## 3 Results
### Antioxidant Capacity  
The antioxidant activity of plant extracts, manifested by their free radical scavenging capacity, is largely attributed to the presence of phenolic compounds [23; 36; 37]. Horseradish is rich in antioxidants, such as polyphenols and flavonoids, which significantly contribute to the prevention and combat of conditions caused by oxidative stress and damage generated by free radicals [26].  
For the antioxidant capacity of the horseradish extracts studied, a significant statistical model was obtained (\(p<0.05\)) with a regression coefficient of R\({}^{2}\) = 0.8953 for the hydroalcoholic extract variant and R\({}^{2}\) = 0.8519 for the aqueous extraction. The mathematical model took the form of the coded Equations (7) and (8):  
\[\begin{split}\text{DPPH (hydroalcoholic solvent)}=96.15-0.0000\text{A}+0.3157 \text{B}+0.239\text{SC}+0.3009\text{AB}+0.1483\text{AC}-0.2289\text{BC}\\ -0.2009\text{A}^{2}+0.2779\text{B}^{2}-0.3746\text{C}^{2}\end{split} \tag{7}\]  
\[\text{DPPH (aqueous solvent)}=82.44+3.36\text{A}-2.38\text{B}+0.0754\text{C}+4.66 \text{AB}+3.82\text{AC}-0.8543\text{BC} \tag{8}\]  
\[\text{A = coded factor representing extraction time (min);}\] \[\text{B = coded factor representing extraction temperature (${}^{\circ}$C);}\] \[\text{C = coded factor representing potency (W);}\] \[\text{AB, AC, BC = interaction effects between variables;}\] \[\text{A}^{2},\text{B}^{2},\text{C}^{2} = quadratic effects of each factor.\]  
The coded equations allow for the evaluation of the influence of each factor on the antioxidant capacity by comparing their associated coefficients.  
Equation (7) highlights the significant positive impact of the linear factor B (temperature), followed by the interaction between A and B (time and temperature) on the antioxidant capacity of the hydroalcoholic horseradish extract. In contrast, a significant negative effect is observed associated with factors such as the quadratic term C\({}^{2}\) and the interaction between factors B and C (temperature and potency).  
In the case of the aqueous extract, Equation (8) shows that among the factors analyzed, the interaction between factors A and B (time and temperature) contributes the most to the increase in the response (antioxidant capacity), followed by the interaction between A and C (time and potency). In contrast, the most pronounced negative influence on the response is exerted by factor B (temperature), followed by the interaction between B and C (temperature and potency).  
Furthermore, the 3D graphs in Figure 3 provide a clearer visualization of the influence of time, temperature, and potency factors on the antioxidant capacity of the horseradish extracts.  
The maximum antioxidant activity of 96.93% was recorded for the extraction with hydroalcoholic solvent at 30 min, 50 \({}^{\circ}\)C temperature, and 140 W potency. When water was used as the solvent, the maximum recorded value was 89.34% at 30 min, 40 \({}^{\circ}\)C temperature, and 200 W potency. The minimum values recorded were 95.13% for the hydroalcoholic solvent at 30 min, 40 \({}^{\circ}\)C temperature, respectively, 80 W potency, and 73.01% for the ultrapure water solvent at 10 min, 50 \({}^{\circ}\)C temperature, and 140 W potency.  
Figure 3: Representation of three-dimensional response surfaces for the combined effect of the factors: temperature and time, potency and time, potency and temperature on the antioxidant activity for extracts in hydroalcoholic solvent (**A–C**) and aqueous solvent (**D–F**) (graphs generated using Design-Expert 13 software).