## 3 Results and Discussion
### Formulation and Optimization of Etoricoxib-Loaded NE (ETB-Ne)  
The formulation and optimization of ETB-NE were carried out using a three-factor, three-level BBD. The responses obtained for various NE formulation trials are presented in Table 3.  
A two-factor interaction (2 FI) model was suggested for PS by the software based on the data of the trials performed. The 2 FI model was significant with a \(p\)-value < 0.0001. The lack of fit was not significant, and thus the model was acceptable. The predicted and adjusted R-squared values of 0.9058 and 0.9664, respectively, were comparable. Further, the observed and fitted values for the PS were in good agreement with each other (Table 3). The analysis of variance (ANOVA) data of the model is provided in Table 4. From the data, it was seen that only two independent factors had a significant influence on the particle size of NE droplets. The oil percent and S\({}_{\text{mix}}\) percent had a highly significant (\(p\)-value < 0.0001) effect on the particle size. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **\(F\)-Value** & \(p\)-Value** \\ \hline Model & 4067.82 & 6 & 677.97 & 72.90 & \textless{}0.0001 & significant \\ \hline A—Oil Percentage & 557.78 & 1 & 557.78 & 59.98 & \textless{}0.0001 & - \\ \hline B—S\({}_{\text{mix}}\) & 3308.91 & 1 & 3308.91 & 355.82 & \textless{}0.0001 & - \\ Percentage & 0.3613 & 1 & 0.3613 & 0.0388 & 0.8481 & - \\ \hline AB & 110.25 & 1 & 110.25 & 11.86 & 0.0074 & - \\ \hline AC & 64.00 & 1 & 64.00 & 6.88 & 0.0277 & - \\ \hline BC & 26.52 & 1 & 26.52 & 2.85 & 0.1255 & - \\ \hline Residual & 83.69 & 9 & 9.30 & - & - & - \\ \hline Lack of Fit & 77.69 & 6 & 12.95 & 6.47 & 0.0769 & not significant \\ \hline Pure Error & 6.00 & 3 & 2.00 & - & - & - \\ \hline Cor Total & 4151.52 & 15 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANOVA data for PS of ETB-NE formulations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Run** & \multicolumn{4}{c}{**Independent Factors**} & \multicolumn{4}{c}{**Dependent Factors**} \\ \cline{2-7}  & **Factor A: Oil** & **Factor B:** & **Factor C:** & **Response 1: Mean Particle** & **Response 2: PDI** \\  & **(\%)** & **S\({}_{\text{mix}}\) (\%)** & **Water (\%)** & **Observed** & **Predicted** & **Observed** & **Predicted** \\ \hline
1 & 20 & 40 & 30 & 190 & 188.29 & 0.665 & 0.6614 \\ \hline
2 & 5 & 40 & 30 & 162 & 163.59 & 0.582 & 0.5714 \\ \hline
3 & 5 & 55 & 50 & 142 & 142.22 & 0.457 & 0.4594 \\ \hline
4 & 10 & 55 & 30 & 156 & 153.03 & 0.481 & 0.4892 \\ \hline
5 & 10 & 40 & 50 & 175 & 176.16 & 0.324 & 0.3565 \\ \hline
6 & 10 & 40 & 50 & 177 & 176.16 & 0.389 & 0.3565 \\ \hline
7 & 20 & 40 & 70 & 182 & 180.72 & 0.641 & 0.6516 \\ \hline
8 & 20 & 55 & 50 & 165.9 & 169.42 & 0.613 & 0.6084 \\ \hline
9 & 10 & 25 & 70 & 192.7 & 194.13 & 0.523 & 0.5147 \\ \hline
10 & 10 & 40 & 50 & 174 & 176.16 & 0.356 & 0.3565 \\ \hline
11 & 20 & 25 & 50 & 200.9 & 199.59 & 0.693 & 0.6906 \\ \hline
12 & 10 & 40 & 50 & 174 & 176.16 & 0.357 & 0.3565 \\ \hline
13 & 5 & 40 & 70 & 170 & 172.02 & 0.452 & 0.4556 \\ \hline
14 & 10 & 55 & 70 & 162 & 158.61 & 0.526 & 0.5200 \\ \hline
15 & 5 & 25 & 50 & 198 & 193.39 & 0.549 & 0.5536 \\ \hline
16 & 10 & 25 & 30 & 197 & 198.86 & 0.665 & 0.6710 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The responses obtained (observed and predicted values) for various NE formulation trials. The polynomial equation suggested by the software for PS is provided in Equation (3). From the polynomial equation for PS, we can conclude that an increase in oil percent increases the particle size of NE. Meanwhile, an increase in S\({}_{\text{mix}}\) percentage will decrease the PS of NE. Among these, the higher magnitude for the regression coefficient for the factor B (S\({}_{\text{mix}}\) percent) indicated that the effect of S\({}_{\text{mix}}\) percentage is more on the PS of NE.