## 3 Results and Discussion
### Evaluation of SFE-CO\({}_{2}\) of Hops at 24-45 MPa Pressure  
#### 3.2.1 Central Composite Design and Model Analysis  
At the following steps, the research was targeted to increase SFE-CO\({}_{2}\) yield and recover valuable constituents from _Ella_ hops under significantly shorter extraction time. Since higher P (>25-30 MPa) accompanied by T of 50 \(\pm\) 10 \({}^{\circ}\)C can substantially increase the yield of hop SFE-CO\({}_{2}\) extracts [7], CCD-RSM was employed to optimize the SFE-CO\({}_{2}\) process by testing different experimental conditions at the following P and T levels: P (25-45 MPa) and T (40-60 \({}^{\circ}\)C). The range of \(\tau\) (30-90 min) was determined based on the several preliminary runs at the center P and T values (35 MPa, 50 \({}^{\circ}\)C), indicating negligible change in yield at \(\tau\) > 90 min. Within the selected region of operability, total SFE-CO\({}_{2}\) hop extract yield (RFI) ranged from 13.9 to 27.6 g/100 g HP, while the TEACORAC (RFII) increased from 252 to 375 mg TE/g HP, both well-fitting the predicted values of the designed models (Table 2). Calculated Pearson correlation coefficient of 0.9363 (\(p\) < 0.0001) additionally indicated strong significant positive correlation between the SFE-CO\({}_{2}\) yield and TEACORAC under these conditions. Both models were reasonably reproducible with low variation coefficients (<3%), high determination coefficients (R\({}^{2}\) > 0.96) and good agreement between the adjusted and predicted R\({}^{2}\) values (difference < 0.20), additionally confirming the good fit of the model to the experimental data (Supplementary Materials, Table S1). Based on the ANOVA (Table 3), developed models were statistically significant (\(p\) < 0.05), with \(F\)-values of 51.71 and 35.20 for RFI and RFII, respectively. Time (\(\tau\)) was the primary extraction parameter responsible for the observed changes in both extract yield (\(F\) = 258.72) and TEACORAC (\(F\) = 175.15) under the different experimental conditions. The significance of other model terms for the extract yield decreased as follows: P \(<\) P\({}^{2}\) (showing the non-linear concave relationship between P and RFI) \(<\) T \(<\) P\(\tau\) interaction. The influence of other interactions (PT and P\(\tau\)) and second  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Levels and**} & \multicolumn{3}{c}{**SFE-CO\({}_{2}\) Parameters**} & \multicolumn{3}{c}{**CO\({}_{2}\) Density \({}^{*}\),**} & \multicolumn{2}{c}{**RFI: Extract Yield,**} & \multicolumn{2}{c}{**RFII TEACORAC**} \\  & & & & & **kg/m\({}^{3}\)** & **g/100 g HP** & & **mg TE/g HP** \\ \cline{2-9}  & **P, MPa** & **T**\({}^{\circ}\)**C & **\(\tau\), min** & **Experimental** & **Predicted** & **Experimental** & **Predicted** \\ \hline Center & 35 & 50 & 60 & 899 & 23.24 \(\pm\) 0.56 & 23.91 & 334.22 \(\pm\) 14.15 & 344.65 \\ Axial & 25 & 50 & 60 & 834 & 20.15 \(\pm\) 0.31 & 19.84 & 297.98 \(\pm\) 19.92 & 295.34 \\ Axial & 35 & 40 & 60 & 935 & 25.1  
order terms (T\({}^{2}\) and \(\tau^{2}\)) was not significant. Besides \(\tau\), TEACORAC was mainly affected by the P\({}^{2}\) and P, to a lower extent by P\(\tau\) and T\({}^{2}\), while other factors and their interactions did not exert any significant input towards RFII. The Pareto charts (Figure 2) visualize these effects and indicate that three primary factors (\(\tau\), P and P\({}^{2}\)) together contributed to the \(>\)70% of the observed responses. The following second-order polynomial regression equations describe the empirical relationship between the independent model variables and selected response factors (in terms of coded factors):  
\[ \begin{array}{ll}Yield_{SFE-CO_{2}}&=23.92+2.27\times P-0.94\times T+3.44\times \tau-0.25\times(PT)-0.61\times(P\tau)+0.20\times(T\tau)-1.80\times P^{2}\\ &\quad+0.03\times T^{2}-0.82\times\tau^{2}\end{array}  \tag{5}\]  
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