Statistical Analysis

 

 

Statistical Analysis

 

 

Research study

To investigate the relationship between fiscal policy and Foreign Direct Investment (FDI) in Singapore

Specific Objectives

1. To investigate the relationship between Country Risk (CR) and Foreign Direct Investment (FDI) in Singapore.
2. To investigate the relationship between Human Capital (HC) and Foreign Direct Investment (FDI) in Singapore.
3. To investigate the relationship between Market Size (GDP) and Foreign Direct Investment (FDI) in Singapore.
4. To investigate the relationship between Corporate Income Tax Rate (TR) and Foreign Direct Investment (FDI) in Singapore.

Research questions

This study proposes to investigate the following research questions:

1. Is there a significant relationship between Country Risk (CR) and Foreign Direct Investment (FDI) in Singapore?
2. Is there a significant relationship between Human Capital (HC) and Foreign Direct Investment (FDI) in Singapore?
3. Is there a significant relationship between Market Size (GDP) and   Foreign Direct Investment (FDI) in Libya?
4. Is there a significant relationship between Corporate Income Tax Rate (TR) and   Foreign Direct Investment (FDI) in Singapore?

Research hypotheses

H1: There is a significant relationship between Country Risk (CR) and Foreign Direct Investment (FDI) in Singapore?

H2: There is a significant relationship between Human Capital (HC) and Foreign Direct Investment (FDI) in Singapore.

H3: There is a significant relationship between Market Size (GDP) and   Foreign Direct Investment (FDI) in Singapore.

H4: There is a significant relationship between Corporate Income Tax Rate (TR) and   Foreign Direct Investment (FDI) in Libya.

The proposed model to conduct the data analysis is simple linear regression model shown below:

Simple Linear Regression:  

• – Dependent Variable
• – Independent
• – Y-intercept
• – Change in mean of Y when X increases by 1 (slope)
•  –  Random error term

 

Substituting this to the case study we get:

FDI = f (CR, HC, GDP, TR) and the econometric form of the simple linear regression becomes:

FDI_i=β₀+(β_1*CR_i)+(β_2*HC_i)+(β_3*GDP_i)+(β_4*TR_i) + ε_i

Where

CR: Country Risk

HC: Human Capital

GDP: Gross Domestic Product

TR: Corporate Income Tax Rate

ε _i= Random error term.

β = Parameters (β₀ = parameter at the Y-intercept

 

In this case:

The study variables are:

Independent variables are:

1. CR: Country Risk
2. HC: Human Capital
3. GDP: Gross Domestic Product
4. TR: Corporate Income Tax Rate

 

Dependent variable is the Foreign Direct Investment (FDI)

The case study runs from 2000 to 2010 (11 years)

 

In order to test the 6 hypotheses in the study, the relationships between the dependent variable (FDI) with each of the 6 independent variables should be done; hence the model equation will be broken down for each variable to give the following equations:

 

1. Country Risk

FDI_i=β₀+β_1*CR_i+ ε_i

2. Human Capital

FDI_i=β₀+β_2*HC_i + ε_i

3. Market Size (GDP)

FDI_i=β₀+β_3*GDP_i + ε_i

4. Exchange Rate

FDI_i=β₀+β_4*TR_i+ ε_i

 

The data to be used for analysis is as follows:

Table 1: Statistics of the study variables

Year	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010
Net Foreign Direct Investment (FDI)	$43,000	$308,000	$281,000	$80,000	$71,000	$910,000	$1,590,000	$756,200	$1,776,900	$206,000	$938,000
Country Risk (CR), %	45	45	50	50	55	55	55	55	60	60	55
Human Capital (HC)	1801053.8	1872069.2	1943603.2	2005730.2	2067876.2	2127432.9	2189598.9	2253432.3	2306727.316	2352625.4	2379115.6
Market Size (GDP in $ million)	$33,896	$28,420	$19,842	$24,062	$33,384	$44,000	$56,484	$71,803	$93,167	$62,360	$74,232
Corporate Income Tax Rate (T R ), %	30.8	30.8	30.8	30.8	30.8	30.8	40	40	40	40	20

 

 

 

 

 

 

 

 

 

 

 

 

Table 2: The relationship between Corporate Income Tax Rate and Net Foreign Direct Investment

 

 

                                                               

Descriptive Analysis

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Corporate Income Tax Rate	33.16	6.275	11

 

Correlation Analysis

Correlations
		Net Foreign Direct Investment (FDI) in $million	Corporate Income Tax Rate
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.343
	Corporate Income Tax Rate	.343	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.151
	Corporate Income Tax Rate	.151	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Corporate Income Tax Rate	11	11

 

 

The association between Corporate Income Tax Rate (TR) as well as Foreign Direct Investment (FDI) in Singapore is not that significant. This is so because the Pearson correlation is greater than 0.05. In a nutshell, an increase in FDI does not necessarily have a bearing on the corporate income tax rate. The opposite doesn’t add up. The same association is evident in the scatter plot.

