Question

In: Statistics and Probability

The following is a set of data from a sample of n = 11 items: X...

The following is a set of data from a sample of n = 11 items: X 8 6 9 4 7 11 13 5 10 16 19 Y 22 15 25 10 19 31 37 13 27 45 54 a. Calculate the covariance. b. Calculate the coefficient of correlation. c. Describe the relation between the two variables X and Y.

Expert Solution

X: 8 6 9 4 7 11 13 5 10 16 19

Y: 22 15 25 10 19 31 37 13 27 45 54

n = 11

= 9.8182

= 27.0909

a)

x	y	(x-xbar)	(y-ybar)	(x-xbar)*(y-ybar)
8	22	-1.8182	-5.0909	9.2562
6	15	-3.8182	-12.0909	46.1653
9	25	-0.8182	-2.0909	1.7107
4	10	-5.8182	-17.0909	99.4380
7	19	-2.8182	-8.0909	22.8017
11	31	1.1818	3.9091	4.6198
13	37	3.1818	9.9091	31.5289
5	13	-4.8182	-14.0909	67.8926
10	27	0.1818	-0.0909	-0.0165
16	45	6.1818	17.9091	110.7107
19	54	9.1818	26.9091	247.0744
			Total	641.1818

b)

Standard deviation of x = = 4.6652

Standard deviation of y = = 13.7510

The formula of the coefficient of correlation (r) is

c) r = 0.9995

There is a positive relation between x and y.

orchestra answered 2 years ago

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