# Estimation of Methane Gas Production in Turkey Using Machine Learning Methods
## 3 Results and Discussion
The MSE is shown in Equation (3):  
\[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}e_{i}^{2} \tag{3}\]  
where n is the number of datapoints and e is the error value. Three different machine learning techniques were used in this study: logistic regression, artificial neural networks, and support vector regression. In the artificial neural network method, a feedback model consisting of eleven input neurons and one output neuron was developed. As a result of trial-and-error methods, two hidden layers were used, as this gave the most successful result. There were three neurons in each hidden layer. The model is shown in Figure 2.  
After testing various functions for the activation function, the sigmoid function was preferred because it gave the most successful result. One of the parameters that has an effect on the success of the model in artificial neural networks is learning. The feedback learning algorithm was used in this study, and 100 iterations were performed. Figure 3 shows that the error curve decreased non-linearly. In the figure, the \(x\)-axisshows the number of iterations, and the \(y\)-axisshows the error. The scale of the \(x\)-axiswas between 1 and 100 and the \(y\)-axiswas between 0 and 5. The error curve stabilized between the 50 th and 62 th iteration and reached the ideal value. The maximum likelihood method was used to estimate the parameters for the logistic regression model. In this study, the log likelihood value was \(-\)51.022 as a result of 100 iterations. Nonlinear SVR was preferred in the method where support vector regression was used. As a result of the tests for the kernel function, it was decided to use the radial basis function (RBF). The overlapping penalty value of the model was chosen as 10 and the RBF sigma value was chosen as 0.5. The evaluation of regression models is given in Table 4.  
Figure 3: Error plot for ANN. Figure 2: ANN model. Figure 4 shows the coefficient of determination (R\({}^{2}\)) graphs. R\({}^{2}\) shows the rate of explanation of independent variables. In other words, it refers to the variance ratio of the dependent variable explained by the independent variables. Here, zero indicates that the model has 0% explanatory power, and one indicates that the model has 100% explanatory power and that the independent variables are strong in explaining the dependent variable and provide a linear curve [38; 39]. R\({}^{2}\) was 94.9% for logistic regression, 93.6% for artificial neural networks, and 92.3% for support vector regression. These results show that the ideal values were met. The mean absolute error (MAE) graphs are presented in Figure 5. MAE is calculated by averaging the absolute values of the prediction errors. It is often preferred for determining the error values of models because it can be easily interpreted. The MAE value can vary from 0 to \(\infty\). The lower the MAE value, the lower the error value of the model [40; 41]. The MAE metric gives the magnitude of the error as a quantity. In the study, it was seen that the MAE was 0.052 for logistic regression, 0.053 for artificial neural networks, and 0.065 for support vector regression. The MAE was considered to be successful in all three models. Figure 6 shows the mean squared error (MSE) graphs. MSE is a statistical metric that evaluates the error of machine learning methods. MSE is equal to the mean squared difference between predicted values and actual values. MSE is often used in regression models. Because MSE squares the error, it causes major errors to be clearly highlighted. MSE is a metric that ranges from 0 to infinity, and values close to zero are considered better [42; 43]. It was seen that the MSE was 0.005 for logistic regression, 0.006 for artificial neural networks, and 0.009 for support vector regression. The error rate of the models was found to be low and acceptable. According to the error and success evaluation, the order of the models in terms of their success is logistic regression, then artificial neural network and, finally, support vector regression.