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 (data337.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.
( ______ , _____ )

DATA337.dat 

worker  wages   los     size
1       39.098  89      Large
2       54.5509 79      Small
3       54.7531 40      Small
4       38.0461 58      Small
5       65.3705 41      Large
6       64.5411 49      Small
7       37.6291 46      Large
8       51.8097 142     Large
9       49.0284 188     Large
10      51.3934 81      Small
11      72.7339 111     Large
12      69.1645 20      Small
13      62.0596 67      Small
14      48.6839 43      Large
15      68.7403 30      Large
16      58.7213 52      Large
17      44.5489 52      Large
18      66.2596 48      Small
19      52.4863 149     Large
20      39.4228 80      Large
21      45.7535 88      Large
22      43.3795 76      Small
23      80.2623 99      Large
24      53.2303 75      Small
25      74.7305 105     Large
26      38.5734 93      Small
27      55.2474 83      Small
28      69.3101 20      Large
29      56.8112 71      Large
30      51.7271 54      Large
31      42.2559 132     Small
32      59.0411 118     Large
33      55.1768 58      Large
34      43.4161 25      Small
35      66.2072 160     Large
36      57.6893 181     Large
37      55.148  95      Large
38      54.002  26      Small
39      53.0475 22      Large
40      56.7734 37      Small
41      44.9355 114     Small
42      40.9449 21      Small
43      46.054  27      Large
44      72.9952 28      Small
45      54.4882 82      Large
46      60.5352 76      Small
47      60.91   27      Large
48      48.1653 45      Large
49      47.524  87      Small
50      73.2162 19      Large
51      50.7977 153     Large
52      59.6262 126     Large
53      67.6261 46      Large
54      40.7944 114     Small
55      55.7916 104     Small
56      44.0462 48      Large
57      68.6975 51      Small
58      39.4482 88      Large
59      37.2282 134     Small
60      45.1177 194     Large

Answer 1

a) The plot of Wages vs LOS looks as follows. A linear relationship does not seem to exist as the points aren't scattered close to any line.

b) Carry out regression in Excel (Data -> Data Analysis ->Regression, choose LOS as Y-axis and Wages as X-axis). The output from regression is:

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	57.62262468	2.814803777	20.47128	3.21E-28	51.98818	63.25707
LOS	-0.042337943	0.031328145	-1.35143	0.181804	-0.10505	0.020372

Hence, the least-squares regression line is:  

Wages = 57.62 - 0.0423 * LOS

The p-value of the slope coefficient is 0.1818, which is quite high compared to the 95% confidence level threshold of 0.05. Hence, the linear relationship between Wages and LOS is not strong.

c) The negative slope of -0.0423 suggests Wages decrease with LOS. However, the low negative slop coefficient suggests the relationship is very weak. This is further confirmed by the high p-value of the slop coefficient.

d) 95% confidence interval for the slope can be seen from the regression output to be:

(-0.105, 0.0204)