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 (data436.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       68.4515         22      Large
2       48.23           155     Small
3       67.0346     23          Small
4       59.5759         43      Small
5       40.5161         123     Large
6       75.2886         42      Small
7       71.698          115     Large
8       38.2168         67      Large
9       55.9149         114     Large
10      49.813          62      Small
11      56.1435         22      Large
12      50.8353         134     Small
13      41.2628         59      Small
14      63.0899         113     Large
15      38.9848         123     Large
16      44.7797         82      Large
17      41.572          23      Large
18      56.2668         138         Small
19      43.5758         36      Large
20      56.1882         30      Large
21      64.8329         68      Large
22      39.0841         17      Small
23      52.2265         75      Large
24      50.4052         67      Small
25      37.3438         53      Large
26      80.6098         45      Small
27      63.382          88      Small
28      54.2815         51      Large
29      37.1881         140     Large
30      46.5789         28      Large
31      51.9907         48      Small
32      72.726          20      Large
33      58.311          31      Large
34      54.4056         27      Small
35      58.0542         46      Large
36      41.6669         71      Large
37      51.4829         47      Large
38      43.5447         64      Small
39      67.1538         99      Large
40      41.1415         47      Small
41      49.9138         229     Small
42      67.8976         182     Small
43      40.3242         71      Large
44      59.9846         104     Small
45      37.728          89      Large
46      53.3705         25      Small
47      62.1923         57      Large
48      67.7697         23      Large
49      43.6846         40      Small
50      69.6574         27      Large
51      42.4536         168     Large
52      49.0043         172     Large
53      65.1971         41      Large
54      44.8477         47      Small
55      49.0907         36      Small
56      61.9023         25      Large
57      63.3871         61      Small
58      57.2114         133     Large
59      51.7174         38      Small
60      48.4596         163     Large

Answer 1

(a)

Following is the scatter plot of the data :

Scatter plot shows that is a week negative relationship between the variables.

(b)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.16074362
R Square	0.025838511
Adjusted R Square	0.009042624
Standard Error	10.9627444
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	184.8856068	184.8856068	1.53838319	0.219852865
Residual	58	6970.542363	120.1817649
Total	59	7155.42797
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	56.27128295	2.536353065	22.18590295	5.07787E-30	51.19422071	61.34834518
los	-0.035688033	0.028773345	-1.240315762	0.219852865	-0.09328414	0.021908074

Regression equation is

wages = 56.271 -0.036 LOS

t =-1.240

p= 0.2199

P-value is not less than 0.05 so model is not significant.

(c)

For each unit increase in LOS , wages decreased by 0.049 units.

(d)

The confidence interval for slope is :

(-0.093, 0.022)