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 (data252.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.
(  ,  )

Data Set:

worker  wages   los     size
1       45.3951 63      Large
2       74.2778 60      Small
3       57.0387 40      Small
4       94.1572 63      Small
5       58.401  23      Large
6       48.1825 138     Small
7       64.0662 56      Large
8       69.3858 32      Large
9       72.0226 89      Large
10      42.0711 17      Small
11      69.1096 20      Large
12      69.1786 57      Small
13      37.8459 135     Small
14      43.0067 137     Large
15      45.1138 38      Large
16      50.736  82      Large
17      49.4674 210     Large
18      64.289  70      Small
19      49.0542 78      Large
20      56.9337 104     Large
21      38.2117 42      Large
22      65.6989 56      Small
23      81.7696 129     Large
24      44.0736 50      Small
25      39.5651 22      Large
26      64.7169 93      Small
27      52.4025 34      Small
28      54.1658 66      Large
29      50.0073 84      Large
30      49.2068 18      Large
31      60.0456 92      Small
32      47.7387 59      Large
33      78.231  48      Large
34      66.5142 57      Small
35      69.0241 48      Large
36      56.6936 89      Large
37      50.7495 66      Large
38      38.6829 60      Small
39      43.9665 74      Large
40      49.2412 127     Small
41      48.7291 166     Small
42      55.08   108     Small
43      54.9839 21      Large
44      88.1287 98      Small
45      48.2803 83      Large
46      38.3535 53      Small
47      45.1255 17      Large
48      68.1018 51      Large
49      38.0827 15      Small
50      48.8394 59      Large
51      46.5504 56      Large
52      38.0011 86      Large
53      57.6297 68      Large
54      61.8434 153     Small
55      40.5017 80      Small
56      87.9856 30      Large
57      44.0887 97      Small
58      49.8736 41      Large
59      51.4842 83      Small
60      69.2918 92      Large

Answer 1

(a)

We observed that if length of service increases then Wages also increases hence there exists a positive linear association between length of service and Wages. However the relation is not so strong.

(b)

Regression Analysis: Wages versus LOS

The regression equation is
Wages = 56.3 - 0.0081 LOS

Predictor Coef SE Coef T P
Constant 56.266 3.652 15.41 0.000
LOS -0.00807 0.04467 -0.18 0.857

S = 13.7888 R-Sq = 0.1% R-Sq(adj) = 0.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 6.2 6.2 0.03 0.857
Residual Error 58 11027.6 190.1
Total 59 11033.8
Since p-value of F test=0.857>0.05 so we conclude that there is insignificant relationship between length of service and Wages.

Wages =	56.266 -0.00807  LOS
t =	-0.18
P =0.857

(c)

If length of service is increased by 1 month then wages is decreased by 0.00807 unit.

(d) 95% confidence interval for the slope:

(-0.00807-t_0.025,58*0.04467, -0.00807+t_0.025,58*0.04467)=(-0.0975, 0.0813)

where, t_0.025,58=2.0017