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 (data178.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       42.4336 54      Large
2       49.4002 26      Small
3       76.0077 50      Small
4       56.585  73      Small
5       67.1602 110     Large
6       51.3733 24      Small
7       37.9427 128     Large
8       63.4741 101     Large
9       37.206  55      Large
10      50.4002 39      Small
11      47.5953 45      Large
12      55.3889 33      Small
13      56.1207 85      Small
14      37.7831 43      Large
15      88.9089 62      Large
16      37.5299 62      Large
17      44.3064 33      Large
18      44.5789 17      Small
19      42.4566 90      Large
20      39.4867 92      Large
21      61.6999 163     Large
22      50.172  172     Small
23      40.2525 101     Large
24      57.3907 24      Small
25      37.5875 64      Large
26      45.4282 63      Small
27      50.3906 120     Small
28      58.2157 50      Large
29      40.0543 226     Large
30      48.5111 35      Large
31      37.7405 21      Small
32      61.8224 45      Large
33      51.1922 131     Large
34      70.2647 82      Small
35      60.6526 87      Large
36      58.1348 116     Large
37      54.901  73      Large
38      57.686  59      Small
39      55.1436 49      Large
40      79.1504 126     Small
41      65.3631 41      Small
42      44.2196 79      Small
43      51.5813 203     Large
44      39.3628 35      Small
45      52.7649 37      Large
46      53.7204 100     Small
47      55.7018 139     Large
48      41.916  89      Large
49      63.3796 30      Small
50      54.5664 131     Large
51      46.5089 88      Large
52      40.0104 116     Large
53      75.1435 25      Large
54      63.8183 137     Small
55      63.5329 54      Small
56      48.7126 86      Large
57      71.1757 82      Small
58      45.2896 18      Large
59      67.7092 88      Small
60      52.3707 87      Large

Answer 1

solution:

(a)

(b)

Using EXCEL we will carry out the regression analysis . The output for this analysis is given below.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.0079
R Square	0.0001
Adj R Square	-0.0172
Standard Error	11.8228
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.5075	0.5075	0.0036	0.9522
Residual	58	8107.1200	139.7779
Total	59	8107.627486
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	53.1652	3.0309	17.5413	0.0000	47.0982	59.2321
los	0.0020	0.0335	0.0603	0.9522	-0.0650	0.0690

Hence the least squares line would be given by,

Wages = 53.1652 + 0.0020*LOS

For testing the significance of slope we have,

t = 0.0603

P- value = 0.9522

Since the P-value is very high we fail to reject the null hypothesis, and hence the slope is not signifcant.

(c)

Since the slope is positive there is a positive correlation between the variables. Also for increase in every 1 unit of LOS there would be an increase of 0.002 units of Wages.

(d)

The 95% confidence interval of slope would be given by,

(-0.0650,0.0690)

Please download the original EXCEL file in which regression analysis has been carried out from the link given below.

https://www.dropbox.com/s/5ack2qhe7leedwf/data178.xlsx?dl=0