## 5 Results  
We evaluated the effectiveness of the five regression models (XGBoost, CatBoost, LightGBM, AdaBoost, and Histogram-Based Gradient Boosting) was assessed utilizing four principal metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the Coefficient of Determination (R\({}^{2}\)). The findings are encapsulated in Table 3.  
Among the models we analyzed, CatBoost attained the minimal MAE of 0.023, signifying exceptional accuracy in forecasting PV system efficiency. XGBoost and LightGBM demonstrated marginally elevated MAE values of 0.025 and 0.026, respectively, indicating similar performance. Histogram-Based Gradient Boosting had a Mean Absolute Error (MAE) of 0.027, whereas AdaBoost registered the greatest MAE of 0.040, signifying inferior predictive accuracy compared to the other models. MSE and RMSE are metrics that impose greater penalties on larger errors, with RMSE yielding values in the same units as the target variable. CatBoost once more surpassed the other models, with the lowest MSE of 0.002 and RMSE of 0.054. XGBoost and LightGBM had MSE values of 0.003 and RMSE values of 0.061, indicating robust predictive performance. Histogram-Based Gradient Boosting exhibited a mean squared error (MSE) of 0.003 and a root mean squared error (RMSE) of 0.062. AdaBoost demonstrated the highest MSE and RMSE values of 0.004 and 0.068, respectively, highlighting its comparative underperformance in this scenario. The coefficient of determination (R\({}^{2}\)) measures the proportion of variance in the dependent variable that can be predicted by the independent variables. CatBoost attained the greatest R\({}^{2}\) value of 0.90, signifying that it accounts for 90% of the variance in photovoltaic system efficiency based on the internal properties. XGBoost and LightGBM both achieved R\({}^{2}\) values of 0.88, indicating robust explanatory capability. Histogram-Based Gradient Boosting achieved a R\({}^{2}\) of 0.87, but AdaBoost recorded the lowest R\({}^{2}\) score of 0.85. We utilize SHAP and LIME methodologies to elucidate the constructed machine learning models. We offer both global and local explainability findings for CatBoost, identified as the most successful regression model among those evaluated. Initially, global explanations were derived via the SHAP approach to identify the features affecting the regression predictions generated by the CatBoost model for efficiency estimation throughout the entire dataset. The objective was to evaluate the model's behavior comprehensively. The results of the global analysis are illustrated in Figures 4 and 5. Figure 4 illustrates the factors that most significantly influence efficiency predictions throughout the dataset, sorted by relevance. The results indicate that the five primary features influencing efficiency estimation are Solar Irradiation Spread (SIS), Maximum Power (Pmpp), Fill Factor (FF), Maximum Voltage (Vmpp), and Parallel Resistance (Rp). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Regression Models** & **MAE** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline XGBoost & 0.025 & 0.003 & 0.061 & 0.88 \\ CatBoost & 0.023 & 0.002 & 0.054 & 0.90 \\ LGBM & 0.026 & 0.003 & 0.061 & 0.88 \\ AdaBoost & 0.040 & 0.004 & 0.068 & 0.85 \\ HistGradientBoosting & 0.027 & 0.003 & 0.062 & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics of regression models using internal features. Examining Figure 4 elucidates the significance of the solar irradiation distribution. This sun irradiation distribution aids in assessing the extent of usable territory and its optimal utilization. As to [32], while the exact rooftop size is known, the useable area cannot be readily ascertained without accounting for shadowing, irregularities, or locations where panels cannot be put. The projected solar irradiation distribution considers these aspects, facilitating a pragmatic installation strategy.