Answer:
The given data is:
x = (2, 7, 6, 10, 9, 13, 11, 18)
y = (11, 21, 12, 25, 7, 12, 4, 7)
a. The formula used for Sample Covariance is:
where, is mean of X
and is mean of Y
Firstly calculating . We get,
= 9.5
= 12.375
Now, Putting all values in above formula. We get,
Sample Covariance = -8.64
b. Standard Deviation is the square root of sum of square of the distance of observation from the mean.
where, is mean of the distribution.
Using formula we get,
Standard deviation = 4.81
c. Using above formula we get,
Standard deviation = 7.21
d. Correlation Coefficient is calculate by using formula:
where, = Covariance of X and Y
= Standard Deviation of X
= Standard Deviation of Y
Putting all values in above formula, we get,
Correlation Coefficient = -0.25
<em>Correlation Coefficient tell us that X and Y has negative week relationship whereas Sample Covariance tell us that X and Y has negative relationship. It does not tell us strength of relationship.</em>