## 3 Results
### Nanomaterials  
The results of evaluating adequate RSM equations for nanomaterials are presented in Table 6.  
[PERSON] et al. [37] investigated the effect of processing parameters on the aerosol filter of poly nanofiber mats. A three-factorial BBD was used. The variables were \(x_{1}\) concentration; \(x_{2}\), rotation speed; and \(x_{3}\), needle size. The response \(y_{A/\ell}\) was the average fiber diameter. The statistical results of the sequential models showed that the \(p\)-value of the quadratic term was \(<\)0.05. The ANOVA table in this study [37] indicated that the \(p\)-values of \(x_{1}x_{2}\), \(x_{1}x_{3}\), and \(x_{2}\) were \(>\)0.05. That is, these variables did not have a significant effect on the response. However, the full equation was proposed and used to produce the contour and surface response plots [37]. The calculation of the adequate equation with the datasets in the literature is presented in Appendix A.4. The form of this adequate equation is  
\[ \begin{split} y_{\text{Afd}}=277.462+60.375x_{1}+17.001x_{2}+15.8 75x_{3}-42.058{x_{1}}^{2}+34.442{x_{3}}^{2}\\ +17.501x_{1}x_{2}\end{split}  \tag{33}\]  
The variable \({x_{2}}^{2}\) is excluded. That is, there is no quadratic relationship between \({x_{2}}^{2}\) and the response. An adequate equation has a similar accuracy performance to that of a full equation. However, it has a better predictive ability (PRESS = 675.548) than the full equation (PRESS = 1,113,520). Figure 3 reveals the contour plots for the complete and adequate equations. The difference in the equations induces a difference in the distribution of curves between the two figures. The contour and response surface plots produced with the full equation are \begin{table}
\begin{tabular}{p{45.5 pt} p{45.5 pt} p{45.5 pt} p{45.5 pt} p{45.5 pt} p{45.5 pt} p{45.5 pt}} \hline \hline
**Source** & **Reported** & **Contour** & **Acquate** & **Normality** & **Constant Variance** & **Influential Data** \\  & **Equations** & **Response Plot** & & **Test** & **Test** & **Data** \\ \hline Pakolpakcil & Full model & Curve surface & \(y_{\text{Afd}}=\text{f}(x_{1},x_{2},x_{3},x_{1}^{2},x_{3}^{2})\) & Passed & Failed & 12 \\ \hline [PERSON] and [PERSON] [33] & Full model & Curve surface & \(y_{\text{Ethylene}}=\text{full}\) model & Passed & Passed & \(3,5,8,9,11\) \\  & & surface & \(y_{\text{Propylene}}=\text{f}(x_{1},x_{2},x_{3},x_{1}x_{2}^{2},x_{2}^{2})\) & Passed & Passed & 9 \\ \hline [PERSON] et al. [34] & Full model & Curve surface & \(y_{\text{phenol yield}}=\text{f}(x_{1},x_{2},x_{3},x_{4},x_{2}x_{3},x_{4}^{2})\) & Passed & Passed & 9 \\ \[PERSON] et al. [35] & \(\text{log}\ (y_{D}+0.5)\) & \(=\text{f}(x_{1},x_{2},x_{3},x_{4},x_{4},x_{1}x_{2},x_{2}x_{3},x_{2}x_{4},x_{3}x_{ 2}x_{4},x_{3}x_{4},x_{3}x_{4},x_{3}x_{4},x_{3}x_{2}^{2})\) & \(\text{Y}_{\text{D}}=\text{f}(x_{1},x_{2},x_{3},x_{4},x_{4},x_{1}x_{2},x_{2}x_{ 4},x_{3}x_{4},x_{3}x_{4},x_{3}x_{2}^{2})\) & Passed & Passed & None \\ \[PERSON] et al. [36] & Not reported & Curve surface & \(y_{\text{Zine oxide}}=\text{f}(x_{2},x_{3})\) & Passed & Passed & 6, 14 \\ \[PERSON] et al. [38] & Full models for & Curve surface & \(Y_{\text{nth}}=\text{f}(x_{1},x_{2},x_{4})\) & Passed & Passed & 18 \\  & & Curve surface & \(y_{\text{nle}}=\text{f}(x_{1},x_{2},x_{3},x_{4})\) & Passed & Passed & 7, 24, 25 \\  & & Surface surface & \(x_{4},x_{2}x_{3},x_{2}x_{4})\) & Passed & Passed & 3, 25 \\  & & Curve surface & \(y_{\text{nex,ch}}=\text{f}(x_{1},x_{2},x_{3},x_{4})\) & Passed & & 3, 25 \\  & & Curve surface & \(y_{\text{nex,cle}}=\text{f}(x_{1},x_{2},x_{3},x_{4})\) & Passed & & & \\  & & Curve surface & \(x_{3},x_{4},x_{1}x_{3},x_{2}x_{3},x_{2}x_{3},x_{2}^{2})\) & Passed & Failed & 3, 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the evaluation of adequate RSM equations for nanomaterials. presented in the study [37]. An inadequate RSM equation can lead to incorrect observation results. The normality test is passed. However, the constant variance test is failed. One suspicious data point (12 th) is found.