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 (data1.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. This answer has not been graded yet.

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

worker  wages   los     size
1       40.3113 27      Large
2       55.107  27      Small
3       38.1058 74      Small
4       57.7219 83      Small
5       46.6771 27      Large
6       64.063  58      Small
7       65.6169 87      Large
8       73.3311 42      Large
9       61.8764 62      Large
10      52.0509 92      Small
11      78.268  134     Large
12      58.1432 59      Small
13      51.496  68      Small
14      55.2003 72      Large
15      52.1955 128     Large
16      42.2665 113     Large
17      48.5818 96      Large
18      49.8846 51      Small
19      39.0531 56      Large
20      40.1526 117     Large
21      74.4147 76      Large
22      45.492  22      Small
23      39.3931 57      Large
24      37.4409 25      Small
25      66.5625 60      Large
26      38.8955 75      Small
27      70.8136 55      Small
28      39.0265 51      Large
29      78.9962 37      Large
30      44.2759 26      Large
31      39.0486 96      Small
32      79.9377 22      Large
33      38.7287 19      Large
34      42.7196 58      Small
35      51.7346 173     Large
36      50.1328 51      Large
37      52.5434 60      Large
38      72.3328 60      Small
39      37.8399 17      Large
40      79.01   98      Small
41      39.8978 93      Small
42      37.1881 61      Small
43      63.8586 21      Large
44      40.4427 128     Small
45      46.6364 53      Large
46      48.2918 46      Small
47      81.2156 140     Large
48      72.4205 20      Large
49      62.0451 125     Small
50      39.365  99      Large
51      69.575  43      Large
52      44.5857 70      Large
53      45.8328 99      Large
54      57.3187 89      Small
55      46.0313 28      Small
56      65.1028 68      Large
57      37.0506 129     Small
58      70.767  80      Large
59      50.7659 112     Small
60      61.0656 103     Large

Answer 1

a) The scatter plot of wages versus LOS is

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

The least-squares line is

Testing the significance for the slope,

The value of the test statistic t = 0.23

and P-value = 0.817

since p-value >0.05 , so at 5% level of significance, we can conclude that slope is not statistically significant.

d) a 95% confidence interval for the slope