The purpose of this
research is to determine adequate and competitive salaries compared to other companies in the surrounding areas. The variables of interest for this study include the effects of education, experience, gender, and of course
type of work upon the wages paid.
Model 1:
Dependent Variable: Wages
Independent Variable:
Education
Ho: There is
a correlation between wages and education.
Ha: There is no correlation.
The plot indicates a linear
relationship between the independent variable, education and the dependent variable, wage.
WAGE = 1120.25 + 112.45
(education)
If education = 0,
WAGE = 1120.25. The average wage would be $1120.25. For an increase of one year of education the wage increases $112.45.
Using a one-sided test,
α = .05, and n = 49, t-critical = 1.6759 and F-critical = 3.183
t-stat = 3.096 > t-critical,
reject Ho; education has a significant impact on wage.
F-stat = 9.59 > F-critical,
reject Ho; the regression model is statistically significant. R = .17, education explains 17% of the variations in wages.
|
Wage/Education |
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Regression Statistics |
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Multiple R |
0.411813304 |
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R Square |
0.169590198 |
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|
Adjusted R Square |
0.151921904 |
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Standard Error |
596.9981557 |
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Observations |
49 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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|
Regression |
1 |
3420992.456 |
3420992.456 |
9.598561181 |
0.003282646 |
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|
Residual |
47 |
16751119.5 |
356406.7979 |
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|
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Total |
48 |
20172111.96 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Wages |
1120.246681 |
241.4885355 |
4.63892283 |
2.81899E-05 |
634.4344183 |
1606.058943 |
|
Education |
112.4521726 |
36.29650275 |
3.09815448 |
0.003282646 |
39.43302873 |
185.4713165 |
Model 2:
Dependent Variable: Wages
Independent Variables:
Education and Experience
WAGE = 560.71 + 142.74
(EDUC) + 41.98 (EXPER)
Given the years of experience,
the wages increase $142.74 for a one year increase in education. Given the education,
price increases $41.98 for a one year increase in experience. The coefficients
of EDUC and EXPER are statistically significant because of their high t-state values.
T-stat = 4.724 > t-critical. The model is statistically significant
because of its high f-state value. R
increases to .32, indicating that EDUC and EXPER explain 32% of variations in Wage.
This model is a better fit than model one since there is a large percentage of explanation in variation of wages.
|
Regression Analysis |
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Regression Statistics |
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Multiple R |
0.566946595 |
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|
R Square |
0.321428441 |
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Adjusted R Square |
0.29192533 |
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|
Standard Error |
545.4997999 |
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Observations |
49 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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|
Regression |
2 |
6483890.5 |
3241945.25 |
10.89473033 |
0.000133875 |
|
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Residual |
46 |
13688221.46 |
297570.0317 |
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Total |
48 |
20172111.96 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Wage |
560.7099574 |
281.2586478 |
1.993574106 |
0.052147877 |
-5.434328023 |
1126.854243 |
|
EDUC |
142.7445636 |
34.4833303 |
4.139523715 |
0.000146836 |
73.33322085 |
212.1559063 |
|
EXPER |
41.98180184 |
13.08547222 |
3.208275646 |
0.002433357 |
15.64211282 |
68.32149087 |
Model 3:
Dependent Variable: Wages
Independent Variables:
Education, Experience, Clerical, and Gender (female)
This model is not statistically
significant due to the low F-stat values, as well as the low t-stat values. Interestingly,
clerical work has been stereotyped as an industry for women; however education, experience, and the female gender only make
up 19% of the variations in clerical wages for females.
|
Regression Analysis |
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Regression Statistics |
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Multiple R |
0.434357916 |
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R Square |
0.188666799 |
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Adjusted R Square |
-0.014166501 |
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Standard Error |
130.2815765 |
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Observations |
16 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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|
Regression |
3 |
47363.46749 |
15787.8225 |
0.930156927 |
0.456060891 |
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Residual |
12 |
203679.47 |
16973.28917 |
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Total |
15 |
251042.9375 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
1514.037757 |
207.6001376 |
7.293047946 |
9.567E-06 |
1061.715914 |
1966.3596 |
|
EDUC |
7.860215215 |
19.35666924 |
0.406072714 |
0.691836912 |
-34.31434401 |
50.03477445 |
|
EXPER |
10.83094334 |
9.906370879 |
1.093331097 |
0.295710866 |
-10.7531846 |
32.41507128 |
|
AGE |
-6.15142253 |
4.093754291 |
-1.502635989 |
0.158784613 |
-15.07094689 |
2.768101831 |
Model 4:
Dependent Variable: Wages
Independent Variables:
Education, Experience, Age, and Gender (male)
WAGE = 1039.25 + 171.66
(EDUC) + 41.50 (EXPER) – 10.01 (AGE)
Given the years of experience,
the wages increase $171.66 for a one year increase in education. Given the education,
price increases $41.50 for a one year increase in experience; however, given the education, experience and age, the wage decreases
by $10.01 for males. The coefficients of EDUC, EXPER, and AGE are statistically significant because of their high t-state
values. The model is statistically significant because of its high f-state value
4.97 > than F-critical. R increases
to .40, indicating that EDUC and EXPER explain 40% of variations in Wage. This
model is a better fit.
