Y1 (PS) = +145.32 + 56.43 A + 18.29 B <sup>−</sup> 69.42 C + 9.43 AB <sup>−</sup> 3.00 AC <sup>−</sup> 8.25 BC + 42.81 A<sup>2</sup> + 24.35 B2 + 46.23 C<sup>2</sup> (2)

The given equation reflects the quantitative impact of independent variables (A and C) and their interactions in the terms of AB, AC, and BC in the respect of response Y1. The coefficient's *p*-value (0.05) demonstrated that they had a significant effect on Y1. The plus sign of the coefficient denotes a synergistic effect, whereas the minus sign denotes the independent variables' antagonistic effect on response. The factor's high coefficient value demonstrates that it has a significant impact on the preferred response. All selected responses admirably corresponded with the quadratic model. ANOVA and multiple correlation tests were used to verify the model's efficiency (R2). The quadratic model's results, along with ANOVA and the multiple correlation test (R2), are shown in Table 4.

The F-value 131.32 of this model designated that it is significant. *p*-values less than 0.05 for this model terms are considered as significant. A, B, C, A2, B2, and C2 present as significant model terms, while the model's terms are not significant if the value is greater than 0.10. The F-value of 3.78 for the lack of fit indicates that it is non-significant in comparison to the pure error. There is an 11.59% probability that a large lack-of-fit F-value is caused by noise. A relatively insignificant lack of fit is satisfactory, and we only want the model to fit. The adjusted R2 of 0.9865 is relatively close to the predicted R<sup>2</sup> of 0.9280; i.e., the difference between them was less than 0.2. The signal-to-noise ratio is calculated by adequate precision. It is better to have a ratio of more than 4. Our signal-to-noise ratio of 37.895 implies an appropriate signal.

Response surface plots were utilized to further clarify the relationship between the dependent and independent variables. Three-dimensional surface response plots were created to better understand the relationship between the variables and PS. The 3D surface plot, illustrated in Figure 1A, showed that increasing the CS:TPP concentration (mass ratio of 1:1) ultimately resulted in the largest PS formation. The relationship between sonication time and PS was found to be negative, with PS decreasing as sonication times increased. The 3D surface plot in Figure 1B demonstrates the influence of CS:TPP concentrations and sonication times on PS, while PEG 400 concentrations and sonication times on the PS of APG-loaded PEGylated CNPs are shown in Figure 1C.
