.99	6384.01	906.01
80.9	30	2427	6544.81	900
90.3	27.1	2447.13	8154.09	734.41
69.3	29.3	2030.49	4802.49	858.49
73.3	34.3	2514.19	5372.89	1176.49
86	31	2666	7396	961

n	11
sum(XY)	26912.77
sum(X)	881.30
sum(Y)	337.90
sum(X^2)	71204.43
sum(Y^2)	10483.45
Numerator	-1750.80
Denominator	2736.31
r	-0.6398
r square	0.4094
Xbar(mean)	80.1182
Ybar(mean)	30.7182
SD(X)	6.9973
SD(Y)	3.5274
b	-0.2669
a	52.1041

r = -0.640