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 (data481.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.
( _______ ,________ )

Answer all questions please

thank you

worker  wages   los     size
1       46.2755 117     Large
2       47.091  80      Small
3       47.8511 16      Small
4       59.5874 43      Small
5       38.4633 120     Large
6       71.1974 201     Small
7       38.8608 95      Large
8       50.6896 80      Large
9       56.9853 22      Large
10      45.4327 150     Small
11      58.0542 54      Large
12      55.6568 47      Small
13      54.9525 22      Small
14      55.8058 37      Large
15      53.6052 173     Large
16      60.9977 19      Large
17      49.5071 106     Large
18      55.4894 168     Small
19      45.1547 31      Large
20      51.0904 90      Large
21      82.706  53      Large
22      40.0094 85      Small
23      39.7198 78      Large
24      40.4793 130     Small
25      55.226  23      Large
26      67.7592 70      Small
27      37.2332 154     Small
28      62.0567 59      Large
29      48.24   54      Large
30      38.2374 57      Large
31      49.9539 75      Small
32      49.698  95      Large
33      42.1205 131     Large
34      65.2506 42      Small
35      43.5929 41      Large
36      40.8412 62      Large
37      44.0662 147     Large
38      79.6358 33      Small
39      37.1909 56      Large
40      37.3583 172     Small
41      52.1068 108     Small
42      41.5689 39      Small
43      59.9547 59      Large
44      46.6482 136     Small
45      55.733  73      Large
46      43.977  180     Small
47      37.4567 20      Large
48      40.3858 49      Large
49      43.2735 107     Small
50      49.7031 100     Large
51      43.4421 180     Large
52      50.0051 83      Large
53      48.7011 247     Large
54      55.1619 102     Small
55      45.6669 83      Small
56      53.5955 105     Large
57      39.6164 114     Small
58      67.3802 62      Large
59      60.3648 93      Small
60      65.0431 37      Large

Answer 1

(a)

Scatter plot is as follows:

Scatter plot shows a negative and weak relationship between the variables.

(b)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.239415012
R Square	0.057319548
Adjusted R Square	0.041066437
Standard Error	10.21464184
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	367.9701036	367.9701036	3.526681573	0.065418999
Residual	58	6051.656655	104.3389078
Total	59	6419.626759
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	54.96476367	2.611450437	21.04759979	7.73053E-29	49.73737771	60.19214962
los	-0.048238902	0.025687054	-1.8779461	0.065418999	-0.099657126	0.003179322

The regression equation is:

wages = 54.965 - 0.048*LOS

(c)

Slope is negative. It shows that relationship between the variables is negative.

(d)

The 95% confidence interval for slope is

(-0.0997, 0.0032)