## 3 Results
### Statistical Analysis and Fitting of Model of Water Absorption  
The results of ANOVA of the experimental data on water absorption are shown in Table 5. In Table 5, sodium alginate (SA) is factor A, carboxymethyl starch sodium (CMS) is factor B, urea is factor C, calcium chloride (CaCl\({}_{2}\)) is factor D, and polydopamine (PDA) is factor E. The f-value is 4.16, and the \(p\)-value is 0.0001 (\(p<0.05\)), which indicate that the model is significant. The \(p\)-value of lack of fit is 0.1469 (\(p>0.05\)), which indicates that the model has a high degree of fitting with the experimental data. The influence of five factors on WA is as follows: A \(>\) E \(>\) B \(>\) D \(>\) C. The primary items A (SA concentration) and E (PDA concentration) had a significant effect on WA (\(p<0.05\)). The interaction terms AB and BD had a significant effect on WA (\(p<0.05\)). The quadratic terms A\({}^{2}\) and B\({}^{2}\) have significant effects on the results (\(p<0.01\)), C\({}^{2}\), D\({}^{2}\) and E\({}^{2}\) have very significant effects (\(p<0.001\)) while other terms have no significant effect on WA (\(p>0.05\)). Figure 2: Three-dimensional response surface (**a**) and contour plot (**b**) of the concentration of sodium alginate and urea on encapsulation efficiency. Three-dimensional response surface (**c**) and contour plot (**d**) of the concentration of urea and CaCl\({}_{2}\) on 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 & 76,438.20 & 20 & 3821.91 & 4.16 & 0.0001 & significant \\ A: sodium alginate & 3946.98 & 1 & 3946.98 & 4.30 & 0.0105 & \\ B: carboxymethyl starch sodium & 2216.06 & 1 & 2216.06 & 2.41 & 0.0627 & \\ C: Urea & 767.29 & 1 & 767.29 & 0.84 & 0.3344 & \\ D: calcium chloride & 1402.50 & 1 & 1402.50 & 1.53 & 0.1982 & \\ E: polydopamine & 5905.92 & 1 & 5905.92 & 6.43 & 0.0209 & \\ AB & 3410.56 & 1 & 3410.56 & 3.71 & 0.0484 & \\ AC & 265.69 & 1 & 265.69 & 0.29 & 0.5676 & \\ AD & 0.64 & 1 & 0.64 & 0.0007 & 0.6183 & \\ AE & 235.62 & 1 & 235.62 & 0.26 & 0.9902 & \\ BC & 292.41 & 1 & 292.41 & 0.32 & 0.5489 & \\ BD & 2088.49 & 1 & 2088.49 & 2.27 & 0.0393 & \\ BE & 564.06 & 1 & 564.06 & 0.61 & 0.4067 & \\ CD & 203.06 & 1 & 203.06 & 0.22 & 0.6170 & \\ CE & 531.30 & 1 & 531.30 & 0.58 & 0.4205 & \\ DE & 989.10 & 1 & 989.10 & 1.08 & 0.2744 & \\ A\({}^{2}\) & 5187.89 & 1 & 5187.89 & 5.65 & 0.0347 & \\ B\({}^{2}\) & 6066.25 & 1 & 6066.25 & 6.60 & 0.0124 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ANOVA results for the quadratic model of water absorption. Based on the statistical analysis of the experimental results, a second-order polynomial equation is derived. The equations, after removing non-significant items, are shown in Table 6.  
The diagnosis of the model is presented in Figure 3. The datapoints in a normal plot of residuals follow a diagonal representing the expected normal distribution, indicating that the residuals are normally distributed (Figure 3a). As the plot of residuals vs. predicted values shows, the residuals are randomly distributed around zero, indicating that the model is reasonable and has no abnormal values (Figure 3b). The plot of predicted vs. actual values shows that the datapoints are mainly distributed ar \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dependent Variables** & **Symbols** & **Model** \\ \hline Water absorption (\%) & \(Y_{2}\) & \(Y_{2}=195.22+19.46X_{1}-17.34X_{5}+29.20X_{1}X_{2}+30.60\,X_{2}X_{4}-21.28{X_{ 1}}^{2}-25.68{X_{2}}^{2}\) \\  & \(-34.95{X_{3}}^{2}-64.02{X_{4}}^{2}-55.79{X_{5}}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Second-order polynomial equation of the model of water absorption. Figure 3: The normal plot of residuals (**a**), residuals vs. predicted plot (**b**) and predicted vs. actual plot (**c**) for water absorption. decreasing (Figure 4c,d). When the CMS concentration is about 3.6% and CaCl\({}_{2}\) is about 2.0%, the water absorption can reach 197.0%.