The slope for the correlation line when expressed in z-scores is r. Hence when formulated in z-scores, the absolute value of the slope is less than 1 unless the data lie along a single line. The data in this example are productivity measures used to grade 15 employees who work on an assembly line. Each employee was tested once, then a month later.
See table:
# 0f Employees First Test Second Test
1 50 58
2 35 46
3 15 40
4 64 76
5 53 62
6 18 39
7 40 57
8 24 41
9 16 31
10 67 75
11 46 62
12 64 64
13 32 54
14 71 65
15 16 51
TOTALS 611 821
(a) Would you expect the scores to be associated?
(b) Make a scatter plot of the data, with the first test along the x-axis. Describe the relationship if any?
(c) On the basis of correlation, if an employee scores two SDs above the mean of the first test, do you expect him or her to be so far above the mean on the second test?
(d) Find the employee with the highest score on the first test. The score for this employee is not the best on the second test. Does this relative decline mean the employee has become less productive, or can you offer an alternative reason for the relatively lower score?