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 (data126.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       47.6774 99      Large
2       58.7052 17      Small
3       75.9378 108     Small
4       40.9863 85      Small
5       40.1273 125     Large
6       38.1747 159     Small
7       50.1366 86      Large
8       42.5169 46      Large
9       41.7281 18      Large
10      43.4336 32      Small
11      56.8877 74      Large
12      49.2209 81      Small
13      60.5202 112     Small
14      64.6337 55      Large
15      48.167  85      Large
16      47.7709 30      Large
17      80.5519 83      Large
18      49.1823 111     Small
19      51.6707 35      Large
20      51.5514 76      Large
21      62.3329 73      Large
22      62.3087 102     Small
23      38.6566 90      Large
24      71.5847 89      Small
25      50.8582 78      Large
26      53.0636 56      Small
27      47.3662 70      Small
28      55.3155 76      Large
29      37.8308 123     Large
30      46.8266 91      Large
31      38.6313 51      Small
32      44.6185 121     Large
33      50.0416 56      Large
34      54.8089 47      Small
35      40.289  96      Large
36      58.6356 72      Large
37      42.4362 24      Large
38      42.981  48      Small
39      39.7737 25      Large
40      46.8282 84      Small
41      44.5167 40      Small
42      43.334  178     Small
43      45.8879 104     Large
44      45.8208 48      Small
45      39.5825 127     Large
46      46.7052 36      Small
47      47.2575 19      Large
48      62.2932 168     Large
49      65.6368 97      Small
50      57.1809 61      Large
51      40.6493 186     Large
52      53.2475 75      Large
53      54.1171 19      Large
54      47.7903 55      Small
55      55.7675 48      Small
56      38.2663 35      Large
57      70.2633 122     Small
58      78.1077 110     Large
59      47.7368 67      Small
60      40.0295 100     Large

Answer 1

(a)

Following is the scatter plot of the data :

Wages 100 150 LOS

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	0.071564415
	R Square	0.005121466
	Adjusted R Square	-0.012031613
	Standard Error	10.53674074
	Observations	60
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	33.14856836	33.148568	0.298574139	0.586873651
	Residual	58	6439.328516	111.02291
	Total	59	6472.477084
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
	Intercept	49.3482969	3.010822086	16.390307	1.95241E-23	43.32148174	55.37511206
	los	0.018800467	0.034406662	0.5464194	0.586873651	-0.050071949	0.087672882

Regression equation is

wages = 49.348 -0.0188* LOS

t = 0.5464

p= 0.5869

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

(c)

For each unit increase in LOS , wages decreased by 0.0188 units.

(d)

The confidence interval for slope is :

(-0.050, 0.088)