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 (data198.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 53.6215 100 Large 2 57.8746 38 Small 3 43.8878 77 Small 4 55.5148 59 Small 5 42.864 48 Large 6 49.1071 69 Small 7 59.9496 89 Large 8 57.4383 62 Large 9 44.0967 100 Large 10 81.9463 46 Small 11 38.5652 74 Large 12 39.2636 127 Small 13 37.1605 77 Small 14 60.2423 43 Large 15 50.6276 176 Large 16 51.0169 102 Large 17 68.4726 75 Large 18 55.8678 23 Small 19 48.258 140 Large 20 69.1253 149 Large 21 59.5714 106 Large 22 45.9799 75 Small 23 44.3241 63 Large 24 62.2943 111 Small 25 38.1511 47 Large 26 40.9552 30 Small 27 43.0307 18 Small 28 44.1916 189 Large 29 38.2129 26 Large 30 77.9077 59 Large 31 42.9247 96 Small 32 50.7018 53 Large 33 61.5694 66 Large 34 65.8396 127 Small 35 74.5427 57 Large 36 60.9168 57 Large 37 56.7016 145 Large 38 43.0279 42 Small 39 73.0109 28 Large 40 88.3065 85 Small 41 40.9922 72 Small 42 43.4192 77 Small 43 47.3586 18 Large 44 44.1684 168 Small 45 60.7651 77 Large 46 71.8219 122 Small 47 79.5208 37 Large 48 71.3206 143 Large 49 52.0675 70 Small 50 83.887 196 Large 51 48.5477 84 Large 52 46.1038 33 Large 53 43.1893 112 Large 54 62.83 20 Small 55 57.0564 92 Small 56 59.7314 92 Large 57 46.8088 144 Small 58 48.744 55 Large 59 60.8207 28 Small 60 53.4192 26 Large

worker  wages   los     size
1       53.6215 100     Large
2       57.8746 38      Small
3       43.8878 77      Small
4       55.5148 59      Small
5       42.864  48      Large
6       49.1071 69      Small
7       59.9496 89      Large
8       57.4383 62      Large
9       44.0967 100     Large
10      81.9463 46      Small
11      38.5652 74      Large
12      39.2636 127     Small
13      37.1605 77      Small
14      60.2423 43      Large
15      50.6276 176     Large
16      51.0169 102     Large
17      68.4726 75      Large
18      55.8678 23      Small
19      48.258  140     Large
20      69.1253 149     Large
21      59.5714 106     Large
22      45.9799 75      Small
23      44.3241 63      Large
24      62.2943 111     Small
25      38.1511 47      Large
26      40.9552 30      Small
27      43.0307 18      Small
28      44.1916 189     Large
29      38.2129 26      Large
30      77.9077 59      Large
31      42.9247 96      Small
32      50.7018 53      Large
33      61.5694 66      Large
34      65.8396 127     Small
35      74.5427 57      Large
36      60.9168 57      Large
37      56.7016 145     Large
38      43.0279 42      Small
39      73.0109 28      Large
40      88.3065 85      Small
41      40.9922 72      Small
42      43.4192 77      Small
43      47.3586 18      Large
44      44.1684 168     Small
45      60.7651 77      Large
46      71.8219 122     Small
47      79.5208 37      Large
48      71.3206 143     Large
49      52.0675 70      Small
50      83.887  196     Large
51      48.5477 84      Large
52      46.1038 33      Large
53      43.1893 112     Large
54      62.83   20      Small
55      57.0564 92      Small
56      59.7314 92      Large
57      46.8088 144     Small
58      48.744  55      Large
59      60.8207 28      Small
60      53.4192 26      Large

Answer 1

Independent variable (X): Los

Dependent variable (Y): Wages

(a)

Following is the scatter plot:

Scatter plot shows that is a weak positive relationship between the variables.

(b)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.073231365
R Square	0.005362833
Adjusted R Square	-0.011786084
Standard Error	12.88405031
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	51.91135824	51.91135824	0.312721376	0.578168072
Residual	58	9627.927637	165.9987524
Total	59	9679.838995
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	53.31198088	3.436938449	15.51147385	2.66124E-22	46.43220116	60.1917606
los	0.020936732	0.037439506	0.559214964	0.578168072	-0.05400658	0.09588004

Regression equation is

wages = 53.312 +0.021*LOS

t = 0.5592

p= 0.5782

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

(c)

For each unit increase in LOS , wages increased by 0.021 units.

(d)

The 95% confidence interval for slope is :

(-0.054,0.096)