## 2 Materials and Methods
### Algorithm Development and Validation  
The methodology developed in a paper published by [PERSON] et al. [30] consisting on four phases is used to develop the algorithm. First, the independent variables (i.e., GDP \"a\", population \"b\" and RES \"c\") are weighted on a scale between 0 and 1, using Equation (1), so they can be compared on the same value scale. In total, 108 weighting values are obtained. Subsequently, the relation between the calculated weighting values (\(WV_{x_{i}}\)) and the amount of GHGs released into the atmosphere is explored. \[WV_{x_{i}}=\frac{Vx_{i}}{\sum Vx_{i}} \tag{1}\]  
where:  
* \(x\) is the analysed variable (GDP \"a\", population \"b\" or RES \"c\");
* \(i\) is the analysed MS (n = 1, 2, 3, 4, 5, 6... 27);
* \(V_{x}\) is the value of the variable \(x\) for the analysed MS \"i\";
* \(WV_{x_{i}}\) is the weighting value of each variable \(x\) for the analysed MS \"i\". Second, SPSS 28 statistical software is used for a multiple regression analysis (Equation (2)) to obtain the \(\beta\) coefficients--using the data obtained from the twenty-seven MSs--in order to establish the significance that each independent variable will have in the final model. \[y_{i}=\beta_{0}+\beta_{1}x_{1i}+\beta_{2}x_{2i}+\beta_{3}x_{3i}+e_{i} \tag{2}\]  
where:  
* \(y_{i}\) is the amount of GHG emissions estimated for the MS \"i\";
* \(\beta\) is the coefficient that represents how changes in each of the independent variables \"\(x\)\" (\(WV_{a_{i}};\ WV_{b_{i}};\ WV_{c_{i}}\)) influence the dependent variable \"\(y\)\";
* \(e_{i}\) is the residual error, i.e., difference between the observed values (\(y_{i}\)) and those estimated by the model of the dependent variable (\(\hat{y}_{i}\)) (Equation (3)). \[e_{i}=y_{i}-\hat{y}_{i} \tag{3}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Independent Variables**} & \multicolumn{3}{c}{**Dependent Variable—GHG Emissions**} \\ \cline{2-4}  & **Pearson Correlation Coefficient** & **Significance** & **Number of** \\  & & & **Observations** \\ \hline GDP & 0.96 & 0.000 & 27 \\ Population & 0.98 & 0.000 & 27 \\ RES & 0.40 & 0.021 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pearson’s correlation between GHG emissions and the independent variables. Third, Equation (4) is used to merge the three weighting values (\(WV_{a_{i}};\ WV_{b_{i}};\ WV_{c_{i}}\)) into one single coefficient \"Corrected Weighting Value\" (\(FP_{c}\)). \[FP_{i}=(WV_{a_{i}}*\beta_{1})+\left(WV_{b_{i}}*\beta_{2}\ \right)+(WV_{c_{i}}*\beta_{3}) \tag{4}\]  
where:  
* \(FP_{i}\) is the corrected weighting value for the MS \"\(i\)\". Fourth, a statistical analysis to identify outliers in the data set has been performed. The statistical z-score, as a statistical measure that indicates the deviation of a particular observation from the standard deviation, is estimated. For this, the z-score is calculated in all the selected variables: dependent (GHG emissions) and independent (GDP, population and RES). Thanks to the statistical z-score, it is identified that Germany is the only member state that presents an unusual behaviour (outlier) within the European context, in three of the four variables analysed (GHG emissions, GDP and population), so it is discarded in the successive steps. In fact, Germany is the largest economy of the European Union and its industry is highly technological, with an emphasis on the metallurgy and chemistry sectors [31]. However, as a result of 2011's decision to shut down all nuclear power plants by 2022, coal is still responsible for 37% of Germany's electricity production [32], in contrast with the Integrated Energy and Climate Programme (Integrierte Energie-und Klimaprogramm, 2007), which required the reduction of emissions by 40% in 2020 [33]. For this reason, CO\({}_{2}\) emissions in the country had a growth rate of 0.1% in the period 2007-2017, opposite to the EU's trend [34].