|
Regression Analysis |
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Male Multiple Regression |
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Regression Statistics |
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Multiple R |
0.635408856 |
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R Square |
0.403744414 |
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Adjusted R Square |
0.322436834 |
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Standard Error |
611.7949359 |
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Observations |
26 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
3 |
5575816.887 |
1858605.629 |
4.965642992 |
0.008810879 |
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Residual |
22 |
8234446.96 |
374293.0436 |
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Total |
25 |
13810263.85 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Wage |
1039.247964 |
675.0367264 |
1.539542848 |
0.137932579 |
-360.692516 |
2439.188445 |
|
EDUC |
171.6585553 |
46.81766224 |
3.666534106 |
0.001355421 |
74.56466697 |
268.7524437 |
|
EXPER |
41.49941882 |
19.56462852 |
2.121145248 |
0.0454162 |
0.924862836 |
82.07397481 |
|
AGE |
-10.00546519 |
12.4536289 |
-0.803417644 |
0.430328847 |
-35.83271064 |
15.82178026 |
Model 5:
Dependent Variable: Wages
Independent Variables:
Education, Experience, Age, and Gender (female)
Wage = 1205.24 + 10.18
(EDUC) + 46.81 (EXPER) – 2.72 (AGE)
Given the years of experience,
the wages increase $10.18 for a one year increase in education. Given the education,
price increases $46.81 for a one year increase in experience; however, given the education, experience and age, the wage decreases
by $2.72 for females. The coefficients of EDUC, EXPER, and AGE are statistically significant because of their high t-state
values. The model is statistically significant because of its high f-state value
5.54 > than F-critical. R increases
to .467, indicating that EDUC and EXPER explain 47% of variations in Wage. This
model is the best fit.
|
Regression Analysis |
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|
Female Multiple Regression |
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Regression Statistics |
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Multiple R |
0.683131 |
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R Square |
0.466667963 |
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Adjusted R Square |
0.382457641 |
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Standard Error |
260.7066771 |
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Observations |
23 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
3 |
1129973.411 |
376657.8038 |
5.54169553 |
0.006620486 |
|
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Residual |
19 |
1291391.458 |
67967.97148 |
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Total |
22 |
2421364.87 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Wage |
1205.238913 |
315.614503 |
3.818705735 |
0.001159205 |
544.6501675 |
1865.827658 |
|
EDUC |
10.18057892 |
32.58735053 |
0.312408918 |
0.758132566 |
-58.02552945 |
78.3866873 |
|
EXPER |
46.81046708 |
12.65051317 |
3.700282071 |
0.001518767 |
20.33263877 |
73.28829538 |
|
AGE |
-2.720920146 |
6.384596755 |
-0.426169459 |
0.67477347 |
-16.0840347 |
10.64219441 |
Conclusion:
Beginning with the
scatter chart, it is evident that those individuals with education beyond the eighth grade earn increasingly higher wages. In addition, wages increase in every model with additional years of experience. Therefore, wages increase with an increase in education and experience. When I worked with model 3 testing to see which wages were higher for clerical, men or women, I encountered
that only 18% of wages were affected by gender, clearly not as statistically significant as other models.
I discovered that when
working with the coefficient of AGE I faced a problem of multicollinearity because wage increased with years of experience
and education, but age produced a negative for both male and female. Clearly
age is a variable affecting variation in wage, but it would appear to be the wrong sign.
I chose model 5
as the best fit since all regression coefficients and the entire model are significant.
In addition the R is the highest for all models at 47%. Since this model is chosen, it would be pertinent that our company review the pay scale and take into consideration
when making changes that education and experience are factors in determined wages. Even
though age and gender do appear to play a role in the regression analysis, it may not be wise to include those factors when
making changes to the pay scale, since it would be against equal opportunity laws.
