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 (data408.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.
( ____ , ____ )

work# wages     los     size
1       69.2413 34      Large
2       40.0111 19      Small
3       70.6251 194     Small
4       49.3129 29      Small
5       55.6213 80      Large
6       44.6338 42      Small
7       39.6074 20      Large
8       49.9032 50      Large
9       39.5058 139     Large
10      60.0777 110     Small
11      47.509  39      Large
12      51.8078 36      Small
13      55.3064 140     Small
14      38.8426 144     Large
15      59.1806 29      Large
16      50.1731 109     Large
17      44.784  35      Large
18      37.8216 103     Small
19      60.3116 123     Large
20      80.9877 137     Large
21      50.576  18      Large
22      46.3306 91      Small
23      47.9091 69      Large
24      58.5582 85      Small
25      63.9038 74      Large
26      44.5448 34      Small
27      49.5359 85      Small
28      48.9933 56      Large
29      57.1764 130     Large
30      52.9005 38      Large
31      63.7324 35      Small
32      37.9304 49      Large
33      39.3526 55      Large
34      64.5674 116     Small
35      61.2771 29      Large
36      46.991  113     Large
37      74.5818 55      Large
38      41.5655 22      Small
39      51.3884 71      Large
40      40.896  47      Small
41      40.7185 45      Small
42      57.1712 70      Small
43      42.7096 90      Large
44      49.8057 132     Small
45      38.0929 30      Large
46      41.3269 30      Small
47      64.3603 50      Large
48      53.1662 129     Large
49      39.1688 30      Small
50      55.8157 99      Large
51      63.1372 43      Large
52      62.6847 30      Large
53      46.9151 47      Large
54      80.2559 168     Small
55      51.5097 53      Small
56      57.0483 151     Large
57      85.3793 76      Small
58      68.0978 69      Large
59      45.4022 73      Small
60      58.0315 33      Large

Answer 1

a)

There is no linear relationship between wages and LOS.Linear regression might not be most appropriate.

b)

wages = 47.40627 + 0.07950 los

t = -3.2807

p value = 0.001643

c)

SINCE P VALUE FOR THE SLOPE IS < 0.05.WE REJECT H_0.Therefore we conclude that the there is a significant difference in relationship between wages and level of service.

d)

95 percent confidence interval:
(-30.645576 , -7.462001)

R CODE AND OUTPUT: