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 (data297.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.
(  ,  )

data:

worker  wages   los     size
1       52.5003 32      Large
2       42.9112 20      Small
3       44.8013 22      Small
4       47.6345 66      Small
5       57.4056 47      Large
6       42.1011 85      Small
7       80.6868 145     Large
8       61.5946 110     Large
9       43.4947 114     Large
10      46.5104 100     Small
11      70.3836 38      Large
12      59.0304 67      Small
13      48.4712 138     Small
14      42.8046 98      Large
15      53.1633 57      Large
16      65.5307 38      Large
17      76.2445 52      Large
18      44.5201 33      Small
19      41.7859 46      Large
20      67.3025 51      Large
21      56.3646 97      Large
22      45.8435 62      Small
23      37.2773 18      Large
24      55.9512 65      Small
25      53.8214 75      Large
26      60.0009 62      Small
27      50.1449 49      Small
28      40.6285 88      Large
29      46.7619 16      Large
30      38.1294 57      Large
31      38.2563 53      Small
32      56.5517 23      Large
33      46.8022 73      Large
34      53.0068 27      Small
35      39.6801 33      Large
36      54.6719 193     Large
37      55.4562 44      Large
38      40.0471 90      Small
39      38.2987 134     Large
40      38.1887 137     Small
41      62.77   66      Small
42      57.0192 37      Small
43      54.1235 122     Large
44      38.6294 38      Small
45      73.5348 167     Large
46      41.8152 92      Small
47      54.049  90      Large
48      51.0795 25      Large
49      60.5716 68      Small
50      57.972  62      Large
51      52.8388 112     Large
52      47.4715 66      Large
53      61.9632 74      Large
54      65.7441 30      Small
55      41.1799 46      Small
56      49.2086 124     Large
57      41.9043 46      Small
58      53.8185 31      Large
59      52.6962 98      Small
60      57.4416 109     Large

Answer 1

a)

I think linear regression is not appropriate

as data looks very scattered

b)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.1168
R Square	0.0136
Adjusted R Square	-0.0034
Standard Error	10.2374
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	84.0780	84.0780	0.8022	0.3741
Residual	58	6078.7051	104.8053
Total	59	6162.7831
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	49.7182	2.7158	18.3070	0.0000	44.2819	55.15446517
los	0.0299	0.0334	0.8957	0.3741	-0.0370	0.096863944

y^= 49.7182 + 0.0299 LOS

t = 0.8957

p-value = 0.3741

since p-value > alpha

we fail to reject the null hypothesis

we conclude that coefficient is not significant

c)

slope is 0.0299

it means on average wage increase by 0.0299 when LOS increase by 1 unit

d)

95% confidence interval for slope is (-0.037,0.0969)

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