## 4 Results and Discussions
### Regression Results and Comparisons  
The EANN was trained as a predictor in the SVR-EANN hybrid model to achieve superior results for BFP prediction without considering the least significant factor determined by the SVR model. The age attribute was removed for SVR-EANN during the training, and the obtained results of the proposed SVR-EANN hybrid model were compared to the results of other benchmark models: feed-forward NN [36], SVR [29], DT [37], RF [38], LR [39], XGBoost [40], and GradBoost [41].  
The network structure of the FFNN included an input layer, a single hidden layer with 20 neurons, and an output layer with a single neuron. The determination of the hidden neuron numbers was based on the training of the FFNN using a hidden neuron interval of 5-30 and epochs 10-1000. The highest result was obtained using 20 hidden neurons and 50 epochs with the Adam optimizer.  
DT was implemented using mean squared error (MSE) criteria for constructing the DT for regression studies. GradBoost and RF were trained with 100 and 150 estimators, respectively. The learning rates of XGBoost and GradBoost were defined as 0.3 and 0.085. The number of estimators and the learning rates of RF, GradBoost, and XGBoost were determined after several trial-and-error experiments by validating the results using 4-fold cross-validation.  
The final parameters of SVR were considered the same as the proposed hybrid model, and C, \(\gamma\), and \(\varepsilon\) values were set to 5, 0.0313, and 0.25, respectively. The EANN was considered with twenty hidden and five hormone neurons and trained 50 epochs after searching the parameters similar to the FFNN search.  
SVR-EANN achieved superior results by obtaining 0.991, 0.0125, and 3.15% R\({}^{2}\), RMSE, and rRMSE results, while the EANN without left-out sensitivity analysis obtained 0.8928, 0.0464, and 13.55% R\({}^{2}\), RMSE, and rRMSE results. The difference between the results of SVR-EANN and EANN shows the importance of data selection and the efficiency of the SVR-EANN. On the other hand, the FFNN, with its superior architecture and parameters, obtained lower results since it achieved 0.857, 0.0622, and 19.69% R\({}^{2}\), RMSE, and rRMSE results.  
LR obtained the R\({}^{2}\), RMSE, and rRMSE results of 0.918, 0.0396, and 11.43%, since SVR achieved 0.968, 0.024, and 7.69%. The DT (R\({}^{2}\) = 0.969, RMSE = 0.0216, rRMSE 6.98%) and tree-based ensemble models, RF (R\({}^{2}\) = 0.974, RMSE = 0.0198, rRMSE 6.32%), XGBoost (R\({}^{2}\) = 0.98, RMSE = 0.0178, rRMSE 5.91%), and GradBoost (R\({}^{2}\) = 0.98, RMSE = 0.0182, rRMSE 5.99%) achieved relatively higher results than other models; however, they could not out-perform the proposed SVR-EANN model. Table 4 presents all results of the models in the test stage obtained in this study. Figure 6 shows the regression line of the testing stage using a scatter plot of the EANN, FFNN, and the proposed SVR-EANN.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Removed Parameter** & **RMSE** \\ \hline BMI & 0.0564 \\ \hline Abdominal C & 0.1509 \\ \hline Weight & 0.0341 \\ \hline Gender & 0.1223 \\ \hline Height & 0.0708 \\ \hline WHR & 0.0589 \\ \hline Age & 0.0157 \\ \hline \hline \end{tabular} Note: RMSE\({}_{0}\) = 0.0122 (Normalized)  
\end{table}
Table 3: Coefficients of correlation matrix between the variables.