## 3 Results and Discussion
### Optimal Green Solvent Design for Antioxidant Extraction from Lemon Balm
#### 3.3.1 Fitting the Models for Predicting Antioxidant Capacity  
A BBD factorial model requiring 15 experimental runs was employed to study the responses of CUPRAC, ABTS, and DPPH of LB extracts prepared by UAE with a new DES (ChCl:U). Experimental results were fitted to the PCM, and the least-squares method was used to calculate the regression coefficients for linear, quadratic, and interaction terms. Figure 6: Effect of DES–UAE conditions (ChClU molar ratio, water content, and extraction time) on CUPRAC, ABTS, and DPPH of LB extracts. Bars with different letters indicate significant differences (one-way ANOVA and Duncan test, \(p<0.05\)). The following regression Equations (4)-(6) were obtained  
\[ \begin{split}\text{CUPRAC}=758.70-1561.40\text{ChCl}:\text{U}+2.02 \text{WC}-46.43\text{t}+703.69\text{(ChCl}:\text{U)}^{2}-0.16\text{WC}^{2}+0.94 \text{t}^{2}\\ +28.16\text{ChCl}:\text{U}\times\text{WC}+37.00\text{ChCl}:\text{U} \times\text{t}+0.55\text{WC}\times\text{t}-12.69\text{(ChCl}:\text{U)}^{2} \times\text{WC}\\ -17.06\text{(ChCl}:\text{U)}^{2}\times\text{t}\end{split}  \tag{4}\]  
\[ \begin{split}\text{ABTS}=537.00-832.97\text{ChCl}:\text{U}-10.41 \text{WC}-29.39\text{t}+380.58\text{(ChCl}:\text{U)}^{2}-0.005\text{WC}^{2}-0. 047\text{t}^{2}\\ +13.27\text{ChCl}:\text{U}\times\text{WC}+34.00\text{ChCl}:\text{U} \times\text{t}+0.83\text{WC}\times\text{t}-4.94\text{(ChCl}:\text{U)}^{2} \times\text{WC}\\ -18.33\text{(ChCl}:\text{U)}^{2}\times\text{t}\end{split}  \tag{5}\]  
\[ \begin{split}\text{DPPH}=260.12-591.14\text{ChCl}:\text{U}+9.93 \text{WC}-26.07\text{t}+267.10\text{(ChCl}:\text{U)}^{2}-0.19\text{WC}^{2}+0. 35\text{t}^{2}\\ +4.14\text{ChCl}:\text{U}\times\text{WC}+24.90\text{ChCl}:\text{U} \times\text{t}+0.33\text{WC}\times\text{t}-1.74\text{(ChCl}:\text{U)}^{2} \times\text{WC}\\ -11.26\text{(ChCl}:\text{U)}^{2}\times\text{t}\end{split}  \tag{6}\]  
The ANOVA results for the predicted response PCM are presented in Table 5.  
The ANOVA test revealed that the PCMs adequately represent responses of AC values for LB extracts. The high R\({}^{2}\) values (0.9658-0.9992) indicate that generated PCMs were adequate for the description of the effects of three independent variables (ChCl:U, WC, and t) on the antioxidant potential of LB measured by three analytical methods (CUPRAC, ABTS, and DPPH). Moreover, the adjusted R\({}^{2}\) values (0.9961, 0.8405, and 0.8620 for CUPRAC, ABTS, and DPPH, respectively) were also high and indicated a good correlation between experimental and predicted results. The calculated R\({}^{2}\) and adjusted R\({}^{2}\) values were higher \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **df** & **SS** & **MS** & **F-Value** \\ \hline \hline \multicolumn{5}{c}{CUPRAC} \\ Regression & 11 & 119,139.5 & 10830.9 & 413.2 * \\ Residual & 3 & 120.5 & 40.2 & \\ Lack-of-fit & 1 & 68.1 & 68.1 & 2.6 \\ Pure error & 2 & 52.4 & 26.2 & \\ Total & 14 & 119,260.0 & & \\ R\({}^{2}\), Adjusted R\({}^{2}\) & & 0.9992, 0.9961 & & \\ \multicolumn{5}{c}{ABTS} \\ Regression & 11 & 37,749.5 & 3431.8 & 4.3 \\ Residual & 3 & 1586.91 & 529.0 & \\ Lack-of-fit & 1 & 0.01 & 0.01 & \(1\times 10^{-5}\) \\ Pure error & 2 & 1586.9 & 793.5 & \\ Total & 14 & 39,336.41 & & \\ \multicolumn{5}{c}{R\({}^{2}\), Adjusted R\({}^{2}\)} & 0.9658, 0.8405 & & \\ \multicolumn{5}{c}{DPPH} \\ Regression & 11 & 17,320.8 & 1574.6 & 5.2 \\ Residual & 3 & 603.4 & 201.1 & \\ Lack-of-fit & 1 & 0.2 & 0.2 & \(6.6\times 10^{-4}\) \\ Pure error & 2 & 603.2 & 301.6 & \\ Total & 14 & 17,924.2 & & \\ R\({}^{2}\), Adjusted R\({}^{2}\) & & 0.9704, 0.8620 & & \\ \hline \hline \end{tabular}
* Significant at \(p<0.05\).  
\end{table} 
Table 5: Analysis of variance (ANOVA) results for the studied responses: CUPRAC, ABTS, and DPPH values of lemon balm extracts prepared using choline chloride/urea as a deep eutectic solvent. than 80%, which represented that the model predictions were highly confirmative of the experimental data.