## 3 Results  
The following section presents the outcomes of the analysis, emphasizing the first- and second-degree equations obtained via the optimization procedure. Quantitative results, inclusive of statistical analyses and graphical comparisons, are provided. Specifically, the equations are plotted alongside the observed data, and the error rates between these equations and the reference equation against the observed data are depicted. Furthermore, the statistical error rates are presented to offer further insight into the performance and accuracy of the derived models. This thorough examination aims to offer insights into the efficacy and reliability of the derived equations in describing the underlying phenomena. Table 1 presents the mathematical expressions of both obtained equations, and Figure 4 represents the surface defined by each equation. Figure 4a shows the dataset (red points) against the planar surface of the first-degree equation (blue surface). Likewise, Figure 4b, represents the dataset (red points) against the surface generated by the second-degree equation (blue surface). Reaching the DPT is unfeasible under conditions falling below the delineated threshold, as depicted by the red line in Figure 2. Additionally, the practical limitations of commercial cooling systems render temperatures below approximately 5-7 \({}^{\circ}\)C [41; 42] unattainable, further constraining the applicability of predictive models in real-world scenarios. To address this, adjustments were made to the Magnus-Tetens' equation to preclude erroneous values below 0 \({}^{\circ}\)C. Furthermore, empirical data revealed that relative humidity rates of 20% become feasible only upon attaining temperatures exceeding 25 \({}^{\circ}\)C. Consequently, the observed dataset was restricted to relative humidity rates surpassing this threshold to optimize the utility of available data points. Notably, this study scrutinized approximately 9000 data points encompassing temperatures ranging from 5 to 50 \({}^{\circ}\)C and relative humidity spanning from 20 to 100%, with each parameter measured at 300 intervals between the minimum and maximum values. To calibrate and validate predictive models like the second-order polynomial, a large dataset is crucial. While, theoretically, only a few points are required to fit a polynomial, these would not suffice to ensure the model's robustness, accuracy, and reliability across a wide range of conditions. The extensive dataset of 9000 points allows for capturing the inherent variability in the observed phenomena, thereby refining the model to generalize well to unseen data. This comprehensive approach ensures that the model not only fits the given data accurately, but also performs reliably under various conditions, preventing overfitting and improving predictive capabilities. In essence, the large dataset serves to enhance the model's validity and utility, making the predictions more trustworthy and applicable in real-world scenarios. Figure 5 illustrates the error rates of each equation relative to the observed values, providing both 2D and 3D perspectives. The 3D plots represent a surface, encompassing regions beyond the specified boundaries, creating a waterfall-like visualization near the limits. Dark blue shades denote lower error values, indicative of temperatures below 0 \({}^{\circ}\)C, while yellow hues signify higher errors, associated with temperatures above 0 \({}^{\circ}\)C. Conversely, the 2D representations employ a contour plot method to present a heatmap of error distribution across temperature and relative humidity ranges. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Equation** & **Non-Optimized** & **Optimized** \\ \hline
1 st Degree & 0.9063-\(X+0.3458\)-\(Y-28.1317\) & 0.8912-\(X+0.3595\)-\(Y-27.9842\) \\
2 nd Degree & \(-0.00037\)-\(X^{2}+1.2175\)-\(X-0.0035\)-\(Y^{2}+0.7474\)-\(Y-43.8711\) & \(-0.00013\)-\(X^{2}+0.93\)-\(X-0.003\)-\(Y^{2}+0.66\)-\(Y-35.39\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equations obtained.