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 (data426.dat) (see below) 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       55.0977 28      Large
2       60.3942 54      Small
3       55.5375 35      Small
4       48.6244 27      Small
5       56.5636 188     Large
6       38.237  156     Small
7       43.5632 30      Large
8       42.7156 61      Large
9       39.143  65      Large
10      46.1205 23      Small
11      49.5348 68      Large
12      63.0939 76      Small
13      37.3613 57      Small
14      86.4907 44      Large
15      62.1521 103     Large
16      49.2244 51      Large
17      61.2332 63      Large
18      38.775  14      Small
19      47.1923 127     Large
20      38.5997 39      Large
21      38.8533 105     Large
22      46.0433 164     Small
23      64.581  70      Large
24      41.4075 17      Small
25      55.9129 143     Large
26      47.352  107     Small
27      43.1829 22      Small
28      51.886  197     Large
29      51.3497 46      Large
30      60.591  40      Large
31      55.6434 77      Small
32      37.9994 34      Large
33      50.3993 85      Large
34      39.2409 88      Small
35      51.1068 118     Large
36      44.8436 58      Large
37      39.4066 78      Large
38      64.675  47      Small
39      59.4471 142     Large
40      70.2038 93      Small
41      47.4302 168     Small
42      44.8665 33      Small
43      39.4258 27      Large
44      71.8007 69      Small
45      38.5246 46      Large
46      71.9274 68      Small
47      51.5816 22      Large
48      65.4135 18      Large
49      64.9034 76      Small
50      73.0817 97      Large
51      45.4468 35      Large
52      44.2239 56      Large
53      68.4574 87      Large
54      37.7713 60      Small
55      46.0706 86      Small
56      45.3591 62      Large
57      53.7606 21      Small
58      104.9657        74      Large
59      40.4731 71      Small
60      60.6301 97      Large

Answer 1

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 (data426.dat) (see below) 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 = 50.7733 + 0.0240 *LOS

t = 0.613

P = 0.5421

Since calculated P=0.5421 >0.05 level of significance, Ho is not rejected. LOS is not significant predictor of wages.

(c) State carefully what the slope tells you about the relationship between wages and length of service. This answer has not been graded yet.

The slope is 0.0240. The slope is positive. When LOS increases, the wages increases.

When LOS increases in one month, the weekly income increases by 0.0240.

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

95% CI = (-0.0543. 0.1023)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.006	n	60
	r	0.080	k	1
	Std. Error	13.236	Dep. Var.	wages
ANOVA table
Source	SS	df	MS	F	p-value
Regression	65.8883	1	65.8883	0.38	.5421
Residual	10,161.2374	58	175.1937
Total	10,227.1257	59
Regression output					confidence interval
variables	coefficients	std. error	t (df=58)	p-value	95% lower	95% upper
Intercept	50.7733	3.2911	15.427	3.43E-22	44.1854	57.3611
los	0.0240	0.0391	0.613	.5421	-0.0543	0.1023