## 3 Results and Discussion  
### Extraction Yield  
Figure 1 presents the effect of the process variables on the responses \(A_{AR}\) and \(C_{C\!\!\!\!  
The liquid-to-solid ratio (L/S) has a great impact on the examined responses. The extraction yield increased with increasing ratio. A similar trend was reported by many researchers [12; 28; 29]. A higher ratio results in a larger concentration gradient during diffusion from the solid into the solution and in excessive swelling of the plant material, increasing the contact surface area between the material and the solvent [30].  
Figure 1: Main effects plots presenting the effect of \(\beta\)-cyclodextrinrin concentration (C\({}_{\beta\text{od}}\), mg/mL), liquid-to-solid ratio (L/S, mL/g), and temperature (T, \({}^{\circ}\)C) (**a**) on extract antiradical activity (A\({}_{\text{AR}}\), \(\mu\)mol TRE/g) and (**b**) on caffeine extraction yield (C\({}_{\text{Cd}}\)).  
The positive effect of extraction temperature on \(A_{AR}\) and \(C_{Caf}\) is presented in Figure 1. It is widely recognized that temperature enhances mass transfer by improving the extraction rate; a fact that can be attributed to the effect of temperature on the vapor pressure, surface tension, and viscosity of the solvent. Moreover, the increase in the yield may be associated with the increased ease with which solvent diffuses into cells and the enhancement of desorption and solubility at high temperatures [31]. Previous studies have reported a decrease of extract antiradical activity with temperature due to the possible degradation of polyphenic compounds [32].  
The regression coefficients were calculated and the data was fitted to second-order polynomial equations:  
\[\begin{split}\text{A}_{\text{AR}}(\text{{}^{\text{umol}\ TRE}}/ \text{g})&=12.32-0.474*\text{C}_{\beta\ cd}+\ 0.714*\text{L}/\text{s}-\ 0.191*\text{T}+\ 0.022*\text{C}_{\beta\ cd}^{2}-\ 0.008*\text{(L}/\text{s})^{2}\\ &\quad+0.006*\text{T}^{2}+\ 0.035*\text{C}_{\beta\ cd}*\text{L}/\text{s}- 0.017*\text{C}_{\beta\ cd}*\text{T}-0.006*\text{L}/\text{s}*\text{T}\end{split} \tag{4}\]  
\[\begin{split}\text{C}_{\text{Caf}}(\text{{}^{\text{mg}}}/\text{g} )&=2.660-0.036*\text{C}_{\beta\ cd}+\ 0.039*\text{L}/\text{s}+\ 0.032*\text{T}+\ 0.280*\text{T}^{2}-\ 0.500*\text{T}^{ 2}-\ 0.500*\text{T}^{ 3}*\text{(L}/\text{s})^{2}\\ &\quad-0.260*\text{T}^{2}+0.020*\text{T}^{0}-3*\text{C}_{\beta\ cd}* \text{L}/\text{s}+\ 0.460*\text{T}^{0}-3*\text{C}_{\beta\ cd}*\text{T}+\ 0.170*\text{T}^{ 3}*\text{L}/\text{s}*\text{T}\end{split} \tag{5}\]  
The coefficient of determination, R\({}^{2}\), for A\({}_{\text{AR}}\) and C\({}_{\text{Caf}}\) was 0.729 and 0.969, respectively, indicating that 72.9% and 96.9% of the total variability in the responses could be explained by the specific models. According to the regression analysis, the temperature, the liquid-to-solid ratio, and their quadrates significantly influence the extraction yield (\(p<0.05\)).  
The measured and the predicted values of the responses are analytically depicted in Table 2. The extraction conditions of 9.25 mg/mL (C\({}_{\beta\ cd}\)), 30 mL/g (L/S), and 80 \({}^{\circ}\)C (T) are the optimum conditions. Under these conditions, the predicted values of antiradical activity and caffeine content were 30.56 \(\upmu\)mol TRE/g dry matter and 4.733 mg/g, respectively, whereas the observed experimental values were 30.324 \(\upmu\)mol TRE/g dry matter and 4.761 mg/g, respectively.