Testing for Multiple Regression

Test for Multiple Regression (Part One & Two)

WaldenU

02/05/2021

Testing for Multiple Regression

Part 1

A multiple regression model is employed when we need to predict the output for one variable, mostly taken as a dependent variable with the help of two or more other variables independent in their impact.

Research Question

· Does there exist an association between the democracy level, the index of infrastructure and the way it handles its economic index?

H0 = There is no association among the country’s democracy level, infrastructure and economic indices.

Dependent Variable: Democracy level of the country

Independent Variables: Infrastructure and economic indices

In this study, we have utilized statistical measure of correlation to analyze the relationship among the independent and dependant variables. When analyzing the variables with a multiple regression model, each variable is regarded as a metric; therefore, we measure them as interval-ratio variables.

Statistical Analysis

Model Summary

R	0.375
R-square	0.140
Adjusted R-square	0.140
Std. error	2.659

Analysis of Variance (ANOVA)

ANOVA
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	43447.546	2	21723.773	3072.393	.000b
	Residual	266287.201	37661	7.071
	Total	309734.748	37663

Coefficients
Particular	Un-standardized Factors	Standardized Factors	t	Sig.
	B	Std. Error	Beta
(Continual)	1.887	.049		38.668	.000
Infrastructure Directory	.159	.005	.191	31.786	.000
Conduct of Economy Index	.187	.005	.226	37.648	.000

Explanation

In the model summary table, R-square's value is given as 0.375, and the value of adjusted r-square is 0.140. As we are currently dealing with more than one independent variable in multiple regressions, it is figured out from the table that 145 of a country’s democracy level is dependent on the indices of economy and infrastructure.

ANOVA table shows that this study is statistically significant as the level of significance is .00, which is lower compared to the reference significance level of .05.

The coefficient of correlation is further utilized, and results are given in the coefficient table. The un-standardized coefficients show that for every one-unit increase in a country's infrastructure index, the democracy level will increase by .159 units. For each one-unit increase in the country's handling of the economy, the level of democracy will change by .187 units. The null hypothesis is rejected as the significance values for two independent variables is .00. Thus, it can be concluded that the democracy level of a country has a positive correlation with the infrastructure index and handling of the economic index.

This study has significant implications for social change. When a government handles its economy well and boosts its infrastructure level through transparent governmental projects, its citizens will have more faith in the administration system. This will encourage them to participate in the decision-making process while choosing a government hence increasing the level of democracy.

Part 2

In the above part, we have discussed the multiple regressions. In this part, we have used the dummy variable in place of an actual variable to compute the results with the same research question. Particular changes are required while using dummy variables that need to be categorical in nature. The independent variables, infrastructure index and handling economic index do not have categories; therefore, they cannot mimic dummy variables. For this reason, one of the independent variables is replaced with "internet usage," which is categorical and can be coded in the three categories given below:

1= Often 2= Rarely 3= Reference Value = Never

By the rule of Wagner (2016), dummy variables are created by subtracting "1" from the given categories of the dummy variable. In the present case, the selected dummy variable "internet usage" has three categories, so we will have two dummy variables as “often” and “rarely” while “never” will be treated as a reference.

Research Question

· Does there exist an association between the democracy level of a country, internet usage and the way it handles its economic index?

H0 = There is no association among the country’s democracy level, internet usage and economic index.

Statistical Analysis

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Durbin-Watson
first	0.346	0.119	0.119	2.684	1.579

ANOVA
Variable	Sum of Squares	df	Mean Square	F	p-value
	Regression model	41197.662	3	13732.554	1906.585	.000b
	Residual	303629.659	42155	7.203
	Total	344827.321	42158

Coefficients
Particular	Unstandardized Factors	Standardized Factors	t	Sig.	Collinearity Figures
	B	Std. Error	Beta			Tolerance	VIF
(Continual)	2.876	.039		73.619	.000
Regularly	-.408	.049	-.038	-8.353	.000	.985	1.015
Occasionally	-.302	.037	-.037	-8.088	.000	.985	1.015
Conduct of Economy Index	.286	.004	.342	74.815	.000	1.000	1.000

Explanation

Durbin Watson's statistics typically range from 0 to 4, with the values of below 1.0 and above 3.0, which shows serious correlations. This model showed a Durbin Watson statics of 1.579, which shows no correlation reported between the residuals. The model also shows a significance value of .000, which is clearly below the constant and standard value of .05; thus, the significance also shows no correlation. The model adjusted R square value is 0.119, which means about 11.9% of the country's variations are firm by the difference in both the conduct of economy index and the internet practice.

The reference category included the variable of “Never," which means that the variable will receive a code of zero for the other independent variables. The co-efficiency table shows the value of frequency is -0.408, which shows the country shows population practices internet has a democracy level of 0.408 units compared to the countries that don't exercise this practice. The co-efficient value of “rarely" shows a value of -0.302, which shows that the country whose population uses the internet rarely or sometimes has an average democracy level of 0.303 units, which is less than the country whose population never uses the internet.

All co-efficient tested resulted in a significance value of .000, which shows a minor relationship between the variables. Also, the co-efficient table shows there were no assumptions recorded, as the value of VIF was 1.015, which is low than the standard value of VIF. Laureate education (2016) shows that the value of VIF close to 10 or above shows serious collinearity. The histogram model shows a positive skew in the residuals. Independent variables correlate or associates with the dependent variables, but no assumptions were recorded or encounter.

This study has significant implications of social changes as the statistical analysis verifies that the democracy level of a country is influenced by the use of the internet in population. Through internet usage, people would be more aware of the changes made in their socio-economic structure. They would have an eye on the performance of the government. At the same place, a country handling its economic index well reflects a strong administration and good governance.

References

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ` ed.). Thousand Oaks, CA: Sage Publications

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ` ed.). Thousand Oaks, CA: Sage Publications. Chapter 11, “Analysis of Variance” (pp. ` 325-371)

Laureate Education, I. (2016). Correlation and bivariate regression. [Video file] Baltimore.

Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science ` statistics (6th ed.). Thousand Oaks, CA: Sage Publications.

Test for Multiple Regression (Part One & Two)

WaldenU

02/05/2021

Test for Multiple Regression (Part One & Two)

WaldenU

02/05/2021