## 4 Result and Discussion
### Regression Model Performance  
The chart in Figure 6 uses a logarithmic scale to display the MSE values, which allows for a clear visual representation of differences across multiple values. Lower MSE values indicate better model performance as they signify that the model's predictions are closer to the actual values (the content below shows numbers estimated to five decimal places). This method processes the data by considering a 12 h cycle, which could be useful for capturing daily patterns that repeat on a half-day basis. When analyzing the cycling 12 method, it is observable that for SVR, the MSE is very low at around 0.10717, indicating that this model has performed well with the 12 h cycle data preprocessing. However, for the Polynomial and Linear Regression models, the cycling 12 preprocessing does not yield the lowest MSE, suggesting that these models may not benefit as much from this preprocessing method as SVR. The cycling 24 method considers an entire 24 h cycle, potentially capturing daily patterns. For KNN, just like with the cycling 12, the MSE is exceedingly low at around 0.01508, implying that KNN is particularly well-suited to benefit from the cycling approach. Polynomial Regression and SVR are slightly improved in MSE with cycling 24 compared to cycling 12, indicating some benefit from considering the entire daily cycle. Upon examining the Mean Absolute Error (Figure 7) across various regression models and data preprocessing methods, cycling 12 and cycling 24 methods offer substantial improvements in predictive accuracy over the original and positional methods. Specifically, for Linear Regression, cycling 12 and cycling 24 achieve a drastically lower MAE, which is 0.00024 and 0.00002, respectively, with cycling 24 edging out as the most effective, suggesting its superior capability in capturing daily patterns within the data. Polynomial Regression also benefits from the cycling approaches, albeit to a lesser degree, with cycling 12 (0.00160) outperforming cycling 24 (0.00214). Support Vector Regression reflects a similar trend, with cycling 12 (around 0.10680) reducing the MAE more than cycling 24 (around 0.16090) when compared to positional encoding. Remarkably, the K-Nearest Neighbor Regression model exhibits the most pronounced improvement with cycling 24 at around 0.00773, reaching the lowest MAE among all the preprocessing methods, underscoring the value of a complete 24 h cycle in capturing the inherent temporal dynamics of the dataset. Figure 6: MSE for four different regressions. These findings highlight the effectiveness of incorporating cyclical temporal information into the preprocessing phase, particularly for models sensitive to time-based patterns. In Figure 8, the RMSE values suggest that Linear Regression benefits significantly from the cycling 12 (0.00031) and cycling 24 (0.00020) methods, showcasing much lower errors compared to the original (2.84823) and positional (0.07078) methods. This indicates a strong fit of the model to the data when temporal cycles are considered. The RMSE for Polynomial Regression and Support Vector Regression, while lower for cycling 12 and cycling 24 than for positional, does not dramatically improve, as observed with Linear Regression. K-Nearest Neighbor Regression was also enhanced, with cycling 12 at around 0.34340 and cycling 24 at around 0.12270, suggesting that these models have a better ability to capture the central tendency of the data in a more accurate way with cycling-based preprocessing. Figure 8: RMSE for four different regressions. Figure 7: MAE for four different regressions. Figure 9, focusing on Med AE, presents a similar trend. Linear Regression again shows a marked improvement with the cycling 12, at around 0.00024, and cycling 24, at around 0.00013, methods, with Med AE dropping significantly. This metric confirms that the central tendency of the predictions made by the Linear Regression model aligns closely with the actual values when cyclic patterns are integrated into the data preprocessing.