 

Regression Analysis

 

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Corporate Income Tax Rate	33.16	6.275	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Corporate Income Tax Rate
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.343
	Corporate Income Tax Rate	.343	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.151
	Corporate Income Tax Rate	.151	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Corporate Income Tax Rate	11	11

 

 

Variables Entered/Removedb
Model	Variables Entered	Variables Removed	Method
1	Corporate Income Tax Ratea	.	Enter
All requested variables entered. Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.343a	.118	.020	609670.033
Predictors: (Constant), Corporate Income Tax Rate Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

 

 

 

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	4.456E11	1	4.456E11	1.199	.302a
	Residual	3.345E12	9	3.717E11
	Total	3.791E12	10
Predictors: (Constant), Corporate Income Tax Rate Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	(Constant)	-482937.000	1035389.929		-.466	.652
	Corporate Income Tax Rate	33641.467	30724.659	.343	1.095	.302	1.000	1.000
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
				(Constant)	Corporate Income Tax Rate
1	1	1.984	1.000	.01	.01
	2	.016	11.176	.99	.99
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	189892.33	862721.69	632736.36	211097.309	11
Residual	-656721.688	914178.313	.000	578383.778	11
Std. Predicted Value	-2.098	1.089	.000	1.000	11
Std. Residual	-1.077	1.499	.000	.949	11
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

The regression equation is

FDI = -2.3+0.153*TR

The representation does not exhibit any significance because Pearson Correlation ANOVA is greater than 5%. The benchmark variable as well as the interceptor is equally not significant at 0.05% level.

 

Table 3: The relationship between Country Risk and Net Foreign Direct Investment

 

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Country Risk (CR), %	53.18	5.135	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Country Risk (CR), %
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.546
	Country Risk (CR), %	.546	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.041
	Country Risk (CR), %	.041	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Country Risk (CR), %	11	11

 

 

 

The association between Country Risk (CR) and Foreign Direct Investment (FDI) in Singapore.is not significant because of Pearson value that is higher than 0.005. Implicitly, an increase in foreign direct outlay does not necessary lead to an increase in the country risk and the scatter plot illustrates this in black and white.

Regression Analysis

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Country Risk (CR), %	53.18	5.135	11

 

 

 

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Country Risk (CR), %
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.546
	Country Risk (CR), %	.546	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.041
	Country Risk (CR), %	.041	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Country Risk (CR), %	11	11

 

 

Variables Entered/Removedb
Model	Variables Entered	Variables Removed	Method
1	Country Risk (CR), %a	.	Enter
All requested variables entered. Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.546a	.298	.220	543819.832
Predictors: (Constant), Country Risk (CR), %

 

 

 

 

 

 

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1.129E12	1	1.129E12	3.818	.082a
	Residual	2.662E12	9	2.957E11
	Total	3.791E12	10
Predictors: (Constant), Country Risk (CR), % Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	(Constant)	-2847857.759	1788742.844		-1.592	.146
	Country Risk (CR), %	65447.069	33492.872	.546	1.954	.082	1.000	1.000
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
				(Constant)	Country Risk (CR), %
1	1	1.996	1.000	.00	.00
	2	.004	21.772	1.00	1.00
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

 

The regression equation is

FDI = -16.85+0.369*CR

The representation is not significant at 0.05% level owing to the Pearson Correlation value of ANOVA which is greater than 5%. Both the interceptor and the benchmark variable is significant at 0.05% level. This representation implies that in the event of an increase in foreign direct investment does not necessary lead to an increase in the country risk and the scatter plot illustrates this in black and white.

 

 

Table 4: The relationship between Human Capital and Net Foreign Direct Investment

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Human Capital (HC)	2118115.00	197198.777	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Human Capital (HC)
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.578
	Human Capital (HC)	.578	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.031
	Human Capital (HC)	.031	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Human Capital (HC)	11	11

 

 

 

 

Foreign Direct Investment (FDI) as well as Human Capital does not exhibit a strong association owing to a higher Pearson correlation value. In reality, an increase in human capital culminates does not necessarily have an impact on foreign direct investment; however the opposite will never be any truer. The scatter plot demonstrates this reality.

 

Regression Analysis

 

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Human Capital (HC)	2118115.00	197198.777	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Human Capital (HC)
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.578
	Human Capital (HC)	.578	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.031
	Human Capital (HC)	.031	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Human Capital (HC)	11	11

 

 

Variables Entered/Removedb
Model	Variables Entered	Variables Removed	Method
1	Human Capital (HC)a	.	Enter
All requested variables entered. Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.578a	.334	.260	529635.412
Predictors: (Constant), Human Capital (HC) Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1.266E12	1	1.266E12	4.514	.063a
	Residual	2.525E12	9	2.805E11
	Total	3.791E12	10
Predictors: (Constant), Human Capital (HC) Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	(Constant)	-3189428.774	1806037.273		-1.766	.111
	Human Capital (HC)	1.805	.849	.578	2.125	.063	1.000	1.000
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
				(Constant)	Human Capital (HC)
1	1	1.996	1.000	.00	.00
	2	.004	22.575	1.00	1.00
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	60595.44	1103715.25	632736.36	355847.672	11
Residual	-849913.313	828270.063	.000	502456.270	11
Std. Predicted Value	-1.608	1.324	.000	1.000	11
Std. Residual	-1.605	1.564	.000	.949	11
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

