## 4 Performance Analysis
This all-encompassing performance advantage not only demonstrates the power of our model in handling complex prediction tasks, but also shows its clear superiority in direct comparison with other traditional and optimization models, providing an efficient and reliable solution to address difficult prediction problems. To visualize the predictive results, we used scatter plots to intuitively demonstrate the relationship between model predictions and actual values. By comparing the closeness to the perfect prediction line (y = x), we effectively assessed the model's predictive accuracy. The model prediction result charts listed in Table 5 are shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **MAE** & **MSE** & **MAPE** & **R2** \\ \hline SVM & 1.799 & 9.934 & 10.567 & 0.935 \\ KNN & 1.333 & 4.890 & 9.696 & 0.968 \\ Random Forest & 1.203 & 5.714 & 0.316 & 0.963 \\ MLP & 1.158 & 2.667 & 21.736 & 0.982 \\ LightGBM & 1.826 & 9.824 & 3.847 & 0.936 \\ XGBoost & 1.058 & 4.145 & 0.140 & 0.973 \\ Optuna–SVM & 1.072 & 2.405 & 7.723 & 0.984 \\ Optuna–KNN & 1.004 & 2.127 & 0.363 & 0.986 \\ Optuna–Random Forest & 1.127 & 4.789 & 0.251 & 0.969 \\ Optuna–MLP & 1.068 & 2.286 & 18.624 & 0.985 \\ Optuna–LightGBM & 0.891 & 1.772 & 0.163 & 0.988 \\ Optuna–XGBoost & 0.891 & 2.102 & 0.171 & 0.986 \\ Optuna–LightGBM–XGBoost (Ours) & **0.652** & **0.939** & **0.136** & **0.994** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of predictive performance analysis among different models. Figure 6: _Cont._  
Figure 6: Comparison of predictive results and actual emissions across different models. The traditional SVM, KNN, random forest, LightGBM, and XGBoost models exhibit wider distributions of data points around the perfect prediction line, especially in the prediction of extreme values. This suggests variability in performance across different data segments. In addition, MLP exhibits deviations within smaller data segments, potentially affecting its accuracy in specific scenarios. The Optuna-SVM, Optuna-KNN, Optuna-random forest, Optuna-LightGBM, and Optuna-XGBoost models show improvements in both the aggregation of predictions around the line y = x and a reduced spread of outliers, highlighting the benefits of hyperparameter optimization. The Optuna-LightGBM-XGBoost model clearly demonstrates data points that are closer to the perfect prediction line compared to baseline models such as SVM, KNN, random forest, MLP, LightGBM, and XGBoost, as well as their optimized versions via Optuna. The data points are highly concentrated around the perfect prediction line and closely coincide with it, indicating excellent predictive accuracy. In contrast, the scatterplots of the baseline model and its optimized version show a wider distribution of data points and more outliers, exhibiting greater fluctuations in the predictions, especially in the prediction of extreme values. The Optuna-LightGBM-XGBoost model not only matches the overall trend better, but also demonstrates superior consistency, stability, and accuracy of the data points. The experimental results validate the exceptional performance of our proposed Optuna-LightGBM-XGBoost fusion model in establishing the relationship between electricity and carbon emissions. The model achieved optimal results across key performance indicators, including mean absolute error (MAE), mean squared error (MSE), mean absolute percentage error (MAPE), and the coefficient of determination (R\({}^{2}\)), highlighting the model's superiority in precision and generalization capability. In the comparison of the predicted results to the perfect prediction line, our model adheres closely to this line across both lower and higher target value ranges, further confirming its excellent predictive accuracy and robust generalization. Hence, estimating the carbon emissions of coal-fired power plants using electricity production data is not only feasible but also effective, underscoring the tight link between electricity production and carbon emissions.