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 (data45.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.

As increase 1 unit in the independent variable (wages), the average change in the dependent variable (Los) is ??//.

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope.
(  ,  )

worker  wages   los     size
1       37.3992 63      Large
2       64.7929 102     Small
3       38.495  38      Small
4       66.1083 124     Small
5       38.6552 102     Large
6       52.1579 39      Small
7       46.307  70      Large
8       45.7795 41      Large
9       43.4066 59      Large
10      71.3603 32      Small
11      45.8326 84      Large
12      46.8145 31      Small
13      40.8481 19      Small
14      58.1816 152     Large
15      49.0047 153     Large
16      65.035  147     Large
17      57.275  32      Large
18      58.6007 139     Small
19      47.7213 93      Large
20      59.5509 73      Large
21      48.8784 83      Large
22      66.2058 19      Small
23      60.7252 34      Large
24      50.6957 40      Small
25      41.0456 20      Large
26      46.4612 68      Small
27      42.5717 117     Small
28      42.7551 16      Large
29      40.3404 36      Large
30      37.1373 27      Large
31      94.0428 19      Small
32      64.1811 27      Large
33      65.1248 95      Large
34      39.5958 85      Small
35      50.6298 114     Large
36      85.5969 82      Large
37      44.2446 43      Large
38      40.3853 89      Small
39      54.0249 73      Large
40      41.7716 84      Small
41      53.0517 70      Small
42      71.1145 77      Small
43      100.6858        25      Large
44      56.1299 65      Small
45      42.312  97      Large
46      44.9882 27      Small
47      44.392  73      Large
48      43.9313 144     Large
49      43.1781 70      Small
50      80.845  144     Large
51      48.5315 133     Large
52      74.1724 87      Large
53      38.8199 95      Large
54      56.2838 44      Small
55      46.4557 173     Small
56      38.1081 87      Large
57      72.9656 44      Small
58      49.6886 67      Large
59      41.4145 23      Small
60      61.6381 27      Large

Answer 1

a)

wages 120 100 80 60 E 0 0 20 40 60 80 100 120 140 160 180 200 40 20

linear regression does not seem appropriate

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.0295
R Square	0.0009
Adjusted R Square	-0.0164
Standard Error	14.4096
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10.4846	10.4846	0.0505	0.8230
Residual	58	12042.9503	207.6371
Total	59	12053.4349
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	54.0444	3.7706	14.3333	0.0000	46.4968	61.5920
los	-0.0102	0.0454	-0.2247	0.8230	-0.1010	0.0806

y^ = 54.0444 - 0.0102 x

t = -0.2247

P = 0.8230

c)

As increase 1 unit in the independent variable (wages), the average change in the dependent variable (Los) is 0.0102 less

d)

95% confidence interval of slope = (-0.1010,0.0806)