## 3 Results and Discussions
### Influence of Vacuum Impresation Parameters on Soluble Phenols into Apple Slices
The polynomial model (Equation (4)) was refined by removing non-significant terms (\(p>0.05\)) to enhance its predictive capability [30]. The predicted and experimental data demonstrated a strong correlation (R\({}^{2}\): 0.9905 and R-adjusted: 0.9881) with a relative error below 10% (Table 1). Furthermore, the model's efficacy was supported by a non-significant lack of fit (\(p>0.05\)), indicating robust predictive power [34]. Additionally, the R\({}^{2}\) value is a crucial indicator of model fitness [35]. [PERSON] et al. [21] reported R\({}^{2}\) values of 0.98 after VI of carrot juice in apple tissue (lack of fit = 0.4189). Similar trends were reported in apple cubes vacuum-impregnated with grape juice for total soluble solids (R\({}^{2}\) = 0.943, lack of fit = 0.06) and luminosity (R\({}^{2}\) = 0.955, lack of fit = 0.10). However, for the total soluble phenols, the R\({}^{2}\) value was 0.694 (lack of fit = 0.06), which did not show an acceptable adjustment [19]. [PERSON] et al. [30] after vacuum impregnation of \(\beta\)-carotene from carrot juice in _Pachyrhius erosus_, using RSM analysis, reported that polynomial models with R\({}^{2}>0.8\) exhibited adequate adjustments; in contrast, models with R\({}^{2}>0.6\) were unsuitable for predicting experimental values. The second-order polynomial equation demonstrated that the parameters associated with vacuum impregnation of apple slices comprised linear and quadratic coefficients of impregnation time, restoration time, and vacuum impregnation, as well as the interactions between impregnation time \(\times\) restoration time and impregnation time \(\times\) vacuum pressure (\(p<0.05\)). Total soluble phenols(mg GAE/100 g fresh weight) = 48.12 - 42.82\(X_{T\!T}\) + 4.52\(X_{T\!T}\)2 - 21.61\(X_{RT}\) + 6.43\(X_{RT}\)2 - 425.28\(X_{VP}\) - 1149.13\(X_{VP}\)2 + 0.98\(X_{T\!T}\) + \(X_{RT}\)2 - 0.33\(X_{T\!T}\)2 * \(X_{RT}\) - 175.64\(X_{T\!T}\) * \(X_{VP}\)  
Figure 2 illustrates the effect of impregnation time (\(Y\)-axis) and restoration time (\(X\)-axis) at different vacuum pressures (\(-0.4\) to \(-0.2\) bar) on the VI of TSP (\(Z\)-axis) from HS extract into apple slices. These plots were based on the polynomial model presented in Equation (4). The three-dimensional representations facilitated the visual identification of the area exhibiting the highest VI of TSP in apple slices. It was observed that the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Source 1**} & \multicolumn{4}{c}{**Analysis of Variance**} & \multicolumn{2}{c}{**Regression Coefficients Soluble**} \\  & **SS 2** & **DF 3** & **MS 4** & **F-Value** & **Phenolic Content \(\beta\)-Coefficient** \\ \hline Mean/intercept & - & - & - & - & 48.12 * \\ X\({}_{iT}\) & 7291.45 & 1 & 7291.44 & 1409.37 * & \(-\)42.82 * \\ X\({}_{T\!T}\)2 & 1963.00 & 1 & 1963.00 & 379.42 * & 4.52 * \\ X\({}_{RT}\) & 4063.72 & 1 & 4063.72 & 785.42 * & \(-\)21.61 * \\ X\({}_{RT}\)2 & 1679.09 & 1 & 1679.09 & 324.55 * & 6.43 * \\ X\({}_{VP}\) & 811.60 & 1 & 811.59 & 156.87 * & \(-\)425.84 * \\ X\({}_{VP}\)2 & 1462.70 & 1 & 1460.69 & 282.72 * & \(-\)1149.13 * \\ X\({}_{T\!T}\)*X\({}_{RT}\) & 5.25 & 1 & 5.20 & 1.015 ** & \(-\)0.56 ** \\ X\({}_{T\!T}\)*X\({}_{RT}\)2 & 302.15 & 1 & 302.15 & 58.40 * & 0.98 * \\ X\({}_{T\!T}\)2 *X\({}_{RT}\) & 51.77 & 1 & 51.765 & 10.00 * & \(-\)0.33 * \\ X\({}_{T\!T}\)*X\({}_{VP}\) & 266.94 & 1 & 266.94 & 51.59 * & \(-\)175.64 * \\ X\({}_{T\!T}\)*X\({}_{VP}\) & 3747.13 & 1 & 3747.13 & 724.28 * & 15.62 * \\ X\({}_{RT}\)*X\({}_{VP}\) & 0.03 & 1 & 0.031 & 0.06 ** & \(-\)0.51 ** \\ Lack of fit & 57.05 & 3 & 19.01 & 3.676 ** & \\ Pure error & 165.55 & 32 & 5.174 & & \\ R-square & 0.9905 & & & & \\ R-Adjust & 0.9881 & & & & \\ Total SS & 23,643.64 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance using a quadratic model and regression coefficients, with vacuum impregnation conditions on the soluble polyphenols content from aqueous extracts of _Hibiscus sabdarifa_ calves in apple slices.