## 3 Results
### RSM Model and Analysis of Variance  
RSM was used to investigate the effects of hydrolysis temperature (115-135 \({}^{\circ}\)C), extraction time (15 min-35 min) and H\({}_{2}\)SO\({}_{4}\) concentration (0.05 M-0.2 M) on the oligosaccharideshenko fraction ED-F1 with potential prebiotic from _E. denticultum_. Several studies have successfully employed this method in optimizing hydrolysis parameters to obtain corncob xylooligosaccharides from a microwave-assisted hydrolysis [PERSON] et al. (2019), deriving glucomannologosaccharides from copra meal hydrolysis [PERSON] et al. (2019) and enzymatic hydrolysis to obtain galacto (arabino)-oligosaccharide from potato rhamnogalacturonan [PERSON] et al. (2019). ED-F1 fraction was selected to be optimized due to its significant and highest prebiotic activity score against five commercial probiotics. HMF was also measured as it is directly associated with the decomposition of hexoses under heat treatment and was known to be a potential carcinogen at high amounts. Three hydrolysis parameters were selected as factors and the operating range were narrowed. These parameters have been shown to significantly affect ED-F1 fraction yield. The factors were assigned as hydrolysis temperature (X\({}_{1}\)), hydrolysis time (X\({}_{2}\)) and H\({}_{2}\)SO\({}_{4}\) concentration (X\({}_{3}\)) (Table 1). Several researchers also have emphasized these to be vital factors that highly affect low or mild acid hydrolysis procedures to obtain oligosaccharidesrides [PERSON] et al. (2019); [PERSON] et al. (2019); [PERSON] et al. (2019). The Box-Behnken model was selected for the design of the experiment considering the restriction of operability in the selected factor (maximum heating temperature of the autoclave). Not only does the Box-Behnken design accommodate for a minimum number of experiments, but it also efficiently allows estimating first order and second order coefficients of the model and provides supportive analysis on the interactions between the variables [PERSON] et al. (2019). The three selected factors were assigned a lower, center point and upper level designated in code of \(-\)1, 0, +1, respectively, in which the central point and the experimental points are equidistant. From the 17 experiments, a quadratic model was adjusted to the responses (ED-F1 and HMF), and the regression coefficients for the linear, quadratic, and interaction terms were calculated and statistically evaluated using ANOVA. Table 2 shows the statistical analysis of the regression coefficients of the complete polynomial models for the yield of ED1-F1 and HMF. Based on the ANOVA (\(p\leq 0.05\)), the linear first-order effect was significant for all factors (temperature X\({}_{1}\), time X\({}_{2}\), H\({}_{2}\)SO\({}_{4}\) concentration X\({}_{3}\)), the quadratic second-order effect was significant only for temperature and H\({}_{2}\)SO\({}_{4}\) concentration for both ED-F1 yield and HMF. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Independent Variables 1**} & \multicolumn{3}{c}{**Responses 2**} \\ \hline Std. & X\({}_{1}\) & X\({}_{2}\) & X\({}_{3}\) & ED-F1 Yield & \\ Order & Temperature (\({}^{\circ}\)C) & Time (Min) & H\({}_{2}\)SO\({}_{4}\) (M) & (g/100 g) & \\ \hline  
\hline \hline \end{tabular} \({}^{1}\) X\({}_{1}\) Temperature: hydrolysis temperature; X\({}_{2}\) Time: hydrolysis time and X\({}_{3}\) H\({}_{2}\)SO\({}_{4}\): sulfuric acid concentration. \({}^{2}\) ED-F1: _E. denticulum_ fraction 1; HMF: 5-hydroxymethyl furfural.  
\end{table} 
Table 1: Box–Behnken experimental design layout and observed responses of oligosaccharide fraction yield (ED-F1) and HMF by-product. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Regression Coefficients 1**} \\ \cline{2-5}
**Model Parameters** & \multicolumn{3}{c}{**ED-F1 Yield**} & \multicolumn{3}{c}{**HMF**} \\ \hline  & **Full Quadratic Model** & \begin{tabular}{c} **Reduced** \\ **Quadratic Model** \\ \end{tabular}  & \ \begin{tabular}{c} **Full Quadratic Model** \\ \end{tabular}  &