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 the length of service (LOS) relate to wages? The data here 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.
(  ,  )

Here is the data needed:

worker  wages   los     size
1       58.9152  111     Large
2       46.1906  51      Small
3       41.3041  101     Small
4       48.081   68      Small
5       38.7386  27      Large
6       66.3566  57      Small
7       79.8173  91      Large
8       54.7264  80      Large
9       57.4545  127     Large
10      61.1902  62      Small
11      40.1532  56      Large
12      60.8378  165     Small
13      39.5874  234     Small
14      56.8797  147     Large
15      39.5076  88      Large
16      48.1116  157     Large
17      41.8152  56      Large
18      68.4901  111     Small
19      47.5558  125     Large
20      73.1005  179     Large
21      63.9432  60      Large
22      56.4083  112     Small
23      46.2288  112     Large
24      49.648   20      Small
25      47.8469  87      Large
26      47.0067  37      Small
27      42.5046  83      Small
28      38.5577  40      Large
29      75.117   64      Large
30      38.4845  24      Large
31      64.6729  84      Small
32      43.062   40      Large
33      92.8911  38      Large
34      78.786   59      Small
35      52.4093  85      Large
36      50.908   96      Large
37      40.2716  74      Large
38      42.846   83      Small
39      61.5447  26      Large
40      47.4162  57      Small
41      42.8452  61      Small
42      40.9315  17      Small
43      46.9331  55      Large
44      37.503   90      Small
45      49.8791  124     Large
46      50.1629  107     Small
47      48.3365  117     Large
48      77.2224  110     Large
49      38.0983  152     Small
50      59.676   37      Large
51      41.4523  29      Large
52      40.2629  139     Large
53      49.8064  44      Large
54      58.1542  45      Small
55      49.8369  71      Small
56      38.3218  85      Large
57      83.2245  84      Small
58      58.7219  53      Large
59      55.5074  19      Small
60      45.6475  83      Large

Answer 1

applying regression on above given data:

b)

Wages =52.226+0.006*LOS

t=0.149

p value =0.882

c)this tell us that 1 unit increase on LOS increase wage on average by 0.006.

d)95% confidence interval for the slope =-0.072 ; 0.083