# Comparative Analysis of Machine Learning Methods for Predicting Energy Recovery from Waste
## 3 Results  
Pearson's correlation analysis was conducted to discern interdependencies among the input energy variables, with findings detailed in Table 4. No variable was highly correlated, so all parameters were included in further analyses. The first modeling method analyzed was ElasticNet, for which the best model was obtained with alpha set to 1 and lambda set to a very low value of 0.0001. Table 5 provides an exhaustive breakdown of all the key metrics. By setting alpha to 1, the strategy shifted toward the use of a lasso regression, emphasizing the importance of selecting significant features. The choice of a low lambda value, 0.0001, indicated a slight regularization effect to preserve the flexibility of the model. The performance of the model was remarkable, with a Mean Squared Error of 2372.8, demonstrating its ability to fit the data set. The model's prediction error spread was captured by a Root Mean Squared Error of 48.7114. In addition, the model's prediction accuracy was highlighted by a Relative Importance of Errors of 0.3012. The Mean Absolute Error of 36.97 underscored the model's consistent predictive ability. The regression analysis of the entire data set with the ElasticNet model is shown in Figure 2. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Variable** & **EPTU** & **EP** & **FEC** & **GDPMP** & **RRMW** & **DMC** & **ETR** & **SERS** \\ \hline EPTU & 1.00000 & 0.749484 & 0.490864 & 0.443991 & 0.502364 & \(-\)0.101240 & 0.064623 & 0.005785 \\ EP & 0.749484 & 1.000000 & 0.312311 & 0.716978 & 0.505365 & \(-\)0.025537 & \(-\)0.152443 & 0.048732 \\ FEC & 0.490864 & 0.312311 & 1.000000 & 0.132517 & 0.453852 & \(-\)0.241893 & 0.161477 & \(-\)0.209181 \\ GDPMP & 0.443991 & 0.716978 & 0.132517 & 1.000000 & 0.546917 & 0.248230 & \(-\)0.155644 & \(-\)0.157976 \\ RRMW & 0.502364 & 0.505365 & 0.453852 & 0.546917 & 1.00000 & \(-\)0.003523 & \(-\)0.196494 & 0.044154 \\ DMC & \(-\)0.101240 & \(-\)0.025537 & \(-\)0.241893 & 0.248230 & \(-\)0.003523 & 1.00000 & \(-\)0.256747 & 0.478000 \\ ETR & 0.064623 & \(-\)0.152443 & 0.161477 & \(-\)0.155644 & \(-\)0.196494 & \(-\)0.256747 & 1.000000 & \(-\)0.314553 \\ SERS & 0.005785 & 0.048732 & \(-\)0.209181 & \(-\)0.157976 & 0.044154 & 0.478000 & \(-\)0.314553 & 1.000000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation analysis results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quality Indicator** & **Formula** & **Meaning of Symbols** \\ \hline Regression value (R) & \(\text{R}(y^{\prime},y^{*})=\frac{\text{cov}\left(y^{\prime},y^{*}\right)}{ \sigma_{y}\sigma_{y}^{2}}\), & \(\text{Re}<0,1>\) & \(\text{oy}^{\prime}\)—standard deviation of reference values of the energy recovery, \\ Mean Squared Error (MSE) & \(\text{MSE}=\frac{1}{n}\sum\limits_{n=1}^{n}\left(\hat{y}_{i}-\hat{y}_{i}\right)^{2}\) & \(\text{ory}^{*}\)—standard deviation of predicted values \\ Root Mean Square Error (RMSE) & \(\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{q}}\) & \(\text{the energy recovery,}\) \\ Relative Importance of Errors (RIE) & \(\text{RIE}=\frac{\left\|y^{\prime}-y\right\|}{\left\|y\right\|}\) & \(\text{y}_{i}\) is the actual value of the energy recovery \\ Mean Absolute Error (MAE) & \(\text{MAE}=\frac{1}{N}\sum\limits_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)\) & \(\text{the model}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quality indicators used to evaluate the received models. The second analyzed method for modeling the energy recovery is decision trees. The process involved varying the number of trees within a range from 50 to 200 trees, with a step of five trees. The best DT modeling results were obtained for 115 trees. The graph in Figure 3 shows the MSE for different numbers of trees in a DT model. The model's consistent predictive ability was underscored by a MAE of 12.0148. Additionally, its performance was remarkable, with a MSE of 253.57, demonstrating its ability to fit the dataset. The prediction error spread was captured by a RMSE of 15.9239.