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 (data197.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       55.2228 62      Large
2       72.6471 43      Small
3       64.7938 28      Small
4       83.1899 52      Small
5       74.6722 77      Large
6       45.3301 156     Small
7       43.6869 16      Large
8       54.4083 253     Large
9       41.5534 134     Large
10      43.4756 79      Small
11      64.5044 105     Large
12      51.4939 172     Small
13      46.8273 39      Small
14      61.5737 59      Large
15      40.4888 192     Large
16      42.5272 77      Large
17      44.0275 98      Large
18      49.1887 45      Small
19      41.9127 110     Large
20      44.5922 59      Large
21      45.2959 41      Large
22      67.5828 63      Small
23      49.1524 119     Large
24      49.6111 26      Small
25      41.2403 62      Large
26      64.3923 114     Small
27      48.8709 73      Small
28      53.2818 55      Large
29      52.4652 26      Large
30      38.5335 65      Large
31      42.8304 56      Small
32      62.9239 25      Large
33      37.9765 42      Large
34      60.7783 105     Small
35      64.4702 78      Large
36      63.7232 89      Large
37      56.527  41      Large
38      50.0613 188     Small
39      40.3449 59      Large
40      48.4422 37      Small
41      72.214  55      Small
42      44.3634 79      Small
43      68.0063 81      Large
44      52.1295 120     Small
45      40.9163 72      Large
46      54.7163 24      Small
47      42.0233 35      Large
48      115.9302        24      Large
49      39.8092 127     Small
50      40.779  40      Large
51      37.6496 65      Large
52      49.833  121     Large
53      53.0945 143     Large
54      76.8681 34      Small
55      53.227  24      Small
56      44.4872 136     Large
57      59.3171 111     Small
58      59.3403 79      Large
59      44.9148 19      Small
60      45.3378 72      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	0.172756348
	R Square	0.029844756
	Adjusted R Square	0.013117941
	Standard Error	13.63805762
	Observations	60
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	331.8637583	331.8637583	1.784246219	0.186846826
	Residual	58	10787.80371	185.9966157
	Total	59	11119.66747
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
	Intercept	57.11788229	3.340242044	17.09992316	2.52936E-24	50.43166144	63.80410314
	los	-0.048599752	0.036383683	-1.335756796	0.186846826	-0.121429605	0.024230102

Regression equation is

wages = 57.118 -0.049* LOS

t =-1.336

p= 0.1868

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 :

(-0.121, 0.024)