## 2 Materials and Methods
### Data Preparation, Validation, and Performance Evaluation  
Since the dataset did not contain missing values, only a data normalization procedure was applied in the data preparation phase. Even though the normalization of data into a certain range is not an obligatory process for regression tasks, the normalization of the data has a significant effect on the performance of neural networks in terms of computational cost and prediction accuracy [31]. We normalized the data using Min-Max normalization, for which the formula is provided in Equation (6).  
\[x_{norm}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{6}\]  
where \(x\), \(x_{norm}\), \(x_{max}\), and \(x_{min}\) are the input, normalized, maximum, and minimum observed values (instances) of the corresponding data attribute, respectively.  
Figure 3: Conceptual structure of SVR model [31].  
The main purpose of using machine learning models for regression problems is to achieve reliable results, which are difficult to obtain using traditional methods without prior knowledge and a deep understanding of the concept. However, due to overfitting problems in many ML models, the model's performance at the training stage is not always coherent with its performance at the test stage, making it impossible to obtain accurate prediction results for other unseen datasets. This makes it vital to validate the models to overcome the overfitting issues.  
Different types of validation processes exist in the literature (k-fold cross-validation, holdout validation, leave-one-out validation, etc.), but the k-fold cross-validation was employed in this study because of its dependable precision estimation with a relatively small variance. In this way, we partitioned the dataset into k-number of equal subsets and used each subset for both testing and training. During the training of the models, a single subset was used for testing while the others were used for training.  
Our study considered 4-fold cross-validation, which divided the dataset into 75%-25% training and testing ratio for each validation.  
A robust and consistent evaluation is essential to analyze the obtained results. In our study, we considered three common evaluation metrics for regression problems--the coefficient of determination root mean square error (RMSE), (R\({}^{2}\)), and the relative root mean square error (rRMSE)--to evaluate the obtained results. RMSE, which only differs from mean square error (MSE) by taking its square root, considers the summation of the squared difference between the observed and predicted data points. This leads RMSE to not consider the direction of the error and to find the general error obtained by the model. A lower RMSE value represents superior prediction results. The formula of RMSE is provided in Equation (7).  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\bigl{(}N_{obs_{i}}-N_{prc_{i}}\bigr{)}^{2}}{n}} \tag{7}\]  
where \(n\) is the number of observations, and \(N_{obsi}\) and \(N_{prc}\) denote the observed and predicted data for \(i\)th data.  
R\({}^{2}\) score, which is closely related to the MSE, is used to represent the general prediction ability of the models. It also considers the total sum of squares which is calculated using the observed data and the mean value of observed data. The highest R\({}^{2}\) score (max=1) shows a better prediction ability of the models. Equation (8) shows the formula of the R\({}^{2}\) score.  
\[R\ ^{2}=1-\frac{\sum_{i=1}^{n}\bigl{(}N_{obs_{i}}-N_{prc_{i}}\bigr{)}^{2}}{\sum _{i=1}^{n}\bigl{(}N_{obs_{i}}-\overline{N_{obs}}\bigr{)}^{2}} \tag{8}\]  
where \(\overline{N_{obs}}\) indicates the mean value of observed data values.  
The rRMSE is the percentage variation of RMSE used to show the model's accuracy in terms of percentage. In general, the model's prediction ability is stated as in the highest level while rRMSE < 10%. The formula of rRMSE is provided in Equation (9).  
\[\text{rRMSE}=\frac{\sqrt{\frac{\sum_{i=1}^{n}\bigl{(}N_{obs_{i}}-N_{prc_{i}} \bigr{)}^{2}}{n}}}{\frac{1}{N}\sum_{i=1}^{n}\bigl{(}N_{obs_{i}}\bigr{)}}\ \times\ 100 \tag{9}\]