## 6 Results and Discussion
### Model Developed with Average Data Excluding Outliers  
For the data used in Section 6.2, the data sets used with the same input variables have different output variable values. If there are many cases similar to this, it may be difficult to train the ML model. To eliminate this, one output data set value should be matched to one possible input data set value. For this purpose, average data are used. For training and testing of the model, 90% of the total data was used for training and 10% was used for testing. * Total data sets: 310 data sets;
* Training data sets: 279 data sets;
* Test data sets: 31 data sets. The four machine learning models (random forest, neural network, gradient boosting, and AdaBoost) were run, and the results of training and testing for each model are shown in Table 10a,b below. As tabulated in Table 10a, the gradient boosting model with training data provides the highest determination coefficient, \(R^{2}\) = 0.982, followed by \(R^{2}\) = 0.973 from AdaBoost, then 0.887 from the random forest model. The neural network model showed the lowest \(R^{2}\) value as 0.679. As tabulated in Table 10b, the gradient boosting model provides the highest determination coefficient, \(R^{2}\) = 0.915, followed by \(R^{2}\) = 0.893 from the random forest model, then 0.876 from the AdaBoost model. The neural network model showed the lowest \(R^{2}\) value as 0.730. Three sets of data were used to develop the ML models in this study. The MSE, RMSE, MAE, and \(R^{2}\) calculated with the average data excluding outliers were compared to the MSE, RMSE, MAE, and \(R^{2}\) calculated with both the original data and the grouped data excluding outliers. As a result of comparing the values in Tables 8-10, the ML model developed with average data excluding outliers most closely matched the predicted value and the observed value. Figure 12 depicts the actual values against the predicted values of log\(N\) for machine learning models developed with the average data excluding outliers. The results of the gradient boosting model fit a straight line better than the other ML models, which indicates that the gradient boosting model is more accurate for predicting the log\(N\). The scattered data of the gradient boosting model are closer to the linear regression line than the scattered data of the other models. Compared to the other models, the scatter plot of the neural network model does not fit well and its prediction is slightly off, which has a larger dispersity of scatter points. Among the four ML models developed with the average data excluding outliers, the gradient boosting model most closely fits the observed data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{(**a**)} \\ \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(R^{2}\) \\ \hline Random forest & 0.296 & 0.544 & 0.379 & 0.795 \\ \hline Neural network & 0.479 & 0.692 & 0.510 & 0.668 \\ \hline Gradient boosting & 0.275 & 0.524 & 0.359 & 0.809 \\ \hline AdaBoost & 0.282 & 0.531 & 0.355 & 0.805 \\ \hline \multicolumn{3}{c}{(**b**)} \\ \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(R^{2}\) \\ \hline Random forest & 0.321 & 0.566 & 0.414 & 0.791 \\ \hline Neural network & 0.419 & 0.647 & 0.500 & 0.726 \\ \hline Gradient boosting & 0.301 & 0.549 & 0.397 & 0.803 \\ \hline AdaBoost & 0.315 & 0.561 & 0.417 & 0.794 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: (**a**). Result of ML models with training data excluding outliers. (**b**). Result of ML models with testing data excluding outliers. Figure 12: Predicted vs observed data in model developed.