# Estimation of Methane Gas Production in Turkey Using Machine Learning Methods
## 3 Results and Discussion  
In this study, three different methods, namely, logistic regression, artificial neural network, and support vector regression, were used to predict methane gas in Turkey. The study system is shown in Figure 1.  
Eleven independent variables were used to predict methane gas, which was the dependent variable of the study. The independent variables were Turkey's population, GDP, coal share in electricity, number of cattle, natural gas share in electricity, industrial production index, agriculture greenhouse gas emission, agricultural area, waste greenhouse gas emission, cattle meat production, and paddy production area. For each independent variable, there were thirty-one annual data between 1990 and 2020. The min-max method was used for normalization in the study. A linear transformation was performed on the original data. In this normalization, the relationships between the original data values were preserved, and the largest and smallest values in a group of data were considered [34]. All other data were normalized according to these values. This method is a scaling technique where the data are rescaled to be between 0 and 1. The result of having a limited range between 0 and 1 in this process is that it suppresses the effect of outliers and allows for smaller standard deviations [35]. Cross-validation measures the success of the model by creating validation clusters from the data set. Testing with a single data set may not be sufficient. For this reason, it is very important to perform k-fold cross-validation, that is, to create more than one machine learning model from a single data set, to check these models with different test sets, and to average the accuracy of all of them. The data set was clustered according to the k-layer cross-validation applied as training and test data. When ten layers of cross-validation were applied to the data, nine parts were used to develop the model and the remaining one part was used to test the model. This process was repeated 10 times. Each time, it  
Figure 1: Working system. took a different validation set as the test set and used the remaining 9 sets to improve the model [36; 37]. The coefficient of determination (R2) is a statistical measure that examines how differences in one variable can be explained by differences in a second variable when predicting the outcome of a particular event. In other words, the coefficient of determination is a statistical metric that measures how well a statistical model predicts an outcome. This coefficient assesses how strong the linear relationship between two variables is. The outcome is represented by the dependent variable of the model. The lowest value of R2 is 0 and the highest value is 1. It is the proportion of variance in the dependent variable that is explained by the model [38; 39]. The R2 is shown in Equation (1):  
\[\text{R}^{2}=1-\frac{\text{UnexplainedVariation}}{\text{TotalVariation}} \tag{1}\]  
The MAE (mean absolute error) is a statistical metric that measures the average magnitude of errors in a set of predictions without considering their direction. It is calculated by taking the absolute difference between the predicted values and the actual values and averaging it across the data set. MAE only measures the magnitude of errors and is not concerned with their direction. The lower the MAE, the higher the accuracy of a model [40; 41]. The MAE formula is shown in Equation (2):  
\[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}\lvert e_{i}\rvert \tag{2}\]  
The MSE (mean squared error) is a model evaluation metric often used in regression models. MSE is equal to the mean squared difference between predicted values and actual values. Since MSE squares the error, it causes large errors to be clearly highlighted. MSE is a metric that ranges from 0 to infinity and values closer to zero are considered better. For MSE values calculated for the same data set, the lower the MSE value, the more accurate the model [42; 43].