In: Math
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.
Covariance formula:
N : Sample Size
Y |
Y-![]() |
(Y-![]() |
X |
X-![]() |
(X-![]() |
(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 |
![]() |
![]() |
![]() |
![]() |
![]() |
||
Mean |
![]() |
![]() |
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 : rX,Y
Sample Correlation = 0.345269671
As correlation is positive and less than 0.5 ; which interprets into a weak positive correlation