Question

worker  wages   los     size
1       67.3728 191     Large
2       45.0543 73      Small
3       47.6712 245     Small
4       55.2308 28      Small
5       44.5342 28      Large
6       57.6219 59      Small
7       42.3414 62      Large
8       39.8142 15      Large
9       40.2441 118     Large
10      45.527  73      Small
11      38.0868 103     Large
12      78.2699 35      Small
13      37.8019 92      Small
14      51.876  33      Large
15      67.7545 109     Large
16      57.9416 81      Large
17      39.7792 156     Large
18      56.5957 44      Small
19      44.4662 55      Large
20      46.2812 44      Large
21      41.7772 19      Large
22      49.9668 158     Small
23      49.3883 71      Large
24      60.8322 119     Small
25      40.8312 92      Large
26      70.8078 29      Small
27      45.9471 59      Small
28      40.1592 140     Large
29      41.7016 70      Large
30      41.1706 147     Large
31      50.3009 37      Small
32      50.2356 59      Large
33      38.5676 106     Large
34      43.5234 69      Small
35      48.8122 36      Large
36      60.8026 93      Large
37      59.5493 73      Large
38      51.8564 59      Small
39      44.0914 116     Large
40      38.1062 30      Small
41      37.2152 23      Small
42      79.1323 44      Small
43      68.0236 104     Large
44      55.758  103     Small
45      45.6928 191     Large
46      43.2591 47      Small
47      45.6069 29      Large
48      47.2263 54      Large
49      67.7312 101     Small
50      66.7496 21      Large
51      59.2571 41      Large
52      38.9462 172     Large
53      53.7731 138     Large
54      43.9827 79      Small
55      48.9315 145     Small
56      43.8694 53      Large
57      51.6545 49      Small
58      47.6007 193     Large
59      54.86   26      Small
60      48.2207 40      Large

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 (data4.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.

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope.

Answer 1

(a) The plot is given below:


The points are scattered in the graph above and we can say that there is NO Linear Relationship between the two variables. Hence, linear regression is NOT appropriate.

(b) Wages = 51.8848 + (-0.0190) * los
t = -0.7373
p = 0.4639
Since p-value > alpha = 0.05 (level of significance), we can say that the slope is not significant. This means that the independent variable "los" is not suitable to be used in the model to predict "Wages".

(c) Here, the slope is 0.4639. This means that if a particular woman works for 1 more month, then her wage is likely to be increased by $0.4639.

(d) 95% confidence interval for slope = (-0.0707, 0.0327)

(Please round the number here to the required number of decimal places.)