## 3 Results & Discussion
### Statistical Analysis & Process Optimization  
#### 3.2.1 Regression Model Equations  
The analysis tool of ANOVA was employed for the statistical analysis of the examined responses. The results of ANOVA are presented and evaluated in Appendix B. The Equations (1) and (2) were applied to fit the experimental responses of yield, extract's total chlorophyll and carotenoid content, as well as antioxidant activity (Table 3) and are presented below:  
\[\begin{split}\text{Yield}=&-115.1271+4.3438\text{ T}+0.2334\text{ P}+1.0443\text{ t}+0.1885\text{ R}-0.0090\text{ TP}-0.0215\text{ T}\text{ t}\\ &-0.0016\text{ P}\text{ t}-0.0374\text{ T}^{2}-0.0012\text{ R}^{2}+0.3828\text{ }10^{-4}\text{ T}\text{ P}\text{ t}+0.8281\text{ }10^{-4}\text{ T}^{2}\text{ P}\end{split} \tag{3}\]  
\[\begin{split}\text{CHL}^{\prime}=&-0.6675+0.0686\text{ T}+0.0120\text{ P}+0.0775\text{ t}-0.0448\text{ R}-0.1400\text{ }10^{-3}\text{ T}\text{ P}+0.3049\text{ }10^{-3}\text{ T}\text{ R}\\ &-0.3119\text{ }10^{-4}\text{ P}\text{ t}+0.1409\text{ }10^{-4}\text{ P}\text{ R}-0.4491\text{ }10^{-4}\text{ P}^{2}-0.0023\text{ t}^{2}\\ &+0.1540\text{ }10^{-3}\text{ R}^{2}\end{split} \tag{4}\]  
\[\begin{split}\text{Chlorophylls}=\exp^{\text{CHL}^{\prime}}\end{split} \tag{5}\]  
\[\begin{split}\text{CAR}^{\prime}=&-1.5102+0.0580\text{ T}+0.0124\text{ P}+0.0964\text{ t}-0.0506\text{ R}-0.1365\text{ }10^{-3}\text{ T}\text{ P}+0.4853\text{ }10^{-3}\text{ T}\text{ R}\\ &-0.4068\text{ }10^{-4}\text{ P}\text{ t}+0.1564\text{ }10^{-5}\text{ P}\text{ R}-0.4901\text{ }10^{-5}\text{ P}^{2}-0.0027\text{ t}^{2}\\ &+0.1296\text{ }10^{-3}\text{ R}^{2}\end{split} \tag{6}\]  
\[\begin{split}\text{Carotenoids}=\exp^{\text{CAR}^{\prime}}\end{split} \tag{7}\]  
\[\begin{split}\text{IC}_{50}=&416.4306-6.7840\text{ T}-1.2351\text{ P}-5.0817\text{ t}-1.1183\text{ R}+0.0237\text{ T}\text{ P}+0.0545\text{ T}\text{ t}+0.0228\text{ T}\text{ R}+0.0061\text{ P t}\\ &+0.0019\text{ P}\text{ R}+0.8633\text{ }10^{-3}\text{ P}^{2}+0.0805\text{ t}^{2}-0.1266\text{ }10^{-3}\text{ T}\text{ P}\text{ t}-0.3453\text{ }10^{-4}\text{ T}\text{ P}\text{ R}-0.1656\text{ }10^{-4}\text{ T}\text{ P}^{2}\end{split} \tag{8}\]  
where yield is expressed in % \(w/w\), carotenoids and chlorophylls are expressed in mg/gextr, and the antioxidant's activity quantitative measure IC\({}_{50}\) is expressed in mgextr/mgDPPH. The correlation of the extract's total phenolic and selected carotenoid content was not accomplished to the desired extent; thus, the corresponding models were not included.  
The ANOVA results (Appendix B) led to a successful data correlation, while the models' satisfactory accuracy and precision are also proved by the affinity of the predicted and experimental data presented in Figure 6. According to the information provided in Appendix B, the extraction yield is considered highly affected by the individual effect of temperature and solvent-to-biomass ratio and the combined effect of temperature, pressure, and duration (T P t). Moreover, chlorophyll content is proved highly dependent on solvent-to-biomass ratio, while the same applies between antioxidant activity and temperature. Finally, all the successfully associated responses were significantly affected by the combined factor of temperature and microwave power (T P).