Question

Part I

We’ll use the “Debt and Taxes” tab in the Lab 5 Excel Workbook

The Economic Data Runs from 1946 (1^st year post WW2) to 2016

Note: This issue is tremendously more complicated than the two variables presented here. This is only a partial look at the issue and there is ample room for debate as causes of the issues at hand.

1) Examining the Relationships

              Create and copy in the following Charts

                             1) Line Chart with “Year”, “Top Bracket %”, and “Debt (Relative to 1946)”

                             2) Scatterplot with “Year” and “Top Bracket %,” choose “Show Trendline”

                             3) Scatterplot with “Year” and “National Debt (Trillions),” choose “Show Trendline”

              a) What trends do you see over time?

              b) Do “Top Bracket %” and “National Debt(Trillions)” appear associated?

              c) What might be a possible confounding factor?

2) Running Regressions

              a) Use “Data->Data Analysis->Regression” with “Top Bracket” as the y variable and

“Year” as the x- variable.

What is your model? Slope t-value? F-Value? R squared?

              b) Run a second regression with “National Debt(Trillions)” as the y variable and

                             “Year” as the x-variable.

What is your model? Slope t-value? F-Value? R squared?

             

c) Run a final regression with “National Debt(Trillions)” as the y variable and

                             “Top Bracket %” as the x-variable

What is your model? Slope t-value? F-Value? R squared?

              d) Based on the R squared from part c) how much of the debts change is due to taxes?

Part II

We will use the “Twins Data” tab in the workbook.

1) Single Variable

              a) Create a Scatterplot of “Wins” and “Runs” (You might need to rescale the axis for each)

              b) Run a Regression with “Wins” as y and “Runs” as x

c) What is your model? Slope t-value? F-Value? R squared?

2) Multivariable

              a) Traditional Stats

                             Run a regression with “Wins” as the y variable and both “Batting Average” and “ERA”

as the two x variables

What is your model? Slope t-values? F-Value? R squared?

              b) Moneyball Stats

                             Run a regression with “Wins” as the y variable and “OPS” and “WHIP” as the x variables

What is your model? Slope t-value? F-Value? R squared?

3) Of the 3 options which model do you feel works the best? Explain.

Year	Top Bracket %	Decimal for Top Bracket	National Debt (Trillions)	Debt (Relative to 1946)
1946	91	0.91	0.271	1.000
1947	91	0.91	0.257	0.948
1948	91	0.91	0.252	0.930
1949	91	0.91	0.253	0.934
1950	91	0.91	0.257	0.948
1951	91	0.91	0.255	0.941
1952	92	0.92	0.259	0.956
1953	92	0.92	0.266	0.982
1954	91	0.91	0.271	1.000
1955	91	0.91	0.274	1.011
1956	91	0.91	0.273	1.007
1957	91	0.91	0.271	1.000
1958	91	0.91	0.276	1.018
1959	91	0.91	0.285	1.052
1960	91	0.91	0.286	1.055
1961	91	0.91	0.289	1.066
1962	91	0.91	0.298	1.100
1963	91	0.91	0.306	1.129
1964	77	0.77	0.312	1.151
1965	70	0.7	0.317	1.170
1966	70	0.7	0.320	1.181
1967	70	0.7	0.326	1.203
1968	70	0.7	0.348	1.284
1969	70	0.7	0.354	1.306
1970	70	0.7	0.371	1.369
1971	70	0.7	0.398	1.469
1972	70	0.7	0.427	1.576
1973	70	0.7	0.458	1.690
1974	70	0.7	0.475	1.753
1975	70	0.7	0.533	1.967
1976	70	0.7	0.620	2.288
1977	70	0.7	0.699	2.579
1978	70	0.7	0.772	2.849
1979	70	0.7	0.827	3.052
1980	70	0.7	0.908	3.351
1981	70	0.7	0.998	3.683
1982	50	0.5	1.142	4.214
1983	50	0.5	1.377	5.081
1984	50	0.5	1.572	5.801
1985	50	0.5	1.823	6.727
1986	50	0.5	2.125	7.841
1987	38.5	0.385	2.340	8.635
1988	28	0.28	2.602	9.601
1989	28	0.28	2.857	10.542
1990	28	0.28	3.233	11.930
1991	31	0.31	3.665	13.524
1992	39.6	0.396	4.065	15.000
1993	39.6	0.396	4.411	16.277
1994	39.6	0.396	4.693	17.317
1995	39.6	0.396	4.974	18.354
1996	39.6	0.396	5.225	19.280
1997	39.6	0.396	5.413	19.974
1998	39.6	0.396	5.526	20.391
1999	39.6	0.396	5.656	20.871
2000	39.6	0.396	5.674	20.937
2001	39.1	0.391	5.807	21.428
2002	38.6	0.386	6.228	22.982
2003	35	0.35	6.783	25.030
2004	35	0.35	7.379	27.229
2005	35	0.35	7.933	29.273
2006	35	0.35	8.507	31.391
2007	35	0.35	9.008	33.240
2008	35	0.35	10.025	36.993
2009	35	0.35	11.910	43.948
2010	35	0.35	13.562	50.044
2011	35	0.35	14.790	54.576
2012	35	0.35	16.066	59.284
2013	39.6	0.396	16.738	61.764
2014	39.6	0.396	17.824	65.771
2015	39.6	0.396	18.151	66.978
2016	39.6	0.396	19.573	72.225

