## 2 Materials and Methods
### Methods
#### 2.2.6 Individual Determination of Carotenoids
The selected model exhibited the highest values of R\({}^{2}\) and adjusted R\({}^{2}\) for ethanol extraction (lycopene: 0.99 and 0.98; DPPH: 0.98 and 0.96; TPC: 0.98 and 0.96; and TPC: 0.76 and 0.46, respectively). These correlations provide insights into the ability of the equation to accurately depict the relationship between independent and dependent variables. For all parameters, this asserts the validity of the proposed parameter prediction model based on the extraction conditions. The accuracy and reliability of the experiments were assessed through the coefficient of variance, indicating the good precision and consistency of the experiments. As can be observed in Table 3, where the evolution of the parameters when acetone is used as a solvent is presented, the main influences on lycopene extraction are the solid/liquid ratio (\(p<0.01\)), the combined effect of the solid/liquid ratio with time (\(p<0.01\)), and the quadratic effect of the solid/liquid ratio (\(p<0.01\)); for DPPH, none of the parameters significantly influences its evolution; for TPC, the solid/liquid ratio (\(p<0.01\)) and the quadratic effect of the solid/liquid ratio (\(p<0.01\)) are significant; and for TFC, the solid/liquid ratio (\(p<0.01\)) is significant. As can be observed in Table 4, where the evolution of the parameters when ethanol is used as a solvent is presented, the main influences on lycopene extraction are the linear effect of the solid/liquid ratio (\(p<0.01\)), temperature (\(p<0.01\)), and the quadratic effect of the solid/liquid ratio (\(p<0.01\)); for DPPH, the linear effect of the solid/liquid ratio (\(p<0.01\)), temperature (\(p<0.01\)), time (\(p<0.01\)), the combined effect of the solid/liquid ratio with time (\(p<0.01\)), and the quadratic effect of the solid/liquid ratio (\(p<0.01\)); for TPC, the linear effect of the solid/liquid ratio (\(p<0.01\)), and the quadratic effect of the solid/liquid ratio (\(p<0.01\)); and for TPC, none of the parameters significantly influences its evolution. As can be observed in Table 5, where the evolution of the parameters when ethyl acetate is used as a solvent is presented, the main influences on lycopene extraction are the linear effect of the solid/liquid ratio (\(p<0.01\)), the linear effect of temperature (\(p<0.01\)), and the quadratic effect of the solid/liquid ratio (\(p<0.01\)); for DPPH, none of the parameters significantly influences its evolution; for TPC, the linear effect of the solid/liquid ratio (\(p<0.01\)); while for TFC, the linear effect of the solid/liquid ratio (\(p<0.01\)), the quadratic effect of the solid/liquid ratio (\(p<0.01\)), and the quadratic effect of temperature (\(p<0.01\)). The second-order polynomial equations for the prediction of lycopene, DPPH, TPC, and TFC, in coded form, are provided in the Supplementary Materials. Surface Response 3D Plots  
In our study, the Box-Benhken design was used to optimize lycopene extraction, DPPH, TPC, and TFC antioxidant activity from tomato seed flour using three parameters (the solid/liquid ratio, time, and temperature). In Figures S1-S12, the evolution of lycopene, DPPH, TPC, and TPC antioxidant activity as a function of the solvent, the solid/liquid