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Math · Statistics And Probability
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We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data379.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

worker  wages   los     size
1       54.4613 30      Large
2       52.7393 110     Small
3       45.9115 76      Small
4       43.5295 144     Small
5       48.4452 61      Large
6       53.7807 75      Small
7       63.4868 58      Large
8       55.2116 63      Large
9       57.6446 18      Large
10      43.2612 45      Small
11      87.5154 94      Large
12      53.0302 80      Small
13      57.1185 57      Small
14      61.2144 34      Large
15      55.766  117     Large
16      66.1595 24      Large
17      39.2468 41      Large
18      60.0683 96      Small
19      68.511  82      Large
20      39.2701 58      Large
21      41.5162 37      Large
22      55.8349 82      Small
23      49.007  90      Large
24      53.7416 167     Small
25      60.9611 98      Large
26      44.1704 124     Small
27      47.8212 23      Small
28      57.4494 21      Large
29      47.3613 130     Large
30      55.9022 175     Large
31      50.0523 84      Small
32      40.9557 70      Large
33      45.676  161     Large
34      55.7805 66      Small
35      37.6204 27      Large
36      50.3576 70      Large
37      38.2685 124     Large
38      55.6212 29      Small
39      50.0847 98      Large
40      62.764  70      Small
41      49.2139 23      Small
42      44.3    30      Small
43      46.0242 24      Large
44      49.7365 18      Small
45      61.2013 94      Large
46      38.3156 30      Small
47      47.5204 59      Large
48      48.9575 66      Large
49      53.7066 162     Small
50      62.5156 32      Large
51      37.7046 40      Large
52      55.8543 98      Large
53      64.3595 35      Large
54      63.7467 131     Small
55      47.2419 19      Small
56      56.4977 116     Large
57      43.1879 35      Small
58      48.7729 18      Large
59      47.7014 146     Small
60      54.3443 74      Large

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

Wages = +  LOS
t =
P =

(c) State carefully what the slope tells you about the relationship between wages and length of service.

(d) Give a 95% confidence interval for the slope.
(  ,  )

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