*4.1. Data Analysis*

Tables A1 and A2 indicate the summarized statistics of input/output factors of 42 countries. In 2017, the values of population, EC, CO2, CH4, N2O, and GDP attained a maximum of 1,386,395,000, 5683.42, 3779.929, 0.2102, 0.0394, and 19,390,604, respectively. The minimum values of population, EC, CO2, and GDP are 2,652,340, 18.051, 12.0054, and 29,549.44, in 2008, 2009, 2009, and 2008, respectively. CH4 and N2O have minimum values of 0.0007, 0.0001, respectively, within 2008–2010.

DEA is sensitive to outliers so that the data are tested for measurement errors. The tested results indicate the presence and significance of variables. The outlier detection in the data is checked by using the SPSS software. Table A3 denotes that all cases are valid. Electricity consumption, GDP, CO2, CH4, and N2O have a small difference excluding population as shown in Figure A1; however, the populations are important for the electricity consumption, so this factor is still kept to take part in the analysis process.

Moreover, before the data are applied to analysis by models in DEA, they must be checked via Pearson correlation between input variables and output variables to ensure "isotonicity". The values of the correlation coefficient range from −1 to +1. We have a perfect linear relationship between two variables if the correlation coefficient is equal to 1. On the contrary, the variable must be removed and reselected when the correlation coefficient is not positive and significant. As shown in Tables A4 and A5, the Pearson correlations of 42 countries in the research range from 0.303741 to 1; thus, the input and output factors have a standard qualification.
