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 (data323.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.

here is the data set :

worker  wages   los     size
1       80.7641 70      Large
2       47.6952 153     Small
3       68.1211 140     Small
4       42.5447 95      Small
5       48.7555 67      Large
6       41.3497 57      Small
7       53.8695 86      Large
8       55.5691 22      Large
9       42.954  113     Large
10      38.8381 66      Small
11      62.0195 32      Large
12      49.806  57      Small
13      52.9859 15      Small
14      40.9619 77      Large
15      56.5876 60      Large
16      45.531  30      Large
17      47.4383 96      Large
18      44.2084 60      Small
19      51.6572 144     Large
20      70.5038 131     Large
21      38.2412 41      Large
22      38.7429 59      Small
23      46.3128 94      Large
24      68.4899 63      Small
25      71.0578 56      Large
26      51.4918 18      Small
27      38.1531 100     Small
28      54.2316 18      Large
29      45.8801 52      Large
30      49.1423 102     Large
31      45.3795 88      Small
32      70.3286 18      Large
33      51.6134 100     Large
34      83.4615 91      Small
35      37.6516 39      Large
36      56.9919 27      Large
37      50.6129 24      Large
38      47.5097 60      Small
39      44.0107 96      Large
40      39.905  92      Small
41      61.5252 45      Small
42      38.3112 110     Small
43      43.332  49      Large
44      47.0086 20      Small
45      37.0101 53      Large
46      70.9395 131     Small
47      42.971  26      Large
48      40.4821 107     Large
49      43.8952 63      Small
50      57.4178 51      Large
51      57.7934 43      Large
52      70.8782 44      Large
53      40.4416 53      Large
54      41.6311 30      Small
55      47.348  66      Small
56      45.9943 74      Large
57      45.7749 25      Small
58      53.1182 56      Large
59      47.113  55      Small
60      46.3262 19      Large

Answer 1

Our objective is to determine whether there exist a linear relationship between Wages and length of service. We have to test the assume that our wages will increase as we gain experience.

(a) Plotting the independent variable on the x-axis and dependent variable wages in the y-axis:

.

Running a linear regression on the given data, using excel, we get:

(b) We get the fitted regression equation:

Wages = Intercept + slope (Length of service)

= 49.745 + 0.017 (Length of service)

To test the significance of slope, the t test statistic is given by:

= 0.404

with p-value of the t test obtained as p =0.688 > 0.05; it implies that the slope is not significant.

(c) Here, the slope 0.017 implies that for every additional month of service, the wage is expected to increase by 0.017 units.

(d) The 95% confidence interval for slope can be obtained using the formula:

=

= (-0.066, 0.100)