The regression equation is

FDI = -105.57+2.049 *HC

The representation is not significant because the P-value is greater than 5% on the Pearson correlation. Both the interceptor as well as the benchmark variable is non-significant at 0.05. In reality, an increase in human capital culminates does not necessarily have an impact on foreign direct investment; however the opposite will never be any truer.

 

Table 5: The relationship between Market Size (GDP) and Net Foreign Direct Investment

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Market Size (GDP in $ million)	49240.91	23945.428	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Market Size (GDP in $ million)
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.743
	Market Size (GDP in $ million)	.743	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.004
	Market Size (GDP in $ million)	.004	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Market Size (GDP in $ million)	11	11

 

 

 

The association between Market Size (GDP) and Foreign Direct Investment (FDI) in Singapore is promising and significant based on the fact that the Pearson value is less than .005.  In reality, if the market size balloon, foreign direct investment is also goes up and the opposite is equally true. This is also evident in the scatter plot.

 

Regression Analysis

 

 

Descriptive Statistics
	Mean	Std. Deviation	N
Net Foreign Direct Investment (FDI) in $million	632736.36	615702.744	11
Market Size (GDP in $ million)	49240.91	23945.428	11

 

 

Correlations
		Net Foreign Direct Investment (FDI) in $million	Market Size (GDP in $ million)
Pearson Correlation	Net Foreign Direct Investment (FDI) in $million	1.000	.743
	Market Size (GDP in $ million)	.743	1.000
Sig. (1-tailed)	Net Foreign Direct Investment (FDI) in $million	.	.004
	Market Size (GDP in $ million)	.004	.
N	Net Foreign Direct Investment (FDI) in $million	11	11
	Market Size (GDP in $ million)	11	11

 

 

Variables Entered/Removedb
Model	Variables Entered	Variables Removed	Method
1	Market Size (GDP in $ million)a	.	Enter
All requested variables entered. Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.743a	.552	.502	434429.979
Predictors: (Constant), Market Size (GDP in $ million) Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

 

 

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	2.092E12	1	2.092E12	11.086	.009a
	Residual	1.699E12	9	1.887E11
	Total	3.791E12	10
Predictors: (Constant), Market Size (GDP in $ million) Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	(Constant)	-307893.924	311392.401		-.989	.349
	Market Size (GDP in $ million)	19.103	5.737	.743	3.330	.009	1.000	1.000
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
				(Constant)	Market Size (GDP in $ million)
1	1	1.907	1.000	.05	.05
	2	.093	4.534	.95	.95
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

 

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	71140.23	1471839.75	632736.36	457420.378	11
Residual	-677345.375	818901.625	.000	412136.465	11
Std. Predicted Value	-1.228	1.834	.000	1.000	11
Std. Residual	-1.559	1.885	.000	.949	11
Dependent Variable: Net Foreign Direct Investment (FDI) in $million

 

The regression equation is

FDI = -1.929+0.000095* GDP

 

The representation is important and significant at 0.05 levels owing to the fact that the P-value of ANOVA table is less than 5%. The benchmark variable is important at 0.05% level although the integrator is not significant for the model. The residual is proportionately distributed as shown by the histogram as well as the normal p-p plot.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

Douglas C. (2000). Montgomery, Design and Analysis of Experiments, 5th ed., John Wiley           and Sons, Inc. New York.

George Casella, Roger L. Berger, (2001). Statistical Inference, 2nd ed., Duxbury Press,.

Johnson, Richard A.; Wichern, Dean W. (2007). Applied Multivariate Statistical Analysis   (Sixth ed.). Prentice Hall.

Peter J. Bickel, Kjell A. Doksum,(2011). Mathematical Statistics, Volume 1, Basic Ideas and         Selected Topics, 2rd ed. Prentice Hall.

Robert V. Hogg, Allen T. Craig, Joseph W. McKean,(2004).  An Introduction to     Mathematical Statistics, 6th ed., Prentice Hall.

Saunders, M., Lewis, P. and Thornhill, A. (2003), “Research Methods for Business            Students”, Third Edition, Prentice-Hall International, New Jersey.

Sen, M. Srivastava,(2011). Regression Analysis — Theory, Methods, and Applications,       Springer-Verlag, Berlin.

Warne, R. Lazo, M., Ramos, T. and Ritter, N. (2012). Statistical Methods Used in Gifted             Education Journals, 2006–2010. Gifted Child Quarterly, 56(3) 134–149.

 

 

 

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