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 (data336.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       44.898  39      Large
2       85.8585 122     Small
3       37.6708 100     Small
4       44.1095 168     Small
5       47.756  25      Large
6       40.8481 22      Small
7       50.5179 27      Large
8       63.4659 70      Large
9       37.2126 86      Large
10      66.0707 95      Small
11      53.5897 56      Large
12      42.5586 18      Small
13      50.3493 129     Small
14      60.3041 75      Large
15      46.2348 93      Large
16      56.1494 23      Large
17      45.4136 15      Large
18      40.9541 44      Small
19      55.3183 26      Large
20      50.7934 58      Large
21      41.2603 79      Large
22      37.3516 19      Small
23      42.1137 30      Large
24      60.4141 88      Small
25      51.9331 119     Large
26      49.6191 20      Small
27      53.1292 116     Small
28      60.8961 62      Large
29      51.3743 31      Large
30      52.4964 42      Large
31      47.748  102     Small
32      47.1194 90      Large
33      60.6775 99      Large
34      70.5214 21      Small
35      39.4673 164     Large
36      50.4703 83      Large
37      66.2801 100     Large
38      62.3078 185     Small
39      43.79   18      Large
40      54.1258 56      Small
41      39.0053 174     Small
42      52.4289 59      Small
43      57.6612 89      Large
44      51.6591 17      Small
45      50.383  73      Large
46      38.2104 40      Small
47      52.421  78      Large
48      45.5227 55      Large
49      62.5477 53      Small
50      43.9493 58      Large
51      76.2546 87      Large
52      56.4322 110     Large
53      37.8525 64      Large
54      37.132  47      Small
55      50.4954 84      Small
56      49.1702 54      Large
57      41.8979 16      Small
58      45.3906 40      Large
59      57.8986 41      Small
60      40.3537 34      Large

Answer 1

Independent variable (X): LOS

Dependent variable (Y): Wages

Following is the scatterplot:

(b)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.183202781
R Square	0.033563259
Adjusted R Square	0.016900557
Standard Error	10.01663268
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	202.0980776	202.0980776	2.014274646	0.161177875
Residual	58	5819.309956	100.3329303
Total	59	6021.408034
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	47.84469954	2.469489932	19.3743246	5.23732E-27	42.90147841	52.78792067
los, X	0.043824151	0.030878356	1.419251439	0.161177875	-0.01798559	0.105633894

The regression line is

wages = 47.8447+0.0438*LOS

The test statistics is:

t = 1.419

p=0.1612

(c)

The slope is: 0.0438

That is for each unit increase LOS, wages increased by 0.0438 units.

(d)

The 95% confidence interval for slope is (-0.0180, 0.1056).