## 3 Results
### Prediction of Carbon Dioxide (CO\({}_{2}\)) Gas Levels  
CO\({}_{2}\) is a stable compound that forms during the gasification of biomass. Although its energy content is lower than CO and H\({}_{2}\), it is an important indicator providing valuable insights into the process. The prediction of CO\({}_{2}\) levels is critical for assessing environmental impacts and achieving low-emission targets in sustainable energy production efforts. Furthermore, CO\({}_{2}\) concentrations are a key parameter affecting the efficiency of the gasification process. The relationship between CO\({}_{2}\) and the input variables of the gasification process is examined in the correlation matrix presented in Figure 5.  
A strong positive linear correlation (0.55) was observed between CO\({}_{2}\) output and the ER variable. This relationship indicates a direct connection between these two variables in energy conversion processes, with higher energy demands being associated with increased CO\({}_{2}\) emissions. In contrast, a strong negative relationship (\(-\)0.43) was found between CO\({}_{2}\) and SB. This can be attributed to changes in process stability or the equilibrium processes occurring during combustion. A weak negative relationship (\(-\)0.27) was observed between CO\({}_{2}\) and FC, which suggests the presence of a latent interaction that may be better explained through nonlinear analysis. On the other hand, the strong negative correlation (\(-\)0.96) observed between C and O explains the chemical equilibrium processes between carbon and oxygen. Similarly, a strong negative correlation (\(-\)0.80) was found between Ash and VM, reflecting processes such as the increase in ash content due to a decrease in volatile components during combustion.  
In the nonlinear analysis, the variables MC (0.56), VM (0.51), and FC (0.56) were found to be determinants of CO\({}_{2}\) output, according to their mutual information values. This highlights the effect of fuel moisture content and volatile component ratios on CH  
Figure 5: Linear and nonlinear relationships between CO\({}_{2}\) output and input variables.  
formation. In contrast, variables such as SB (0.19), ER (0.22), and Temp (0.22) exhibited a limited effect with lower values. The increased importance of O and N in the nonlinear analysis, despite being seen as having low impacts in the linear analysis, suggests that oxygen and nitrogen play an indirect but significant role in chemical reaction processes.  
In conclusion, nonlinear methods are more effective in detecting complex and indirect relationships. These results demonstrate the critical importance of using nonlinear analysis methods in modeling processes. Table 6 presents the prediction performance of machine learning models for CO2 gas levels under optimal and suboptimal conditions.  
When examining the performances of models under optimal conditions for CO2 level prediction, the XGBoost model (RMSE = 3.590, RAE = 8.667, MAPE = 11.616) achieved the best results, closely followed by the GBR model (RMSE = 3.599, RAE = 9.282, MAPE = 11.606). In contrast, the Elastic Net model exhibited the highest error rates, demonstrating significantly lower performance than the other models, with RMSE = 8.911, RAE = 24.923, and MAPE = 43.798.  
Under suboptimal conditions, the XGBoost model outperformed the other models in CO2 level prediction, with RMSE = 6.432, RAE = 17.752, and MAPE = 28.253. This finding reveals that XGBoost can make effective predictions even under harsh conditions. On the other hand, the KNN model shows a significant increase in prediction error.  
Statistical analyses revealed hyperparameter changes significantly impacted model prediction performance (t-statistic = 4.94, \(p\)-value = 0.0017). [PERSON]'s d value (1.7451) indicates that hyperparameter optimization strongly affected model performance. These results highlight the critical importance of selecting the correct hyperparameters to improve the accuracy of CO2 level predictions.