Question

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 (data238.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.

(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.

worker  wages   los     size
1       39.7268 99      Large
2       47.9395 108     Small
3       50.0018 36      Small
4       56.5056 37      Small
5       39.9768 99      Large
6       42.1023 51      Small
7       68.3662 149     Large
8       62.1544 118     Large
9       45.573  151     Large
10      50.4117 83      Small
11      38.4135 53      Large
12      62.4993 40      Small
13      60.3019 58      Small
14      37.6291 26      Large
15      38.3317 104     Large
16      44.7494 158     Large
17      72.8137 58      Large
18      52.989  83      Small
19      73.2051 49      Large
20      39.127  113     Large
21      44.2316 59      Large
22      69.7851 40      Small
23      49.472  26      Large
24      38.5196 77      Small
25      46.0804 69      Large
26      59.7664 118     Small
27      55.661  115     Small
28      58.2214 28      Large
29      57.7969 39      Large
30      46.9105 44      Large
31      38.4955 56      Small
32      58.9224 110     Large
33      53.8302 82      Large
34      43.2473 58      Small
35      50.2706 84      Large
36      50.6164 20      Large
37      49.6558 93      Large
38      78.595  66      Small
39      82.6382 92      Large
40      75.3109 40      Small
41      49.842  131     Small
42      50.6961 61      Small
43      72.7987 38      Large
44      45.2429 101     Small
45      67.4423 121     Large
46      53.2089 102     Small
47      55.595  28      Large
48      63.0091 45      Large
49      60.6773 41      Small
50      44.6185 20      Large
51      39.0958 91      Large
52      63.4885 200     Large
53      54.8688 149     Large
54      53.0166 26      Small
55      42.1089 95      Small
56      71.9169 50      Large
57      61.4371 62      Small
58      50.6912 16      Large
59      53.9664 23      Small
60      39.0164 15      Large

Answer 1

(a)

A linear regression might not be appropriate between the two variables - LOS and Wages, because the data points are not linearly placed. They are randomly scattered.

(b) Wages = 54.156630 + (-0.005862) * LOS.
t = -0.161, p-value = 0.873

(c) If the length of service of a woman increases by 1 month, then her wages is likely to decrease by $0.01 approximately.

(d) 95% confidence interval for the slope = (-0.07867705, 0.06695344).

(Please round the above numbers to the required number of decimal places.)