## 3 Results and Discussion
### Formulation and Optimization of Etoricoxib-Loaded NE (ETB-Ne)
\[\text{PS}=+176.16+8.35\text{A}\,-20.34\text{B}+0.2125\text{C}+5.25\text{AB}\,- 4.00\text{AC}+2.58\text{BC} \tag{3}\]  
Figure 1a shows the contour plot for data of particle size. It was observed that the iso-value curves of the contour plot show more changes on increasing the S\({}_{\text{mix}}\) percentage. This result was in concurrence with the inference from the polynomial equation. Further, the elevation of the response surface was more towards the axis of oil percentage and less towards the axis of S\({}_{\text{mix}}\) percentage (Figure 1b). The individual effects of the factors (Figure 1c) also confirmed that higher values for oil percentage increase PS and higher values for S\({}_{\text{mix}}\) percentage decrease PS. It was also observed that the water percentage did not influence the PS of NE. The predicted versus actual plot shown in Figure 1d shows a good prediction power of the design model. In the case of PDI, a quadratic response surface model was suggested by the software and the model was significant with a \(p\)-value \(<0.0001\). The lack of fit was not significant, and thus the model was acceptable for further use in optimization. The predicted and adjusted R-squared values of 0.9453 and 0.9700, respectively, were in reasonable agreement. Further, the observed and fitted values for the PDI were in good agreement with each other (Table 3). Figure 1: Results of analysis of data of particle size; (**a**) contour plot, (**b**) response surface plot, (**c**) individual factor effects, and (**d**) predicted versus actual plot. The analysis of variance (ANOVA) data of the model for PDI is provided in Table 5. From the data, it was seen that oil percentage, S\({}_{\text{mix}}\) percentage, water percentage, A\({}^{2}\), B\({}^{2}\), and C\({}^{2}\) were significant terms influencing the PDI value. The polynomial equation suggested by the software for PDI is provided in Equation (4). The equation revealed that the influence of independent factors on the PDI was in the order oil percentage \(>\) S\({}_{\text{mix}}\) percentage \(>\)water percentage. The significant effects of A\({}^{2}\), B\({}^{2}\), and C\({}^{2}\) have contributed towards the fitting of the PDI data to a quadratic polynomial equation. PDI = +0.3565 + 0.0715A - 0.0441B - 0.0314C + 0.0030 AB + 0.0265 AC + 0.0468 BC + 0.1289A\({}^{2}\) + 0.0926B\({}^{2}\) + 0.0996C\({}^{2}\)  
The influence of the independent factors is presented in Figure 2. The contour (Figure 2a) and response surface (Figure 2b) plots demonstrate data fitting a quadratic polynomial equation. The iso-value curves are circular in the contour plot and the response surface has a depression towards the middle of the plot. These results indicated that the PDI value decreases towards the mid-value of the selected range of percentage of oil, S\({}_{\text{mix}}\), and water. This was further confirmed by the individual effect plots for the independent factors and is shown in Figure 2c. Further, the predicted and actual values were in a good linear relationship as observed in the plot shown in Figure 2d, and confirmed a high degree of prediction ability of the selected quadratic response surface model. \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 & 0.2164 & 9 & 0.0240 & 54.91 & \(<\)0.0001 & significant \\ \hline A—Oil & 0.0409 & 1 & 0.0409 & 93.40 & \(<\)0.0001 & - \\ Percentage & 0.0156 & 1 & 0.0156 & 35.57 & 0.0010 & - \\ \hline C—Water & 0.0079 & 1 & 0.0079 & 17.98 & 0.0054 & - \\ Percentage & 0.0000 & 1 & 0.0000 & 0.0822 & 0.7840 & - \\ \hline AC & 0.0028 & 1 & 0.0028 & 6.42 & 0.0445 & - \\ \hline BC & 0.0087 & 1 & 0.0087 & 19.97 & 0.0042 & - \\ \hline A\({}^{2}\) & 0.0664 The optimized formula and the predicted responses are shown in Figure 3. Minimum values for PS and PDI were set as the goal for numerical optimization. The desirability was 1 for the suggested formula with 11.5% oil, 38% S\({}_{\text{mix}}\), and 50% water.