Question

3) The following observations are given for two variables.

Y: 5,8,18,20,22,30,10,7

X:2,12,3,6,11,19,18,9

Compute and interpret the sample covariance for the above data.

Compute the standard deviation for x.

Compute the standard deviation for y.

Compute and interpret the sample correlation coefficient.

Answer 1

Covariance formula:

N : Sample Size

	Y	Y-	(Y-)2	X	X-	(X-)2	(X-X)(Y-Y)
	5	-10	100	2	-8	64	80
	8	-7	49	12	2	4	-14
	18	3	9	3	-7	49	-21
	20	5	25	6	-4	16	-20
	22	7	49	11	1	1	7
	30	15	225	19	9	81	135
	10	-5	25	18	8	64	-40
	7	-8	64	9	-1	1	8
Total	=120		=546	=80		=280	=135
Mean	=120/8=15			=80/8=10

As the covariance is positive , when Y increases X also increases.

Standard deviation of X

Standard deviation of X = 6.32455532

Standard deviation of Y

Standard deviation of Y = 8.831760866

Sample Correlation : r_X,Y

Sample Correlation = 0.345269671

As correlation is positive and less than 0.5 ; which interprets into a weak positive correlation