## 4 Results and Discussion
### Regression Model Results
The observed RMSE values are from \(1.675\) to \(7.754\) for category 1 and from \(1.419\) to \(4.095\) for category 2, with the MLP model showing the smallest value for both categories. MAPE values are detected in the range from \(0.027\%\) to \(0.122\%\) for category 1 and from \(0.026\%\) to \(0.096\%\) for category 2, with a minimum value seen for the MLP model in both categories. The coefficient of determination (R) values lies within \(0.716\)-\(0.986\) in category 1 and \(0.889\)-\(0.986\) in category 2, demonstrating an excellent data fit for all models. The MLP model shows the maximum value of R as \(0.986\) in both categories. The statistical pointer U\({}_{95}\) values are from \(25.308\)-\(30.208\) in category 1 and from \(23.431\)-\(24.791\) in category 2, with the RF model showing the smallest values in both categories. In MAE, the values range from \(0.9\)-\(4.025\) in category 1 and from \(0.577\)-\(1.743\) in category 2, with the MLP model again having a minimum value in both categories. For t-stat, the values range from \(0.067\)-\(0.989\) in category 1 and from \(0.312\)-\(1.602\) in category 2, with the minimum for the RF model in category 1 and MLP model in category 2. The erMAX value ranges from \(6.221\) to \(29.115\) in category 1 and from \(7.778\)-\(13.283\) in category 2, with the minimum value for the MLP model in both categories. Figure 3: (**a**) Scatter diagrams of estimated and predicted deposition efficiency for only left and right lung. (**b**) Scatter diagrams of estimated and predicted deposition efficiency for different sections of left and right lung. * Global Performance Indicator (GPI)  
GPI was employed to improve our outcomes and eliminate anomalies in the statistical analysis and model ranking. [PERSON] et al. [28] were the first to introduce GPI as a novel aspect; it is a fantastic way to integrate the effects of many statistical pointers. The particulars of the GPI technique can be found in Ref [29]. Scaled values of statistical parameters (0 to 1) and GPI and ML model ranking are depicted in Table 6. Figure 4 represents the overall GPI estimation. The MLP model ranks 1 st with GPI = 1.603 then the GPR model with GPI = 1.308, followed by the RF model with GPI = \(-\)0.946. The MLP model shows the best performance among all the models in category 1. In category 2, the MLP model again shows top performance, followed by the GPR and RF models. Thus, we selected the MLP model for further analysis. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**MODEL** & **MBE** & **RMS** & **MAPE** & **R** & **U95** & **MAE** & **t-Stat** & **erMAX** & **GPI** & **Rank** \\ \hline \multicolumn{10}{c}{Category 1} \\ \hline RF & 1.000 & 0.625 & 1.000 & 0.526 & 0.000 & 1.000 & 0.000 & 0.248 & \(-\)0.946 & 3 \\ \hline KNN & 0.000 & 1.000 & 0.874 & 0.000 & 1.000 & 0.689 & 1.000 & 1.000 & \(-\)3.162 & 4 \\ \hline GPR & 0.911 & 0.245 & 0.063 & 0.881 & 0.391 & 0.115 & 0.040 & 0.209 & 1.308 & 2 \\ \hline MLP & 0.832 & 0.000 & 0.000 & 1.000 & 0.418 & 0.000 & 0.549 & 0.000 & 1.603 & 1 \\ \hline \multicolumn{10}{c}{Category 2} \\ \hline RF & 0.311 & 0.455 & 1.000 & 0.670 & 0.000 & 0.867 & 0.688 & 0.196 & \(-\)0.652 & 3 \\ \hline KNN & 0.000 & 1.000 & 0.914 & 0.000 & 0.628 & 1.000 & 0.665 & 1.000 & \(-\)3.012 & 4 \\ \hline GPR & 0.304 & 0.227 & 0.186 & 0.856