## 3 Results
### Statistical Analysis and Fitting of Model of Encapsulation Efficiency
The results show that the residuals are randomly distributed around zero, indicating the rationality of the model (Figure 1b). The predicted vs. actual plot compares predictions against actual observations to assess the accuracy of the model [39]. The datapoints should ideally fall along a 45-degree line \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dependent Variables** & **Symbols** & **Model** \\ \hline Encapsulation efficiency (\%) & \(Y_{1}\) & \(Y_{1}=85.33+5.51X_{3}+8.46X_{4}-13.15X_{1}X_{3}-11.49X_{3}X_{4}-13.7{X_{1}}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Second-order polynomial equation of the model of encapsulation efficiency. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(p\)**-Value** & \\ \hline Model & 6239.68 & 20 & 311.98 & 3.03 & 0.0048 & significant \\ A: sodium alginate & 283.92 & 1 & 283.92 & 2.76 & 0.1094 & \\ B: carboxymethyl starch sodium & 3.29 & 1 & 3.29 & 0.032 & 0.8595 & \\ C: Urea & 485.54 & 1 & 485.54 & 4.71 & 0.0396 & \\ D: calcium chloride & 1145.31 & 1 & 1145.31 & 11.11 & 0.0027 & \\ E: polydopamine & 56.96 & 1 & 56.96 & 0.55 & 0.4641 & \\ AB & 124.43 & 1 & 124.43 & 1.21 & 0.2822 & \\ AC & 691.16 & 1 & 691.16 & 6.71 & 0.0158 & \\ AD & 166.92 & 1 & 166.92 & 1.62 & 0.2148 & \\ AE & 249.80 & 1 & 249.80 & 2.42 & 0.1320 & \\ BC & 156.25 & 1 & 156.25 & 1.52 & 0.2296 & \\ BD & 72.51 & 1 & 72.51 & 0.70 & 0.4095 & \\ BE & 59.75 & 1 & 59.7529 & 0.58 & 0.4534 & \\ CD & 528.08 & 1 & 528.08 & 5.13 & 0.0325 & \\ CE & 125.44 & 1 & 125.44 & 1.22 & 0.2803 & \\ DE & 8.41 & 1 & 8.41 & 0.08 & 0.7775 & \\ A\({}^{2}\) & 1637.67 & 1 & 1637.67 & 15.90 & 0.0005 & \\ B\({}^{2}\) & 276.32 & 1 & 276.32 & 2.68 & 0.1140 & \\ C\({}^{2}\) & 18.38 & 1 & 18.39 & 0.18 & 0.6763 & \\ D\({}^{2}\) & 0.10 & 1 & 0.10 & 0.0009 & 0.9760 & \\ E\({}^{2}\) & 106.16 & 1 & 106.16 & 1.03 & 0.3198 & \\ Residual & 2575.59 & 25 & 103.02 & & & \\ Lack of Fit & 2423.52 & 20 & 121.18 & 3.98 & 0.0656 & not significant \\ Pure error & 152.069 & 5 & 30.41 & & \\ Core total & 8815.27 & 45 & & & \\ \hline \hline \end{tabular} Note: The difference is extremely significant (\(p\) < 0.01); the difference was significant (\(p\) < 0.05); the difference was not significant (\(p\) > 0.05).  
\end{table} 
Table 3: ANOVA results for the quadratic model of encapsulation efficiency. where the predicted values equal the actual values. The results (Figure 1c) indicate that the datapoints are mainly distributed near the diagonal. The ANOVA results show that the interactions of X\({}_{1}\)X\({}_{3}\) and X\({}_{3}\)X\({}_{4}\) have significant impacts on encapsulation efficiency. Response surface and contour plots are used to demonstrate the influences of the interaction between the concentration of sodium alginate and urea, and the concentration of urea and CaCl\({}_{2}\) on EE (Figure 2). The results show that the EE will rise with the increase of urea concentration. However, with the increase of sodium alginate concentration, the EE will gradually increase and then decline (Figure 2a,b). The EE can reach 93.7% when the sodium alginate concentration is about 1.7% and urea concentration is about 30%. Additionally, when CaCl\({}_{2}\) concentrations increase as urea concentrations decrease, or decrease as urea concentrations increase, the EE will rise (Figure 2c,d). The EE can reach 98.6% when urea concentration is about 10% and CaCl\({}_{2}\) concentration is about 3%. When the urea concentration is about 30% and the CaCl\({}_{2}\) concentration is about 1%, the EE can reach 95.2%. Figure 1: The normal plot of residuals (**a**), residuals vs. predicted plot (**b**) and predicted vs. actual plot (**c**) for encapsulation efficiency. Figure 2: \(Cont.\)