## 3 Results and Discussion
### Analysis of the Statistical Design of Experiments
#### 3.6.1 Numerical Analysis
In other words, an excess of polyphenols may exert a scavenging role on -OH radicals, thus decreasing the global oxidation of the pollutant. Lastly, it can be observed that the other variables or combinations of variables also have both positive and negative coefficients in the regression equation. However, compared to the previously described coefficients, these values do not have a decisive influence on the target variable. All of the above perfectly aligns with the results obtained in the ANOVA test, as the variables with the greatest influence are those with a \(p\)-value less than 0.05 in the analysis, thereby determining a significant influence on the elimination of crystal violet in ultrapure water. Regarding the removal of methylene blue, again, the concentration of hydrogen peroxide also plays a crucial role in the process. Interestingly, the concentration of polyphenols, as well as the quadratic terms of the concentrations of iron (II) and iron (III), exert a detrimental role in the removal of dye in this case. This suggests an important contribution of the Fenton and Fenton-like processes in the degradation of methylene blue, where Fe (II) and Fe (III) act as catalysts. In the presence of large amounts of polyphenols, these cationic species rapidly reduce into nZVI, with the subsequent loss of efficiency. However, an excess of iron salts, particularly Fe\({}^{2+}\)-, leads to a decrease in the removal percentage of dye. A plausible explanation for this could be the well-known scavenging ability of Fe\({}^{2+}\) cations towards hydroxyl radicals:  
\[Fe^{2+}+\cdot OH\to Fe^{2+}+OH^{-} \tag{12}\]  
Once the regression Equations (10) and (11) have been obtained, thanks to the capabilities of statistical experimental design, it is possible to theoretically predict the experimental conditions that would lead to the optimization (in this case, maximization) of the target variable. The optimal coded values of the operational variables that lead to this theoretical optimum are shown in Table 3.  
For the removal of chrysodine, the model has predicted three possible optima. Therefore, at least theoretically, by operating under those optimal conditions, complete elimination of the dye should be achieved. The experiments were carried out under the optimal conditions provided by the design, resulting in elimination percentages of 98.9% for optimum 1, 99.2% for optimum 2, and 97.3% for optimum 3. These data reflect that although the different optima do not yield the same elimination percentage, they do achieve a higher degree of elimination compared to any of the combinations in the experimental matrix (see Table 2), thus approaching the objective of the model, which is to achieve the highest possible elimination of chrysodine. One important aspect to consider in the obtained results from the different theoretical optima is the concentrations of certain variables, such as hydrogen peroxide. Due to the high cost of this reagent, it is advisable to use the lowest possible concentration while still \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{3}{c}{**Chrysodine**} & \multicolumn{2}{c}{**Methylene Blue**} \\ \cline{2-5}  & **1** & **2** & **3** & \\ \hline Fe(II) & \(-\)0.609945 & \(-\)1.99971 & \(-\)1.79394 & \(-\)0.451465 \\ \hline Fe(III) & 1.92918 & 2.00000 & 0.24663 & 0.15726 \\ \hline H\({}_{2}\)O\({}_{2}\) & 1.0094 & 1.49197 & 1.98174 & 0.534451 \\ \hline Polyphenols & 0.4105 & 0.494255 & 0.42093 & \(-\)1.18908 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coded values corresponding to the maximum removal efficiency of dye. ensuring the desired elimination efficiency. For this reason, considering the very similar elimination values obtained for optimum 1 and 2, from a practical point of view, the values obtained for optimum 1 are more convenient, achieving similar elimination values under more favorable conditions.