Calculation and Interpretation of Covariance, Correlation Coefficient, Probability and Test Statistics

Question 1
a. The covariance is calculated as shown below:
Xi Yi
5 20 -0.5 1.5 -0.75
3 23 -2.5 4.5 -11.25
7 15 1.5 -3.5 -5.25
9 11 3.5 -7.5 -26.25
2 27 -3.5 8.5 -29.75
4 21 -1.5 2.5 -3.75
6 17 0.5 -1.5 -0.75
8 14 2.5 -4.5 -11.25
= 44 148 Σ = -89
= 5.5 = 18.5
 Cov (x, y) = = -89/ 7 = -12.7143
The covariance between x and y variables indicates a negative relationship. In other
words, the salary decreases as the years of experience increases. The magnitude of the
covariance cannot be explained.
b. The negative covariance could be because the salaries are not adjusted upwards to reflect
the changing market values, hence the salaries become compressed over time.
c. The coefficient of correlation is calculated as:
= -0.9904
The variables x and y have a very strong negative relationship which means that as the
years of experience increase, the salary tends to decrease.