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 (data17.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.
(  ,  )

Data set

worker  wages   los     size
1       37.5345 72      Large
2       51.6822 142     Small
3       46.3661 40      Small
4       66.8416 29      Small
5       59.3287 40      Large
6       49.5354 90      Small
7       40.2164 36      Large
8       72.7909 78      Large
9       40.9859 31      Large
10      37.9095 42      Small
11      44.1166 66      Large
12      47.4386 147     Small
13      71.6367 98      Small
14      51.1655 71      Large
15      48.0582 20      Large
16      57.5964 48      Large
17      52.1489 61      Large
18      55.2293 93      Small
19      47.1101 67      Large
20      54.4413 17      Large
21      72.2016 96      Large
22      62.3073 98      Small
23      41.2365 103     Large
24      67.4656 61      Small
25      44.4795 177     Large
26      42.6034 63      Small
27      75.7625 30      Small
28      50.8896 23      Large
29      53.8624 31      Large
30      50.2942 31      Large
31      50.5761 85      Small
32      42.5102 96      Large
33      48.5107 191     Large
34      59.3137 183     Small
35      58.4582 32      Large
36      52.774  85      Large
37      53.3811 138     Large
38      46.1748 34      Small
39      38.2847 49      Large
40      51.688  35      Small
41      49.1279 119     Small
42      52.0886 27      Small
43      45.8742 40      Large
44      43.513  43      Small
45      39.2122 102     Large
46      43.841  61      Small
47      50.739  56      Large
48      44.3547 50      Large
49      46.6934 50      Small
50      43.872  42      Large
51      55.3444 22      Large
52      39.7993 110     Large
53      45.8993 30      Large
54      55.8064 47      Small
55      37.0434 72      Small
56      42.4527 125     Large
57      48.82   34      Small
58      45.7257 151     Large
59      39.3364 62      Small
60      39.8045 17      Large

Answer 1

a)

wages 80 60 50 40 10 0 0 50 100 150 200 250 70 30 20

there does not appear a linear regression between LOS and wages

b)

Applying regression on above data:

wages =-50.197+(-0.002)*LOS

t =-0.065

p value=0.9487

c) slope tells us that per unit increase in LOS will decrease wages by 0.002 on average

d) 95% confidence interval for the slope = -0.058 , 0.054