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 (data438.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.
( , )

worker  wages   los     size
1       48.8329 97      Large
2       78.2535 28      Small
3       48.5138 22      Small
4       41.3975 34      Small
5       46.5544 22      Large
6       50.0827 36      Small
7       49.9522 30      Large
8       41.034  38      Large
9       42.8532 50      Large
10      42.9051 160     Small
11      60.7879 67      Large
12      63.7248 90      Small
13      44.9267 75      Small
14      66.4115 45      Large
15      54.5279 62      Large
16      38.777  33      Large
17      40.5469 74      Large
18      42.0242 33      Small
19      39.4129 151     Large
20      59.0103 145     Large
21      57.4567 17      Large
22      49.0608 38      Small
23      72.6341 141     Large
24      43.5226 36      Small
25      40.3436 56      Large
26      46.0549 88      Small
27      38.4406 133     Small
28      62.0137 44      Large
29      48.8695 116     Large
30      38.204  23      Large
31      44.858  83      Small
32      55.3133 21      Large
33      56.7109 16      Large
34      40.989  34      Small
35      50.3024 90      Large
36      39.6625 26      Large
37      38.9004 88      Large
38      54.0486 83      Small
39      39.6416 134     Large
40      54.4411 69      Small
41      43.3311 101     Small
42      52.6132 124     Small
43      51.0736 114     Large
44      40.7319 119     Small
45      86.2669 46      Large
46      44.7879 38      Small
47      61.0304 27      Large
48      37.5828 90      Large
49      79.3865 32      Small
50      60.6761 155     Large
51      56.5249 42      Large
52      45.8192 60      Large
53      42.2774 143     Large
54      37.538  38      Small
55      79.559  47      Small
56      46.9229 111     Large
57      66.448  55      Small
58      39.1776 96      Large
59      79.3531 119     Small
60      45.389  106     Large

I really don't understand how to do this problem. Can someone explain every step?

Answer 1

ANALYSIS

A)

Using by hand the result would be as follows. the x-axis represents LOS and y-axis represents wage.

Since all points are randomly scattered I can say that there is no linear relationship between LOS and wage.

B)
Wages = 53.145 -0.028 * LOS

Ho: beta1 is not significant. beta1=0
h1: beta1 is significant. beta1 =/= 0
t = -0.73324   
P = 0.4664
With t-0.73324, p>5%, I fail to reject ho and conclude that beta1 is not significant. beta1=0

C)
With a 1 month increase in LOS, there is 0.028 $ decrease in wage. but this value is not significant at 5% level of significance.

D)
95% confidence interval for the slope -> (-0.10449,0.04847 )

This is obtained from the Lower95% and upper 95% in the regression output

PROCEDURE:

Data -> DATA ANALYSIS -> regression
y-axis -> wage
x-axis -> LOS

OUTPUT: