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 (data493.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.

This answer has not been graded yet.

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

worker  wages   los     size
1       44.4711 150     Large
2       45.2146 21      Small
3       74.8957 123     Small
4       72.0558 80      Small
5       39.0496 83      Large
6       47.9774 73      Small
7       51.2293 86      Large
8       69.0781 179     Large
9       39.2668 39      Large
10      53.424  125     Small
11      51.8895 50      Large
12      42.1108 67      Small
13      50.9806 86      Small
14      41.6564 26      Large
15      64.8102 138     Large
16      38.3316 30      Large
17      70.1092 31      Large
18      59.5725 22      Small
19      72.6489 97      Large
20      48.6928 129     Large
21      65.3321 34      Large
22      46.696  56      Small
23      42.9948 100     Large
24      63.7128 106     Small
25      54.0511 170     Large
26      37.2906 56      Small
27      58.9101 44      Small
28      80.6583 206     Large
29      82.063  63      Large
30      68.5583 114     Large
31      48.3471 97      Small
32      43.8155 109     Large
33      58.983  16      Large
34      37.3826 23      Small
35      68.8845 63      Large
36      55.8785 167     Large
37      60.7873 46      Large
38      43.4198 16      Small
39      47.1446 77      Large
40      44.8549 121     Small
41      65.4524 29      Small
42      45.9087 72      Small
43      46.2893 28      Large
44      65.7419 114     Small
45      44.6151 37      Large
46      89.5987 173     Small
47      50.201  25      Large
48      79.3444 55      Large
49      44.7124 62      Small
50      41.2526 63      Large
51      67.4239 138     Large
52      80.865  51      Large
53      50.7154 86      Large
54      40.1463 165     Small
55      56.4553 29      Small
56      49.2739 82      Large
57      58.4318 17      Small
58      58.0383 127     Large
59      52.917  71      Small
60      62.8699 28      Large

Answer 1

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 (data493.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.

1. 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.)

The plot shows linear regression may be appropriate.

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

Wages =	50.1573+  0.0688*LOS
t =	2.0246
P =	0.0475

(c) State carefully what the slope tells you about the relationship between wages and length of service.

When LOS increases by 1, the wages increases by 0.0688.

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope. ( 0.0008 ,  0.1367)

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.2569
R Square	0.0660
Adjusted R Square	0.0499
Standard Error	12.7439
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	665.7099	665.7099	4.0990	0.0475
Residual	58	9419.5636	162.4063
Total	59	10085.2736
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	50.1573	3.1622	15.8617	0.0000	43.8276	56.4871
los	0.0688	0.0340	2.0246	0.0475	0.0008	0.1367