1
Running Head: Check Point 3
Check Point 3
Student name:
Institutional affiliation:
2
Check Point 3
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:
•
Dependent variable: The federal tax income
•
Independent variables: Individual Income taxes, corporate income taxes and Payroll Taxes
3
Check Point 3
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
6
ANOVA
df
Regression
Residual
Total
Intercept
Corporation Income Taxes
Payroll Taxes
Individual Income Taxes
3
2
5
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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Check Point 3
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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Check Point 3
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:
6
Check Point 3
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
7
Check Point 3
relationship is linear and that increase or decrease in any of these independent variables causes a
linear effect on the federal revenue.
8
Check Point 3
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.
1
Running Head: Check Point 1
Check Point 1
Student name:
Institutional affiliation:
2
Check Point 1
Check Point 1
CHECK POINT 1
Model:
The figure below shows the Federal Tax revenue model:
Federal Tax Revenue Model
Excise,
Estate, and
Other taxes
Corporate
Income
taxes
Federal Tax
Income
Income
Taxes
Payroll
Taxes
According to the above federal tax revenue model, it follows that:
•
Dependent variable: The federal tax income is the dependent variable because the amount
of its collection depends on the income taxes, patrol taxes, corporate income taxes, excise,
estate and other taxes.
•
Independent variables: Income taxes and corporate income taxes are the independent
variables.
•
Moderator variables: The payroll taxes, excise, estate and other taxes are the moderator
variables because they determine the relationship between income taxes and federal taxes
3
Check Point 1
Model Description:
My model involves investigating the federal tax income. The research will determine the
relationship between the amount of federal tax income and the payroll taxes, income taxes,
corporate income taxes, excise, estate and other taxes in the United States of America. The
dependent variable will be the federal tax income while the independent variable will be the
corporate income taxes and income taxes. Moreover, the moderate variables will be payroll taxes,
excise, estate and other taxes.
Data source description:
In my research, I will use previous research studies regarding the federal government, with
most of the information being from the US government Website. Moreover, I will also make use
of financial websites such as income tax department to collect high quality information for the
research. In addition, I will contact the US finance office to get detailed information about annual
federal income taxes, total payroll taxes, corporate income taxes, and other taxes. I believe that my
research topic has been previously well researched and vested and am optimistic that I will get the
right information.
4
Check Point 1
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.
1
Running Head: CHECK POINT 4
Check Point 4
Student name:
Institutional affiliation:
Date Submitted:
2
CHECK POINT 4
CHECK POINT 4
For this checkpoint, I will pick the federal income taxes rates as the categorical independent
variable. The nominal federal tax rate in the USA is a flat rate of 21%. However, stated and local
taxes often vary by policy. As such, my model would show the task rates from 2012 to 2017 as it
varies.
Recode of the categorical independent variable, Tax Rates. (Dummy Coding):
Federal Income
Corporation
Payroll Individual
Year Taxes(in Trillion) Income Taxes Taxes
Income Taxes
Tax Rates
2012
2.45
0.2423 0.8453
1.1322
2013
2.77
0.2735 0.9478
1.3164
2014
3.02
0.3207 1.0239
1.3946
2015
3.25
0.3438 1.0653
1.5408
2016
3.27
0.3
1.115
1.546
2017
3.32
0.297
1.162
1.587
Consider the following information:
For this regression dummy coding, the tax rate values are recoded to:
1 -> 1.0
Else -> 0.0
TaxRates into Rates (Tax Rates)
Old Value New Value Value Label
1
2
1
2
1
2
1
2
1
1
2
1
3
CHECK POINT 4
RECODE TaxRates ('1'=1) (ELSE=0) INTO Rates.
VARIABLE LABELS Rates 'Rates'.
The tables below represent the output values of the logit model:
Convergence Informationa,b
Maximum Number of
20
Iterations
Converge Tolerance
.00100
Final Maximum Absolute
3.35851E-5c
Difference
Final Maximum Relative
8.31506E-5
Difference
Number of Iterations
5
a. Model: Multinomial Logit
b. Design: Constant + Year + Year * Rates
c. The iteration converged because the
maximum absolute changes of parameter
estimates is less than the specified
convergence criterion.
Cell Counts and Residualsa,b
Observed
%
Count
%
Residual
Standardized
Adjusted
Residual
Residual
Rates
Year
.00
2012
.500
10.0%
.500
10.0%
.000
.000
.
.000
2013
1.500
30.0%
1.500
30.0%
.000
.000
.
