## 3 Test Results and Discussion
Despite the strong performance of the first-degree regression, the ANN's adaptability to the data provides a distinct advantage in terms of predictive accuracy and robustness. Confirming the results presented in Figures 5 and 6 provides a detailed comparison between the desired outputs and the outputs obtained via the ANN for all samples, totaling 1484. The analysis shows a remarkable similarity in the results, indicating that the artificial neural network underwent effective training and achieved satisfactory performance. In Figure 7, the results of the 148 samples not included in the training phase (those used in the validation phase) are presented for the 4 techniques analyzed. Figure 7a displays the results obtained with the ANN, while Figure 7b-d show the results for polynomial regressions of degrees 1, 2, and 3, respectively. The analysis reveals that the outputs generated by the ANN had greater similarity to the desired outputs, which made them stand out compared to the other techniques. Following this, the first-degree polynomial regression showed relatively good performance, followed by the second-degree, and finally, the third-degree, which exhibited the lowest level of precision. Additionally, Figure 7 includes a specific comparison of 50 randomly selected samples from the 148 samples in the validation phase. This additional comparison further highlights the superiority of the ANN over the other approaches, confirming its effectiveness in accurately predicting the data (energy consumption) for samples not included in the training. The analysis of the different techniques underscores the robustness of the ANN, especially when compared to polynomial regression approaches. This comparison is crucial as it further visualizes the differences in predictive accuracy between the ANN and polynomial regressions. While the first-degree regression performs relatively well, it still falls short of the precision demonstrated by the ANN, especially when handling complex patterns in the energy consumption data. As the polynomial degree increases, the models tend to overfit the data, leading to a reduction in generalization capability, which is clearly highlighted in Figure 7.  
The analysis of the desired outputs (\(\Upsilon_{\text{des}}\)) and the predicted outputs (\(\Upsilon_{\text{ob}}\)) obtained via artificial neural networks (ANN) reveals an approximately linear behavior, as illustrated in Figures 6 and 7. It was observed that increasing the degree of the interpolating polynomial results in decreased prediction accuracy, as evidenced by Table 1, which shows that higher polynomial degrees lead to lower R\({}^{2}\) values. For this reason, the authors decided to limit the polynomial to degree 3. Polynomial regressions struggle to capture complex nonlinear patterns due to their reliance on a fixed functional form, which can lead to overfitting and oscillations. In contrast, artificial neural networks can adaptively model intricate relationships through multiple layers and nonlinear activation functions, allowing them to better capture complex patterns in the data. Figure 6: Results for desired output (target–\(\Upsilon_{\text{des}}\)) for 100% of samples (1484 samples from the 31 days of January 2023) versus output obtained via ANN (\(\Upsilon_{\text{ob}}\)) (training and validation phase). Figure 8a presents a three-dimensional graph of the actual energy consumption (kWh) of the residence, representing the desired output in relation to the 31 days of January 2023 and the 24 h of each day. In contrast, Figure 8b shows a similar graph but with the energy consumption values (kWh) obtained via the ANN.