We assume that our wages will increase as we gain experience and become more val
ID: 3182937 • Letter: W
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 (data408.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.
Below is the data which is seperated in sets of 4. Every four numbers are the worker number, wages, length of service, and size. they follow this order and may need to be seperated into a chart to make more sense. The first one in exampl would be 1, 69.2413, 34, large. then it starts over. Thank you!
worker wages los size 1 69.2413 34 Large 2 40.0111 19 Small 3 70.6251 194 Small 4 49.3129 29 Small 5 55.6213 80 Large 6 44.6338 42 Small 7 39.6074 20 Large 8 49.9032 50 Large 9 39.5058 139 Large 10 60.0777 110 Small 11 47.509 39 Large 12 51.8078 36 Small 13 55.3064 140 Small 14 38.8426 144 Large 15 59.1806 29 Large 16 50.1731 109 Large 17 44.784 35 Large 18 37.8216 103 Small 19 60.3116 123 Large 20 80.9877 137 Large 21 50.576 18 Large 22 46.3306 91 Small 23 47.9091 69 Large 24 58.5582 85 Small 25 63.9038 74 Large 26 44.5448 34 Small 27 49.5359 85 Small 28 48.9933 56 Large 29 57.1764 130 Large 30 52.9005 38 Large 31 63.7324 35 Small 32 37.9304 49 Large 33 39.3526 55 Large 34 64.5674 116 Small 35 61.2771 29 Large 36 46.991 113 Large 37 74.5818 55 Large 38 41.5655 22 Small 39 51.3884 71 Large 40 40.896 47 Small 41 40.7185 45 Small 42 57.1712 70 Small 43 42.7096 90 Large 44 49.8057 132 Small 45 38.0929 30 Large 46 41.3269 30 Small 47 64.3603 50 Large 48 53.1662 129 Large 49 39.1688 30 Small 50 55.8157 99 Large 51 63.1372 43 Large 52 62.6847 30 Large 53 46.9151 47 Large 54 80.2559 168 Small 55 51.5097 53 Small 56 57.0483 151 Large 57 85.3793 76 Small 58 68.0978 69 Large 59 45.4022 73 Small 60 58.0315 33 Large
(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?
(c) State carefully what the slope tells you about the relationship between wages and length of service.
Please give a couple of sentences explaining C.
(d) Give a 95% confidence interval for the slope.
(____, ____)
Wages = ____ + ___ LOS t = ? P = ?Explanation / Answer
Answer:
(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?
Wages = 47.4063
+ 0.0795* LOS
t = 2.392
P = 0.0200
Calculated t=2.392, P=0.0200 which is < 0.05 level of significance.
Ho is rejected. We conclude that slope is significant. The model is useful in predicting wages.
(c) State carefully what the slope tells you about the relationship between wages and length of service.
Please give a couple of sentences explaining C.
When there is an increase of 1 month in length of service, there is an increase of 0.0795 in Wages.
When the length of service is 0, the wages is 47.4063. This is no meaning in interpreting constant here.
Slope is positive, when length of service increases, wage also increases.
(d) Give a 95% confidence interval for the slope.
( 0.0130, 0.1460)
Regression Analysis
r²
0.090
n
60
r
0.300
k
1
Std. Error
11.101
Dep. Var.
wages
ANOVA table
Source
SS
df
MS
F
p-value
Regression
705.0822
1
705.0822
5.72
.0200
Residual
7,147.7844
58
123.2377
Total
7,852.8667
59
Regression output
confidence interval
variables
coefficients
std. error
t (df=58)
p-value
95% lower
95% upper
Intercept
47.4063
2.7951
16.960
3.76E-24
41.8113
53.0013
los
0.0795
0.0332
2.392
.0200
0.0130
0.1460
Wages = 47.4063
+ 0.0795* LOS
t = 2.392
P = 0.0200
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