.000
2014
.500
10.0%
.500
10.0%
.000
.000
.
.000
2015
.500
10.0%
.500
10.0%
.000
.000
.
.000
2016
1.500
30.0%
1.500
30.0%
.000
.000
.000
.000
2017
.500
10.0%
.500
10.0%
.000
.000
.
.000
2012
1.500
21.4%
1.500
21.4%
.000
.000
.000
.000
2013
.500
7.1%
.500
7.1%
.000
.000
.
.000
1.00
Count
Expected
Deviance
4
CHECK POINT 4
2014
1.500
21.4%
1.500
21.4%
.000
.000
.
.000
2015
1.500
21.4%
1.500
21.4%
.000
.000
.
.000
2016
.500
7.1%
.500
7.1%
.000
.000
.
.000
2017
1.500
21.4%
1.500
21.4%
.000
.000
.000
.000
a. Model: Multinomial Logit
b. Design: Constant + Year + Year * Rates
Logit Regression Equation:
logistic regression year with payroll taxes & individual income taxes/categorical = rates
5
CHECK POINT 4
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.
1
Running Head: CHECK POINT 5
Check Point 5
Student name:
Institutional affiliation:
Date Submitted:
2
CHECK POINT 5
Check Point 5
CHECK POINT 5
Dichotomous Dependent Variable:
For this checkpoint, I created a dichotomous dependent variable, ‘Fully Paid’ (Yes or No). This
would show weather the taxes are fully paid in a certain year or not. The dichotomous variable
is as shown in the graph below:
3
CHECK POINT 5
Logit Model:
Cell Counts and Residualsa,b
Observed
Paid
Count
Expected
%
Count
%
Residual
Standardized
Adjusted
Residual
Residual
Deviance
1.00
4.500
64.3%
4.500
64.3%
.000
.000
.
.000
2.00
2.500
35.7%
2.500
35.7%
.000
.000
.000
.000
a. Model: Multinomial
b. Design: Constant + Paid
Cell Counts and Residualsa,b
Observed
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
2.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
1.00
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
2.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
1.00
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
2.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
1.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
2.00
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
1.00
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
2.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
1.00
.500
25.0%
.500
25.0%
.000
.000
.000
.000
2.00
1.500
75.0%
1.500
75.0%
.000
.000
.
.000
2017
a. Model: Multinomial Logit
b. Design: Constant + Paid + Paid * Year
Residual
Residual
1.00
2016
%
Residual
2012
2015
Count
Adjusted
Paid
2014
%
Standardized
Year
2013
Count
Expected
Deviance
4
CHECK POINT 5
Coefficientsb,c
Federal Income
Taxes(in
Corporation
Individual
Year
Paid
Trillion)a
Income Taxesa
Payroll Taxesa
Income Taxesa
2012
1.00
2.45000000000
.242300000000
.845300000000
1.13220000000
0000
000
000
0000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
2.77000000000
.273500000000
.947800000000
1.31640000000
0000
000
000
0000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
3.02000000000
.320700000000
1.02390000000
1.39460000000
0000
000
0000
0000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
3.25000000000
.343800000000
1.06530000000
1.54080000000
0000
000
0000
0000
3.27000000000
.300000000000
1.11500000000
1.54600000000
0000
000
0000
0000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
.000000000000
.000000000000
.000000000000
.000000000000
000
000
000
000
3.32000000000
.297000000000
1.16200000000
1.58700000000
0000
000
0000
0000
2.00
2013
1.00
2.00
2014
1.00
2.00
2015
1.00
2.00
2016
1.00
2.00
2017
1.00
2.00
a. Sum of the coefficients is not zero for some combinations of levels of independent
factors. The generalized log-odds ratio is not computed.
b. Model: Multinomial Logit
c. Design: Constant + Paid + Paid * Year
5
CHECK POINT 5
Logistic Function:
Logit function is the algorithm of odds:
logit(x) = log(x / (1 – x))
Below is a plot representing the logit function:
6
CHECK POINT 5
References
Bewick, V., Cheek, L., & Ball, J. (2005). Statistics review 14: Logistic regression. Critical Care (London,
England), 9(1), 112-118. http://dx.doi.org/ 10.1186/cc3045
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York, NY: John Wiley &
Sons Inc.
Peng, C. J., & So, T. H. (2002). Logistic regression analysis and reporting: A primer. Understanding
Statistics, 1(1), 31-70.
...

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