Question

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

x	y
4	18.2
5	18.05
6	14.8
7	12.65
8	8.7
9	4.65
10	2.7

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Answer 1

Solution:

X	Y	XY	X^2	Y^2
4	18.2	72.8	16	331.24
5	18.05	90.25	25	325.8025
6	14.8	88.8	36	219.04
7	12.65	88.55	49	160.0225
8	8.7	69.6	64	75.69
9	4.65	41.85	81	21.6225
10	2.7	27	100	7.29

n	7
sum(XY)	478.85
sum(X)	49.00
sum(Y)	79.75
sum(X^2)	371.00
sum(Y^2)	1140.71
Numerator	-555.80
Denominator	564.34
r	-0.9849
r square	0.9700
Xbar(mean)	7.0000
Ybar(mean)	11.3929
SD(X)	1.7078
SD(Y)	4.8984
b	-2.8357
a	31.2429

r = -0.985