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 again a month later.
First Test Second Test
50...........58
35...........46
15...........40
64...........76
53..........62
18..........39
40..........57
24.............41
16.............31
67............75
46............62
64............64
32............54
71............65
16..........51
(a) Would you expect the scores to be associated?
(b) Make a scatterplot of these data, with the first test along the x-axis. Describe the relationship, if any.
(c) On the basis of the correlation, if an employee scores two SDs above the mean on the frst 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?