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

worker  wages   los     size
1       46.3791 34      Large
2       37.3643 28      Small
3       58.9662 89      Small
4       47.4511 24      Small
5       98.45   90      Large
6       51.3039 205     Small
7       78.8469 52      Large
8       48.6907 47      Large
9       52.1521 39      Large
10      76.5752 147     Small
11      64.5643 32      Large
12      47.7774 28      Small
13      39.4675 16      Small
14      75.3756 25      Large
15      42.7038 95      Large
16      37.3256 21      Large
17      47.6141 24      Large
18      39.0678 64      Small
19      41.587  34      Large
20      64.102  50      Large
21      72.0744 79      Large
22      69.4551 99      Small
23      49.7729 57      Large
24      46.8856 72      Small
25      62.1589 38      Large
26      51.3016 106     Small
27      38.2666 135     Small
28      46.6623 17      Large
29      41.256  44      Large
30      50.9605 40      Large
31      52.8366 53      Small
32      47.635  74      Large
33      61.0205 79      Large
34      62.3736 82      Small
35      38.8286 52      Large
36      56.931  31      Large
37      72.1109 20      Large
38      70.1955 87      Small
39      70.9977 84      Large
40      60.4625 50      Small
41      69.0306 86      Small
42      47.8044 17      Small
43      66.7418 128     Large
44      40.8045 99      Small
45      56.4676 95      Large
46      82.3129 37      Small
47      49.438  102     Large
48      60.0954 28      Large
49      49.7582 27      Small
50      70.0533 155     Large
51      68.4439 56      Large
52      43.1397 42      Large
53      37.8087 154     Large
54      39.9629 102     Small
55      50.4422 42      Small
56      41.7852 162     Large
57      52.8019 63      Small
58      85.8806 119     Large
59      50.1035 25      Small
60      77.1412 122     Large

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.

(___,___)

Answer 1

a)

Data distribution seems to be a weak correlation between two variables.

b) LOS mean= 68.4

Wages mean= 55.96612

Wages= a+b*Los

Standard error:

Standard error for SLOPE:

Hypothesis test:

P-value: 0.230272

c) The test is not significant and failed to reject H0. There is no significant relationship between two variables.

d) 95% confidence interval for slope:

t-critical: