exploratory data analysis

Here is a clear demonstration with detailed explanations of exploratory data analysis and correlation. Correlation is employed to test the strength between two variables. Exploratory data analysis is simply applied to know more about the variables in the data set.

Dataset: Data used QoG

The QoG standard data is one of the largest datasets. It contains over 100 data sources with more than 2000 variables. The QoG is constantly updated, and I have used my study on the last version of 2019. It contains both cross-sectional data and time series, meaning that QoGdataset contains information on countries since 1946, which is very good if a researcher is interested in countries as a unit of analysis. However, one should be more careful if this dataset is considered to be useful because there may be some countries in the current dataset that no longer exist now as well as other countries that had not existed before but are now because of either reunification or secession of some countries. Despite that, most part of the dataset is constantly updated and, therefore, can be considered as authentic and useable for research purposes.

Exploratory Data Analysis

The Dependent variable

Economic development

Taking the GDP per capita as a variable is deemed more suitable than other variables that measure the same in the data used. Economic strength or economic development shows the same correlation between Democracy and other independent variables. To operationalize economic development, we also used the QoG dataset 2013, whereby the GDP per capita is chosen. The reason is that the GDP per capita is of the instrument used to measure economic development or performance. For the sake of accuracy, this paper uses the Geary-Khamis dollar, or as it is called the international dollar. The Geary-Khamis is a hypothetical unit (GK$) that has the purchasing power of the US dollar. (QoG: 2013). The GK$ is a recognized currency used in studies and other economic contexts.

The Independent variables

Democracy

Democracy is the independent variable to measure the concept of Democracy. I have used the index of Democracy in QoG standard dataset 2013. It is a value scale 0 to 10 founded on several other scale values intended to measure Democracy, which include civil liberty, democratic political culture, electoral process and pluralism, political participation, and functioning government. When it comes to Democracy, it can be used both nominal and interval variables. The index of Democracy uses a scale of measurement whereby the status of Democracy ranges from 0 to 10 where 0 is no democracy, and 10 is indicating higher Democracy.

Social cohesion

Social cohesion is used to define the sense of solidarity and strength of relationship showcased by members of a given nation, region, or community. Social cohesion is normally determined by several indicators, one of which is the amount of social capital collectively held by a given community. Social capital relates to the shared group resources present in a community, such as the knowledge of a job vacancy held by a close family friend. Therefore, social capital is accessed through social networks formed with other members of society. Social cohesion is a concern with the development of shared values, facing common challenges, creating a sense of togetherness, promoting group engagement across different community activities, and lastly, mitigating social disparities in terms of wealth distribution and income levels.

Ethnic fractionalization

Ethnic fractionalization is associated with the determination of sizes, socio-economic distribution, geographical location, and a number of distinct cultural groups within a given country like Japan or Egypt. These cultural features may relate to customs, traditions, ethnicity, religion, language, and language. In most cases, these features are used in the monopolization of power and social exclusion.

Trade openness

Trade openness is used to define the inward or outward orientation of an economy. Outward orientation is used to refer to economies that seize trading opportunities with other countries, while inward orientation defines countries to avoid or fail to take advantage of trading opportunities with other countries/economies. Good examples of trade policies that are directly linked to the establishment of either outward or inward orientation are scale economies, market competitiveness, technologies, infrastructure, import-export regulations, and trade barriers.

Education

We are not just dealing with the conventional interpretation of education, which is the acquisition of knowledge and skills through a series of teaching, self-learning, or apprenticeship. We are also dealing with the assessment of quality education, which focuses on the proper cognitive development of learners as they progress through the education system.

Exploratory Analysis

Before regression is run on the data, several things were checked to see if the assumptions of the models hold. Q-Q plot for GDP per capita was plotted along with natural log transformation to see the normality of the dependent variable.

It is clear that the natural log transformation is much closer to the normality assumption than the variable directly. Further analysis has been done on the log of per capita GDP. Since it is a bijective transformation that is strictly increasing, the comparison will be preserved. A scatter plot for all the independent variables with the dependent variable is plotted to check for the linearity of relationships.

Onwards

Correlation Analysis

Per Capita GDP vs. Democracy

The correlation between variable per capita GDP and democracy indicator is 0.089, which is small, as indicated by the test of significance of the correlation coefficient, which yields a p-value of 0.315. This indicates that there may not be a strong linear relationship between the two variables.

Per Capita GDP vs. Democracy

The correlation between variable per capita GDP and democracy indicator is 0.128, which is small, as indicated by the test of significance of the correlation coefficient, which yields a p-value of 0.146. This indicates that there may not be a strong linear relationship between the two variables.

Per Capita GDP vs.Social Capital

The correlation between variable per capita GDP and social capital is 0.128, which is significant, as shown by the said test of a significant correlation coefficient, which yields a p-value of 0.146. This indicates that there may not be strong linear relationships between the two variables.

Per Capita GDP vs.Ethnic fractionalization

The correlation between variable per capita GDP and ethnic fractionalization is -0.340, which is small, as indicated by the test of significance of the correlation coefficient, which yields a p-value of 0.001. This shows that there is a strong negative linear relationship between the two variables. This variable may play an important role in explaining variability in per capita GDP.

Per Capita GDP vs.trade openness

The correlation between variable per capita GDP and trade openness is 0.385, which is small, as indicated by the test of significance of the correlation coefficient, which yields a p-value of 0.001. This indicates that there is a strong positive linear relationship between the two variables.

Per Capita GDP vs.Education

The correlation between variable per capita GDP and education is 0.483, which is a high positive value,which is significant, as shown by the test of significance of the correlation coefficient, which yields a p-value of 0.001. This indicates that there may be strong linear relationships between the two variables.

Log per capita GDP with variables

A similar correlation study is carried out with log per capita GDP and the explanatory variables.

Correlations
	log_GDP_PC	Education	Democracy	Social_capital	Ethnic_fractionalization	Trade_Openness
log_GDP_PC	Pearson Correlation	1	.530^**	.262^**	.275^**	-.442^**	.504^**
Sig. (2-tailed)		.000	.003	.002	.000	.000
N	163	50	130	130	148	115
Education	Pearson Correlation	.530^**	1	.575^**	.482^**	-.270	.205
Sig. (2-tailed)	.000		.000	.000	.069	.277
N	50	53	49	49	46	30
Democracy	Pearson Correlation	.262^**	.575^**	1	.856^**	-.086	.437^**
Sig. (2-tailed)	.003	.000		.000	.331	.000
N	130	49	136	136	129	92
Social_capital	Pearson Correlation	.275^**	.482^**	.856^**	1	-.063	.421^**
Sig. (2-tailed)	.002	.000	.000		.477	.000
N	130	49	136	136	129	92
Ethnic_fractionalization	Pearson Correlation	-.442^**	-.270	-.086	-.063	1	-.511^**
Sig. (2-tailed)	.000	.069	.331	.477		.000
N	148	46	129	129	154	111
Trade_Openness	Pearson Correlation	.504^**	.205	.437^**	.421^**	-.511^**	1
Sig. (2-tailed)	.000	.277	.000	.000	.000
N	115	30	92	92	111	116
**. Correlation is significant at the 0.01 level (2-tailed).

The correlations are similar to that with the original variables, but now the social capital and Democracy is also significant variable.

Regression Models

The purpose of regression analysis in the study is to identify and measure the strength of relationships between variables and attribute economic development to various chosen features. Statistical tests such as the t-test and F-test have been used to test the significance of the model. The first model was fitted between GDP per capita and Democracy. All the variables chosen are scale variables, and hence there was no need for the introduction of dummy variables. This model attributes the role of Democracy in the economic development of the country. Since there are a lot of missing values in the dataset, it has been imputed by the mean of the variable. The result from SPSS is presented in the below table:

Model Summary^b
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.062^a	.004	-.002	19105.42550
a. Predictors: (Constant), Democracy
b. Dependent Variable: GDP_per_capita
ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	237204598.344	1	237204598.344	.650	.421^b
Residual	60957886336.257	167	365017283.451
Total	61195090934.601	168
a. Dependent Variable: GDP_per_capita
b. Predictors: (Constant), Democracy
Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	T	Sig.	95.0% Confidence Interval for B
B	Std. Error	Beta	Lower Bound	Upper Bound
1	(Constant)	14543.353	4641.833		3.133	.002	5379.117	23707.590
Democracy	639.450	793.235	.062	.806	.421	-926.611	2205.512
a. Dependent Variable: GDP_per_capita

It is clear from the above model that Democracy alone can not explain a significant part of the variation in the per capita GDP. However, it may be interesting to see the effect of Democracy after controlling by some other variables. One point to note here is that the scale of per capita GDP is very large, anda natural log is taken to get the per capita GDP to a smaller scale. Next, regressions are carried out on the log of per capita GDP. The model is again fit with log GDP per capita as the dependent variable and Democracy as the independent variable.

Model Summary^b
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.208^a	.043	.037	1.15660
a. Predictors: (Constant), Democracy
b. Dependent Variable: log_GDP_PC
ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	10.053	1	10.053	7.515	.007^b
Residual	223.400	167	1.338
Total	233.453	168
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Democracy
Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	T	Sig.	95.0% Confidence Interval for B
B	Std. Error	Beta	Lower Bound	Upper Bound
1	(Constant)	8.481	.281		30.182	.000	7.927	9.036
Democracy	.132	.048	.208	2.741	.007	.037	.226
a. Dependent Variable: log_GDP_PC

This time, however, the p-value for the F-test for the significance of the model is significant, and the test for significance of Democracy is also significant. However, the model is only able to explain 4.3% of the variation in the log of GDP per capita, which is indicated by R² of 0.043. After this interesting finding, a new variable is introduced in regression after controlling by Democracy, which is education. The reason this variable was chosen was because of the strong belief that education is the highest asset for Human resources, and education, society, or country develops more. However, this point is not supported by the data as the significance of variable education is not high. The change in R² is negligible, and the model has similar explaining power as before. Below is the SPSS output after entering the variable education.

ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	10.053	1	10.053	7.515	.007^b
Residual	223.400	167	1.338
Total	233.453	168
2	Regression	13.023	2	6.511	4.904	.009^c
Residual	220.430	166	1.328
Total	233.453	168
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Democracy
c. Predictors: (Constant), Democracy, Education
Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B
B	Std. Error	Beta	Lower Bound	Upper Bound
1	(Constant)	8.481	.281		30.182	.000	7.927	9.036
Democracy	.132	.048	.208	2.741	.007	.037	.226
2	(Constant)	7.957	.449		17.726	.000	7.071	8.843
Democracy	.110	.050	.174	2.208	.029	.012	.209
Education	.014	.010	.118	1.495	.137	-.005	.033
a. Dependent Variable: log_GDP_PC

Model Summary^c
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.208^a	.043	.037	1.15660
2	.236^b	.056	.044	1.15234
a. Predictors: (Constant), Democracy
b. Predictors: (Constant), Democracy, Education
c. Dependent Variable: log_GDP_PC

Clearly, the variable education was not significant and was removed at this stage. Although, it will be added again after controlling with other variables to see its effect. For now, it’s time to add a third variable to the list. Trade openness is introduced along with Democracy to see what the effect of it on economic development is. Intuitively, this should be strongly related, and intuition is supported by the data.

Model Summary^c
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.208^a	.043	.037	1.15660
2	.421^b	.177	.167	1.07577
a. Predictors: (Constant), Democracy
b. Predictors: (Constant), Democracy, Trade_Openness
c. Dependent Variable: log_GDP_PC

ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	10.053	1	10.053	7.515	.007^b
Residual	223.400	167	1.338
Total	233.453	168
2	Regression	41.344	2	20.672	17.862	.000^c
Residual	192.110	166	1.157
Total	233.453	168
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Democracy
c. Predictors: (Constant), Democracy, Trade_Openness

Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	T	Sig.	95.0% Confidence Interval for B
B	Std. Error	Beta	Lower Bound	Upper Bound
1	(Constant)	8.481	.281		30.182	.000	7.927	9.036
Democracy	.132	.048	.208	2.741	.007	.037	.226
2	(Constant)	6.712	.429		15.646	.000	5.865	7.559
Democracy	.072	.046	.114	1.570	.118	-.019	.163
Trade_Openness	.270	.052	.378	5.200	.000	.167	.372
a. Dependent Variable: log_GDP_PC

The model with Democracy and Trade Openness is significant, and the variable trade openness is significant as well. An interesting point to note that after the inclusion of trade openness, the variable Democracy is no longer significant. So, the next model has been implemented with Trade openness and adding the social capital and ethnic fractionalization. These two variables are added together as they are elements of society and culture. Ideally, it is not expected to have a significant effect on economic development. The results from SPSS is given in the tables below:

ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	38.489	1	38.489	33.364	.000^b
Residual	194.964	169	1.154
Total	233.453	170
2	Regression	59.263	3	19.754	18.939	.000^c
Residual	174.191	167	1.043
Total	233.453	170
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Trade_Openness
c. Predictors: (Constant), Trade_Openness, Social_capital, Ethnic_fractionalization

Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B	Collinearity Statistics
B	Std. Error	Beta	Lower Bound	Upper Bound	Tolerance	VIF
1	(Constant)	6.958	.399		17.443	.000	6.170	7.745
Trade_Openness	.290	.050	.406	5.776	.000	.191	.389	1.000	1.000
2	(Constant)	7.953	.534		14.890	.000	6.898	9.007
Trade_Openness	.176	.054	.247	3.261	.001	.070	.283	.779	1.284
Social_capital	.110	.052	.146	2.126	.035	.008	.212	.948	1.055
Ethnic_fractionalization	-1.411	.351	-.297	-4.022	.000	-2.103	-.718	.817	1.223

Model Summary^c
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
R Square Change	F Change	df1	df2	Sig. F Change
1	.406^a	.165	.160	1.07407	.165	33.364	1	169	.000
2	.504^b	.254	.240	1.02130	.089	9.958	2	167	.000
a. Predictors: (Constant), Trade_Openness b. Predictors: (Constant), Trade_Openness, Social_capital, Ethnic_fractionalization c. Dependent Variable: log_GDP_PC

The result suggests that the social capital and ethnic fractionalization both are statistically significant variables at explaining variability at log GDP. The R² also increases to 0.254, which indicates that the model can explain the 25.4% of the variability in the dependent variable. At last, regression is fit with all variables included seeing the effect of Democracy and education. But both of the new included variables turn out to be insignificant, and the R² change was minimal. Hence the final model was decided to have Trade openness, social capital, and ethnic fractionalization.

Model Summary^c
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
R Square Change	F Change	df1	df2	Sig. F Change
1	.504^a	.254	.240	1.02130	.254	18.939	3	167	.000
2	.513^b	.263	.241	1.02124	.009	1.010	2	165	.366
a. Predictors: (Constant), Social_capital, Ethnic_fractionalization, Trade_Openness b. Predictors: (Constant), Social_capital, Ethnic_fractionalization, Trade_Openness, Education, Democracy c. Dependent Variable: log_GDP_PC

Final Model

A final regression model is fitted with the variables significant at the last step in the diagnostics and checked for multicollinearity and other assumptions.

On seeing the residual and predicted variable plot, it can be thought of as independent without heteroscedasticity as there’s no apparent pattern in the plot.

Model Summary^b
Models	R	R-Squar	Adjusted R-Squar	Std. Errors of the Estimate	Change Statistics
R Squar Change	F Change	df1	df2	Sig. F Change
1	.504^a	.254	.240	1.02130	.254	18.939	3	167	.000

ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	59.263	3	19.754	18.939	.000^b
Residual	174.191	167	1.043
Total	233.453	170
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Trade_Openness, Social_capital, Ethnic_fractionalization

Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B	Collinearity Statistics
B	Std. Error	Beta	Lower Bound	Upper Bound	Tolerance	VIF
1	(Constant)	7.953	.534		14.890	.000	6.898	9.007
Trade_Openness	.176	.054	.247	3.261	.001	.070	.283	.779	1.284
Ethnic_fractionalization	-1.411	.351	-.297	-4.022	.000	-2.103	-.718	.817	1.223
Social_capital	.110	.052	.146	2.126	.035	.008	.212	.948	1.055
a. Dependent Variable: log_GDP_PC

In the VIF metric for testing multicollinearity, none of the variables have VIF>5, which indicates that there’s no multicollinearity present. For outlier analysis, Cook’s distance metric was saved for the final model, and cases were rearranged in decreasing order of magnitude. The threshold of 0.05 is used for outlier detection. Only two outliers have Cook’s distance higher than the threshold, which is North Korea and Venezuela. The regression is fit again after removing these variables, and the result turns out to be pretty much the same with a little better R².

Model Summary^b
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
R Square Change	F Change	df1	df2	Sig. F Change
1	.524^a	.275	.262	1.00583	.275	20.866	3	165	.000
a. Predictors: (Constant), Trade_Openness, Social_capital, Ethnic_fractionalization
b. Dependent Variable: log_GDP_PC

ANOVA^a
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	63.331	3	21.110	20.866	.000^b
Residual	166.930	165	1.012
Total	230.260	168
a. Dependent Variable: log_GDP_PC
b. Predictors: (Constant), Trade_Openness, Social_capital, Ethnic_fractionalization

Coefficients^a
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	Collinearity Statistics
B	Std. Error	Beta	Tolerance	VIF
1	(Constant)	7.808	.568		13.745	.000
Social_capital	.095	.052	.124	1.830	.069	.958	1.044
Ethnic_fractionalization	-1.428	.353	-.300	-4.040	.000	.798	1.253
Trade_Openness	.205	.057	.274	3.635	.000	.770	1.298
a. Dependent Variable: log_GDP_PC

ACF and PACF for the unstandardized residual are also plotted. There does not seem to be any serious autocorrelation in the residuals, indicating that the independence assumption of regression holds.

After testing, the final model is decided with the dependent variable as log GDP and outliers, North Korea, and Venezuela removed. The model is able to elaborate on the 27.5% variation found in log per capita GDP.