## 3 Results
### Influence of the Factors on the Reponses  
From the second-order models (Equations (4)-(6)), the influence of each factor on the responses (bicorude yield, and nitrogen and oxygen contents in the biocrude) was represented (Figure 3), and the binary interactions between factors were plotted in Figure 4. Besides, ANOVA analysis (Tables S1-S3, in Supplementary Materials) showed the significant factors and interactions within 95% confidence intervals.  
Figure 2: Residual analysis against the values obtained from the mathematical models for the responses: (**a**) biocrude yield, (**b**) nitrogen content in the biocrude and (**c**) oxygen content in the biocrude.  
Figure 4: Binary interactions for: (**a**) biocrude yield, (**b**) nitrogen content and (**c**) oxygen content.  
Figure 3: Effect of main factors on (**a**) biocrude yield, (**b**) nitrogen content in the biocrude and (**c**) oxygen content in the biocrude.  
Considering the effect of the three factors on the biocrude yield, Figure 3a shows how the temperature (\(X_{T}\)) was a significant factor (\(p\)-value = 0.000) and positively influenced the biocrude yield. Therefore, higher yields were obtained at high temperatures. This result is consistent with that described by other authors [27]. Reaction time (\(X_{t}\)) had a significant influence (\(p\)-value = 0.0013). However, in this case, the biocrude yield decreased as the reaction time increased. On the other hand, the influence of the biomass concentration (\(X_{CS}\)) on the biocrude yield was not significant (\(p\)-value = 0.6177). For biocrude yield, the binary interactions of temperature with reaction time and biomass concentration and reaction time-biomass concentration (\(X_{T}X_{t}\), \(X_{T}X_{CS}\) and \(X_{t}X_{CS}\), respectively) (Figure 4a) had \(p\) values < 0.05 (0.0061, 0.0487, and 0.0042, respectively) and, therefore, they had a significant influence on the response. The binary interaction temperature-reaction time (\(X_{T}X_{t}\)) showed a negative influence, while the interactions between temperature-biomass concentration and reaction time-biomass concentration (\(X_{T}X_{CS}\) and \(X_{t}X_{CS}\), respectively) were positive. Regarding nonlinearity, only the quadratic term of temperature (\(X_{T}^{2}\)) was significant (\(p\)-value = 0.0023), with a positive influence on the biocrude yield.  
Considering the nitrogen content (Figure 3b), only the main effect of the biomass concentration (\(X_{CS}\)) can be regarded as significant (\(p\)-value = 0.0087). An increase in the biomass concentration generated a higher concentration of nitrogen in the biocrude, which negatively affects the quality of the biocrude. Besides, the temperature and reaction time did not show a significant effect on the N content (\(p\)-value = 0.4511 and 0.3316, respectively). In addition, the binary interactions and the quadratic terms for the nitrogen content (Figure 4b) were not significant (\(p\)-values > 0.05).  
In the same way, the main factor corresponding to the biomass concentration (\(X_{CS}\)) exerted a significant effect (\(p\)-value = 0.0101) on the content of oxygen in the biocrude (Figures 3c and 4c), which had a positive impact in reducing the content of this heteroatom in the biocrude, increasing its quality. The results of the ANOVA analysis showed that both the binary interactions and the quadratic terms were not significant since they had \(p\) values > 0.05.