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 (data393.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.


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

worker  wages   los     size
1       65.1229 24      Large
2       46.2397 34      Small
3       48.067  130     Small
4       56.7184 43      Small
5       46.314  76      Large
6       46.2223 15      Small
7       42.1995 64      Large
8       55.7412 47      Large
9       37.4091 79      Large
10      58.5093 154     Small
11      57.3379 28      Large
12      42.8656 136     Small
13      44.8088 133     Small
14      77.4053 78      Large
15      48.8927 115     Large
16      44.2125 65      Large
17      42.0177 167     Large
18      38.2394 32      Small
19      38.7164 97      Large
20      65.581  187     Large
21      43.3897 57      Large
22      50.1634 68      Small
23      52.668  86      Large
24      59.2598 106     Small
25      79.1054 30      Large
26      40.1483 41      Small
27      56.2467 31      Small
28      62.4825 18      Large
29      48.4094 88      Large
30      70.6421 40      Large
31      69.2177 34      Small
32      60.3709 24      Large
33      71.0116 83      Large
34      38.1429 158     Small
35      51.2402 77      Large
36      44.1567 155     Large
37      73.9482 57      Large
38      41.3124 92      Small
39      52.0047 86      Large
40      88.1481 136     Small
41      37.7559 39      Small
42      67.3698 37      Small
43      47.9039 57      Large
44      44.2461 26      Small
45      59.9857 29      Large
46      38.3378 57      Small
47      57.1175 140     Large
48      59.0108 43      Large
49      38.679  102     Small
50      64.7717 24      Large
51      47.1089 66      Large
52      38.9647 58      Large
53      46.6017 22      Large
54      62.8626 93      Small
55      44.1369 19      Small
56      44.0579 68      Large
57      39.4452 129     Small
58      47.3022 96      Large
59      50.5616 23      Small
60      64.7296 21      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	0.12591265
R Square	0.01585399
Adjusted R Square	-0.00111404
Standard Error	12.0470126
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	135.6019359	135.6019359	0.934344777	0.337749862
Residual	58	8417.569699	145.1305121
Total	59	8553.171635
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	55.0310646	2.962358372	18.57677487	4.2996E-26	49.10126006	60.96086906
los	-0.03384837	0.035017426	-0.966615113	0.337749862	-0.103943368	0.036246621

Regression equation is

wages = 55.031 -0.034* LOS

t =-0.967

p= 0.3377

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

(c)

For each unit increase in LOS , wages decreased by 0.034 units.

(d)

The confidence interval for slope is :

(-0.104, 0.036)