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 (data162.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.

Data Set:

worker  wages   los     size
1       42.3078 40      Large
2       44.0121 36      Small
3       46.122  51      Small
4       45.1671 28      Small
5       46.2362 18      Large
6       49.1255 43      Small
7       62.8503 70      Large
8       56.8422 27      Large
9       54.4156 42      Large
10      53.6614 34      Small
11      63.2144 148     Large
12      46.0673 21      Small
13      78.7749 99      Small
14      63.1945 52      Large
15      43.0515 58      Large
16      71.653  65      Large
17      54.0349 65      Large
18      37.814  73      Small
19      48.5537 55      Large
20      74.7885 103     Large
21      37.5076 95      Large
22      94.457  26      Small
23      59.3541 35      Large
24      37.7513 137     Small
25      56.1559 105     Large
26      65.174  110     Small
27      52.3183 111     Small
28      66.1117 64      Large
29      39.0966 27      Large
30      51.9956 74      Large
31      68.0974 59      Small
32      63.6235 29      Large
33      37.023  79      Large
34      44.9522 90      Small
35      46.7601 62      Large
36      49.0779 91      Large
37      41.1978 112     Large
38      68.2986 27      Small
39      48.9625 173     Large
40      51.6892 18      Small
41      68.4352 67      Small
42      71.5281 46      Small
43      56.7601 42      Large
44      55.8925 27      Small
45      62.2866 113     Large
46      49.8865 31      Small
47      58.8308 48      Large
48      44.7858 49      Large
49      57.2444 152     Small
50      60.0774 31      Large
51      44.075  41      Large
52      56.9571 18      Large
53      53.2775 42      Large
54      60.224  93      Small
55      55.9754 90      Small
56      40.8347 32      Large
57      55.0511 174     Small
58      51.142  59      Large
59      50.4712 38      Small
60      56.0068 19      Large

Answer 1

a) The plot of wages versus LOS is

From the scatter plot, it can be seen that there is no linear relationship between wages and LOS.

b) Using the Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

The least square line is :

wages = 54.32 + 0.0031 los

To test the significance of the slope,

The value of the test statistic

P-value = 0.934

Since P-value > 0.05, so at 5% level of significance we can conclude that the slope is not significantly different from 0.

c) Interpretation of slope : For a 1 month increase in LOS, wages will increase by 0.0031 unit.

d) a 95% confidence interval for the slope