Answer 1

Part.1

Part-1

1 Examine the relationship

2. Scatterplot with Year and Top Bracket % with trendline .

3. Scatter plot with Year and National Debt

Q.2

a. When Top bracket is y variable and year is x variable the Output is

	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	0.929531
	R Square	0.864028
	Adjusted R Square	0.862057
	Standard Error	8.520685
	Observations	71
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	31832.87	31832.87	438.4568	1.31E-31
	Residual	69	5009.543	72.60207
	Total	70	36842.41
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
	Intercept	2106.669	97.75262	21.55102	2.32E-32	1911.658	2301.68	1911.658	2301.68
	Year	-1.0332	0.049342	-20.9394	1.31E-31	-1.13163	-0.93476	-1.13163	-0.93476

The Model is given by

Y(Top Bracket %)=2106.669-1.0332*X(Year)

The t value for intercept is 21.55102 and for slope coefficient or Year t value is -209394

F value is given by 438.4568

R Sq value is 0.864028

B. When National Debt (Trillions) is Y variable and year is x variable then output is:

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.83730135
R Square	0.70107356
Adjusted R Square	0.69674129
Standard Error	2.83266867
Observations	71
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1298.494	1298.494	161.826	9.17E-20
Residual	69	553.6568	8.024012
Total	70	1852.151
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-409.535751	32.49748	-12.6021	1.45E-19	-474.366	-344.705	-474.366	-344.705
Year	0.20867294	0.016404	12.72109	9.17E-20	0.175948	0.241397	0.175948	0.241397

The Model is given by

Y(National Debt)=409.53575+0.286729*X(Year)

The t value for intercept is 12.6021 and for slope coefficient or Year t value is 12.7211

F value is given by 161.826

R Sq value is 0.701074

C. When National Debt (Trillions) is y variable and Top Bracket % is xvarible then output is,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6716638
R Square	0.45113225
Adjusted R Square	0.44317765
Standard Error	3.83837557
Observations	71
ANOVA
	df	SS	MS	F	Significance F
Regression	1	835.5649	835.5649	56.71334	1.44E-10
Residual	69	1016.586	14.73313
Total	70	1852.151
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	12.8663055	1.281564	10.03953	3.96E-15	10.30965	15.42296	10.30965	15.42296
Top Bracket %	-0.15059692	0.019997	-7.53083	1.44E-10	-0.19049	-0.1107	-0.19049	-0.1107

The Model is given by

Y(National Debt)=12.866+0.1506*X(Top Bracket %)

The t value for intercept is 10.04 and for slope coefficient or top Bracket t value is 7.531

F value is given by 56.71334

R Sq value is 0.4511

D. Based on taxes 45% Debt is change .