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 (data273.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.
(  ,  )

worker  wages   los     size
1       43.568  17      Large
2       52.6607 23      Small
3       70.8523 43      Small
4       43.7201 69      Small
5       51.8988 44      Large
6       42.3225 18      Small
7       62.5546 29      Large
8       58.7476 72      Large
9       44.6601 17      Large
10      78.9833 88      Small
11      60.296  43      Large
12      44.3857 80      Small
13      39.5727 77      Small
14      37.6197 38      Large
15      49.7127 59      Large
16      53.0313 132     Large
17      47.5339 39      Large
18      54.1061 33      Small
19      44.3957 17      Large
20      69.9525 157     Large
21      53.0409 123     Large
22      58.7758 135     Small
23      47.412  96      Large
24      59.739  73      Small
25      52.675  17      Large
26      71.6783 89      Small
27      38.1746 79      Small
28      64.7329 26      Large
29      45.5147 57      Large
30      67.9117 190     Large
31      59.5352 59      Small
32      58.4245 163     Large
33      41.4385 38      Large
34      38.785  77      Small
35      48.1772 38      Large
36      43.5119 77      Large
37      45.8749 35      Large
38      55.4921 32      Small
39      47.3276 100     Large
40      37.8443 80      Small
41      57.73   81      Small
42      39.8701 42      Small
43      47.139  274     Large
44      69.5487 81      Small
45      64.2888 25      Large
46      47.2218 114     Small
47      42.6698 78      Large
48      42.318  35      Large
49      39.2739 18      Small
50      46.7315 158     Large
51      58.1415 44      Large
52      49.9305 54      Large
53      66.114  156     Large
54      60.1283 40      Small
55      56.977  73      Small
56      57.5662 149     Large
57      51.684  49      Small
58      39.7218 43      Large
59      73.0966 74      Small
60      63.7039 63      Large

Answer 1

(a)

Independent variable (X): LOS

Dependent variable (Y): Wages

Following is the scatter plot of the data:

90 80 70 60 50 40 30 20 10 0 50 100 150 200 250 300 LOS Wages

Scatter plot shows the linear and positive relationship between the variables.

(b)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.212112429
R Square	0.044991682
Adjusted R Square	0.028526022
Standard Error	10.31218316
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	290.5723659	290.5723659	2.732455343	0.103731549
Residual	58	6167.785053	106.3411216
Total	59	6458.357419
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	49.49177494	2.341056732	21.1407841	6.15963E-29	44.80564079	54.17790909
los	0.044108384	0.026683612	1.653014018	0.103731549	-0.009304667	0.097521436

The regression line is

wages = 49.4918 + 0.0441*LOS

t = 1.653

p=0.1037

(c)

The slope is: 0.0441

That is for each unit increase LOS, wages decreased by 0.0441 units.

(d)

The 95% confidence interval for slope is (-0.0009, 0.0975).