## 3 Results and Discussion
### Partial Least Squares (PLS) Analysis  
PLS analysis was employed to investigate the impact of the main variables (\(X_{1}\), \(X_{2}\), \(X_{3}\), and \(X_{4}\)) of extraction in both OM pulp and OM peels. The PLS results are presented in Figure 4. Plots A and C refer to the OM pulp, and plots B and D refer to OM peels. Figure 4A shows the effect of each parameter on extraction from OM pulp. Starting with parameter \(X_{1}\), it is obvious that the higher value of the liquid-to-solid ratio favors extraction, and a similar pattern is observed for parameter \(X_{3}\), where once again the higher pulsation value seems to be the most appropriate. On the contrary, parameter \(X_{2}\) seems to favor extraction when it is at its minimum value, i.e., the ideal solvent in this case seems to be water. Finally, the extraction duration (\(X_{4}\)) required to obtain the maximum yield is an intermediate extraction duration. Therefore, the optimal conditions for UPAE of OM pulp are established as follows: aqueous extraction for 12 min with a liquid-to-solid ratio of 60 mL/g and 48 pulses/min. The desirability value is 0.94, indicating that this model presents an excellent fit to the experimental data. Figure 4C provides a Variable Importance Plot (VIP) graph, highlighting how important the effect of each parameter is on the extraction of bioactive compounds from OM pulp. The significance value of 1.44 indicates that the most critical parameter is the solvent selection. This is followed by pulsation, whereas the liquid-solid ratio and the duration of extraction do not have a significant impact on the extraction efficiency. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Design**} & \multicolumn{2}{c}{\(L^{*}\)} & \multicolumn{2}{c}{\(a^{*}\)} & \multicolumn{2}{c}{\(b^{*}\)} & \multicolumn{2}{c}{**Color**} \\ \cline{2-9}  & **Pulp** & **Peel** & **Pulp** & **Peel** & **Pulp** & **Peel** & **Pulp** & **Peel** \\ \hline
1 & 49.5 \(\pm\) 0.2 & 48.6 \(\pm\) 0.7 & 46.2 \(\pm\) 0.5 & 44.6 \(\pm\) 0.9 & \(-\)5.9 \(\pm\) 0.8 & \(-\)2.2 \(\pm\) 0.9 & & \\
2 & 41.9 \(\pm\) 0.5 & 39.7 \(\pm\) 0.6 & 34.4 \(\pm\) 0.9 & 31.3 \(\pm\) 0.5 & 2.0 \(\pm\) 1.3 & 3.5 \(\pm\) 1.4 & & \\
3 & 74.8 \(\pm\) 1.4 & 73.8 \(\pm\) 0.2 & \(-\)9.8 \(\pm\) 0.8 & \(-\)11.4 \(\pm\) 0.1 & 38.6 \(\pm\) 3.6 & 51.1 \(\pm\) 1.2 & & \\
4 & 49.1 \(\pm\) 0.9 & 50.2 \(\pm\) 1.4 & 46.7 \(\pm\) 1.6 & 47.7 \(\pm\) 0.9 & \(-\)3.8 \(\pm\) 0.9 & \(-\)4.3 \(\pm\) 1.4 & & \\
5 & 51.7 \(\pm\) 0.5 & 52.2 \(\pm\) 1.2 & 45.9 \(\pm\) 0.8 & 44.6 \(\pm\) 2.4 & \(-\)2.0 \(\pm\) 0.8 & \(-\)6.2 \(\pm\) 0.9 & & \\
6 & 51.9 \(\pm\) 0.6 & 48.1 \(\pm\) 1.2 & 45.1 \(\pm\) 0.8 & 45.4 \(\pm\) 2.4 & \(-\)3.3 \(\pm\) 1.2 & \(-\)2.2 \(\pm\) 0.9 & & \\
7 & 45.9 \(\pm\) 0.4 & 44.6 \(\pm\) 0.5 & 45.4 \(\pm\) 0.9 & 39.6 \(\pm\) 1.4 & 0.4 \(\pm\) 1.4 & 2.8 \(\pm\) 1.3 & & \\
8 & 77.4 \(\pm\) 0.9 & 76.9 \(\pm\) 0.4 & \(-\)5.6 \(\pm\) 0.5 & \(-\)7.2 \(\pm\) 0.5 & 22.3 \(\pm\) 2.1 & 33.3 \(\pm\) 0.8 & & \\
9 & 78.4 \(\pm\) 0.7 & 76.4 \(\pm\) 0.5 & \(-\)3.5 \(\pm\) 0.1 & \(-\)5.6 \(\pm\) 0.5 & 15.8 \(\pm\) 0.5 & 24.2 \(\pm\) 0.9 & & \\ \hline \hline \end{tabular} Values represent the mean of triplicate determinations \(\pm\) standard deviation. The measured \(L^{*}\), \(a^{*}\), and \(b^{*}\) values were utilized to populate the table cells with the extract’s corresponding color, represented by the suitable HEX code.  
\end{table} 
Table 5: Color analysis was measured in both the pulp and peel of _Oputnia macrorhizas_ at various design points. Figure 4: Plots (**A**,**B**) illustrate the optimization of the pulp and peel from _Opuntia macrorhiza_ extracts, respectively, utilizing a partial least squares (PLS) prediction profiler and a desirability function with extrapolation control. Plots (**C**,**D**) display the Variable Importance Plot (VIP) graph, indicating the VIP values for each predictor variable in the pulp and peel extracts, respectively. A red dashed line is drawn at the 0.8 significance level for each variable in plots (**C**,**D**).