## 4 Model Training and Evaluation Methods
### Evaluation Metrics
The RMSE is calculated by taking the square root of the MSE, and it improves interpretability by converting the unit of error to the original data scale [29]. The MSLE is the mean of the squares of the differences between the logarithmic transformations of the true and predicted values. It is especially used with positively skewed data, in cases in which the target variable has a wide range of values [30]. The MaxEr is the maximum value of the absolute differences between actual values and predicted values. This metric is used when it is important that the model does not make even a single prediction that is too inaccurate. It allows evaluation of worst-case performance, which is especially valuable in critical applications [31]. The ExVar is the proportion of variance between the model's predictions and the actual values. This metric measures the proportion of variance explained by the model, with values closer to 1 indicating better model performance [23]. The MedAE shows the median value of the absolute errors between the predicted values and the actual values [29]. The MARE is the absolute difference between the actual and forecast values, divided by the actual values [32]. The MSRE is calculated as the mean of the squares of the relative differences between the actual and the predicted values [33]. The RMSRE is the square root of the MSRE, and provides a determination of the relative errors of the forecasts, converted to their original scale [30]. The RRMSE is the RMSE value divided by the mean of the data, and provides an assessment of the error measure relative to the size of the data [28]. The MBE is used to determine the bias of the model by measuring the average deviation associated with the predicted values [27]. The eMAX value shows the maximum value of all relative errors [34]. Standard deviation is a measure of dispersion that expresses the extent to which observations in a data set deviate from the arithmetic mean [35]. The t-statistic is a test statistic used to assess whether the difference between two sample means is statistically significant [36]. The 95% uncertainty interval shows the range in which the estimated values occur proximate to the true values with a 95% confidence level [37]. The evaluation metrics results of the models without hyperparameter optimization are given in Table 3. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**MetricsMLModels** & **DT** & **RF** & **K-NNs** & **AdaBoost** & **GBM** & **ETR** & **BR** & **SVR** & **HGBR** & **XGBoost** \\ \hline R\({}^{2}\) & 0.8691 & 0.9287 & 0.899 & 0.9174 & 0.9384 & 0.9265 & 0.9184 & 0.95 & 0.9408 & 0.9305 \\ \hline MSE & 0.1083 & 0.059 & 0.0835 & 0.0683 & 0.051 & 0.0608 & 0.0674 & 0.0413 & 0.049 & 0.0575 \\ \hline RMSE & 0.329 & 0.2428 & 0.289 & 0.2613 & 0.2258 & 0.2466 & 0.2597 & 0.2032 & 0.2213 & 0.2398 \\ \hline MAE & 0.26 & 0.188 & 0.2268 & 0.2097 & 0.1793 & 0.1948 & 0.203 & 0.1597 & 0.1754 & 0.1891 \\ \hline MSLE & 0.0185 & 0.0105 & 0.0146 & 0.0116 & 0.0092 & 0.0105 & 0.0118 & 0.0074 & 0.009 & 0.0101 \\ \hline MedAE & 0.2156 & 0.1491 & 0.1806 & 0.1834 & 0.1567 & 0.1595 & 0.1578 & 0.1347 & 0.1472 & 0.161 \\ \hline MaxEr & 1.2878 & 0.8993 & 0.9993 & 0.8398 & 0.9777 & 0.8172 & 0.979 & 0.9745 & 0.9737 & 0.8617 \\ \hline ExVar & 0.8691 & 0.9287 & 0.8993 & 0.9174 & 0.9384 & 0.9265 & 0.9184 & 0.9501 & 0.9408 & 0.9305 \\ \hline MARE & 0.3923 & 0.3789 & 0.4607 & 0.4274 & 0.3497 & 0.3579 & 0.3617 & 0.2866 & 0.3542 & 0.372 \\ \hline MSRE & 6.3221 & 8.119 & 16.0801 & 11.9587 & 6.9601 & 6.5338 & 5.9819 & 4.0173 & 7.5782 & 8.4804 \\ \hline RMSRE & 2.5144 & 2.8494 & 4.01 & 3.4581 & 2.6382 & 2.5561 & 2.4458 & 2.0043 & 2.7528 & 2.9121 \\ \hline RRMSE & 1.3052 & 1.4791 & 2.0815 & 1.7951 & 1.3694 & 1.3269 & 1.2696 & 1.0404 & 1.429 & 1.5116 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Metric results of the ML models, without hyperparameter optimization.