Y3 (% DEE) = +79.13 + 5.62 A +2.67 B <sup>−</sup> 9.05 C + 0.1400 AB + 1.43 AC + 0.7550 BC +1.87 A<sup>2</sup> + +1.68 B<sup>2</sup> +1.75 C2 (3)

It can be concluded from equation 3 that CS:TPP (A) and PEG concentrations (B) both had a positive influence on % DEE, whereas the sonication time (C) had an inverse relationship with % DEE. The final model after ANOVA analysis revealed that A, B, and C factors showed significant effects on the % DEE of APG, as all possessed a *p*-value of <0.05. The model's F-value of 48.35 indicates that it is statistically significant. *p*-values of less than 0.05 are considered significant for model terms. A, B, C, and A<sup>2</sup> are significant model terms in this study. The model terms are not significant if the value is above 0.10. The lack-of-fit F-value of 0.22 indicates that the lack of fit is not significant in comparison to the pure error. The adjusted R2 of 0.9638 is probably close to the predicted R<sup>2</sup> of 0.9426; i.e., the variation was below 0.2. The signal-to-noise ratio is calculated by adequate precision, and it has a ratio that is more than 4. The ratio of 24.988 indicates that the signal is adequate. The obtained design space is acceptable by using this model.

Interaction patterns are analyzed using a 3D-response surface graph. As shown by the 3D-response surface graph in Figure 2A–C, it is apparent that the percent DEE is significantly affected by CS:TPP concentration, PEG concentration, and sonication time. This could be clarified by the interaction of APG with the hydrophobic group of PEGylated CNPs. Increased CS:TPP and PEG concentrations are assumed to increase the number of hydrophobic groups accessible for interactions with the APG (hydrophobic), resulting in improved drug entrapments in NPs [31].
