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 (data81.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 =49.445 X+.033 xLOS t1.026 P= .9370 X 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. 122 X029 X
worker     wages   los     size
1       52.6227 21      Large
2       85.865  96      Small
3       61.7581 65      Small
4       43.6764 173     Small
5       58.733  50      Large
6       38.0873 35      Small
7       38.3659 58      Large
8       59.8889 217     Large
9       62.6846 73      Large
10      43.9656 165     Small
11      69.9273 35      Large
12      52.5823 56      Small
13      46.2363 55      Small
14      40.7646 42      Large
15      45.2743 97      Large
16      52.1446 63      Large
17      40.6916 110     Large
18      73.5716 84      Small
19      71.0977 71      Large
20      52.4982 41      Large
21      58.2381 51      Large
22      39.946  59      Small
23      68.2779 57      Large
24      42.218  38      Small
25      37.6418 22      Large
26      68.1612 38      Small
27      40.5873 70      Small
28      41.3186 15      Large
29      47.9942 37      Large
30      59.675  23      Large
31      42.2016 74      Small
32      51.377  25      Large
33      37.0009 37      Large
34      55.0705 27      Small
35      38.7997 58      Large
36      53.5787 117     Large
37      60.5641 96      Large
38      61.5776 130     Small
39      80.3828 31      Large
40      41.2036 144     Small
41      47.2496 22      Small
42      57.3456 220     Small
43      54.7329 17      Large
44      63.6953 67      Small
45      39.7028 70      Large
46      52.3268 79      Small
47      39.5428 53      Large
48      40.9618 23      Large
49      51.7874 41      Small
50      59.6523 66      Large
51      61.821  125     Large
52      37.1176 163     Large
53      48.1185 112     Large
54      59.1087 93      Small
55      55.0849 110     Small
56      39.8561 39      Large
57      39.0544 90      Small
58      38.5323 31      Large
59      80.3674 39      Small
60      72.6657 97      Large

Answer 1

(a)

Following is the scatter plot of the data :

250 200 ” 150 100 50 0 100 20 0 40 80 60 LOS

Scatter plot shows a week positive relationship between the variables.

(b)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.044173274
R Square	0.001951278
Adjusted R Square	-0.015256458
Standard Error	12.56272919
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	17.89630688	17.89630688	0.113395396	0.737526589
Residual	58	9153.685555	157.8221647
Total	59	9171.581862
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	51.74870241	2.960962463	17.47698698	8.73836E-25	45.82169212	57.67571269
los	0.011604998	0.034462545	0.336742329	0.737526589	-0.057379281	0.080589277

Regression equation is

wages = 51.749+0.012* LOS

t = 0.34

p= 0.7375

P-value is greater than 0.05 so model is not significant.

(c)

For each unit increase in LOS , wages increased by 0.012 units.

(d)

The confidence interval for slope is :

(-0.057, 0.081)