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Running Head: Check Point 3
Check Point 3
Student name:
Institutional affiliation:
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CHECK POINT 3
Proposed Model with three independent variables:
Consider the figure below:
Proposed Federal Tax Model
Corporate
Income
taxes
Federal Tax
Income
Individual
Income
Taxes
Payroll
Taxes
According to the above federal tax revenue model, it follows that:
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Dependent variable: The federal tax income
•
Independent variables: Individual Income taxes, corporate income taxes and Payroll Taxes
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Multiple Regression:
Consider the following information:
Year
Federal Income Corporation
Taxes (in Trillion) Income Taxes
2012
2013
2014
2015
2016
2017
$2.45
$2.77
$3.02
$3.25
$3.27
$3.32
Individual
Payroll Taxes Income
Taxes
0.2423
0.2735
0.3207
0.3438
0.3
0.297
0.8453
0.9478
1.0239
1.0653
1.115
1.162
1.1322
1.3164
1.3946
1.5408
1.546
1.587
For this regression analysis, federal income tax is the dependent variable (Y) while the
Corporation Income tax, Individual Income tax, and payroll taxes are the independent variable (X).
The table below shows the output summary when the independent variable is regress on the
dependent variable:
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.998970662
0.997942384
0.994855961
0.024690139
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ANOVA
df
Regression
Residual
Total
Intercept
Corporation Income Taxes
Payroll Taxes
Individual Income Taxes
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2
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SS
MS
F Significance F
0.591314127 0.19710471 323.3329 0.00308484
0.001219206 0.0006096
0.592533333
Coefficients
Standard Error
-0.001753276
0.130430366
1.468436156
0.581100873
1.100783847
0.575329378
1.021558075
0.4345449
t Stat
-0.01344224
2.5269901
1.91331069
2.35086886
P-value
0.990495
0.127361
0.195829
0.143101
Lower 95%
-0.56294985
-1.0318391
-1.37465867
-0.84813773
Upper 95%
0.559443294
3.968711415
3.576226364
2.891253876
Lower 95.0% Upper 95.0%
-0.562949847
0.559443294
-1.031839104
3.968711415
-1.37465867
3.576226364
-0.848137725
2.891253876
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RESIDUAL
OUTPUT
Predicted Federal
Income Taxes (in
Observation
Trillion)
Residuals
1
2.441149443
0.008850557
2
2.787965993
-0.017965993
3
3.020931672
-0.000931672
4
3.249776789
0.000223211
5
3.245480345
0.024519655
6
3.334695758
-0.014695758
R-squared and significance Model:
According to this table, the value of R-squared = 0.9990 or 99.9%. This value implies that
99.9% of the data collected regarding the federal income tax, corporation income tax, payroll tax,
and individual income taxes will fall on the fitted regression line. In addition, this high R2 also
indicates that P value / high R2 combination will a small value indicating the independent variables
have a direct proportionality with the dependent variable. This implies that increase in corporation
income tax; payroll taxes and individual income taxes will cause an increase in the gross federal
income tax. On the other hand, the significance of this model is 0.0031. This implies that the
model is positively significant.
Slope Coefficients:
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According multiple regression table, the slope coefficients for the independent variables are as
follows:
Corporation income tax= 1.4684; this implies that the hypothesis states: for every 1 trillion increase
in corporation income tax, the federal income tax increases by 1.4684 trillion.
Payroll tax = 1.1008; this implies that the hypothesis states: for every 1 trillion increase in payroll
tax, the federal income tax increases by 1.1008 trillion
Individual income tax = 1.0216; this implies that the hypothesis states: for every 1 trillion increase
in individual income tax, the federal income tax increases by 1.0216 trillion.
As it is evident Corporation income tax, Payroll tax and Individual income tax have significant
slope coefficients.
Regression Equation:
To begin, the regression equation for payroll tax is Y = a + bX. The graph below shows the
regression:
Where a= 0.0188 and b =2.917
Therefore, the regression equation is:
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Federal income tax = 7.7023 payroll tax + 0.7318 trillion
The regression equation for individual income tax shown in graph below:
Therefore, Federal income tax = 1.9619 individual income tax + 0.2284 trillion
The regression equation for corporation tax shown in the graph below:
Therefore, Federal income tax = 7.7023 Corporation tax + 0.7318 trillion
Brief Discussion OF my Model:
According to this regression analysis, there exists a strong positive relationship between
the federal gross revenue collection and the individual income tax, payroll tax, and corporation
tax. The fact that the three independent variables have positive slope coefficients indicates that the
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relationship is linear and that increase or decrease in any of these independent variables causes a
linear effect on the federal revenue.
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References
Fahrmeir, L. (2013). Regression : models, methods and applications. Berlin ; New York:
Springer.
Internal Revenue Service. (2012). Internal Revenue Service Data. U.S. Government Printing
Office.
Weisberg, S. (2005). Applied linear regression. Hoboken, N.J.: Wiley-Interscience.