## 3 Results
### Nanomaterials
Further analysis needs to be performed. [PERSON] and [PERSON] [33] reported optimizing the catalytic performance of synthesized catalysts for the methanol-to-olefin reaction. The BBD experimental design was used. Figure 3: Contour plots of the complete and adequate equations for the average fiber diameter response. The contours present the effect of using the RSM equation on the relationship between the response variables and the influencing variables. (**a**) Full equation. (**b**) Adequate equation. There were three variables: \(x_{1}\), the MW aging time; \(x_{2}\), the US aging time; and \(x_{3}\), the HT time. Two responses are _the yield of ethylene and_ the yield of propylene. Two ANOVA tables for \(y_{ethylene}\) and \(y_{propylene}\) are presented in the literature. For the ethylene yield, \(p\)-values of all variables are \(<\)0.05. The full equation is an adequate representation of the ethylene yield. The R\({}^{2}\) value of ethylene is very close to 1.0 (R\({}^{2}\) = 0.9995). In the ANOVA table of the propylene yield \(y_{propylene}\), the \(p\)-values of \(x_{2}x_{3}\) and \(x_{3}\)\({}^{2}\) were \(>\)0.05. The two variables did not have a significant effect on response \(y_{propylene}\). However, the authors used two full equations to produce the contour and response surface plots [33]. It is inappropriate to use the propylene yield as a measure. The \(x_{3}\) HT time did not have the curved surface condition with \(y_{propylene}\). There are six suspicious data points for \(y_{ethylene}\) and two suspicious data points for \(y_{propylene}\). Further investigation needs to be performed. [PERSON] et al. [34] investigated the factors influencing benzene hydroxylation to phenol using a V/SBA-16 nanoporous catalyst. The CCD was used. The variables were \(x_{1}\), reaction temperature; \(x_{2}\), H\({}_{2}\)O\({}_{2}\) content; and \(x_{3}\), catalyst amount. The response was _the yield of phenol_. In the AVOVA table for response, the \(p\)-value of the \(x_{1}x_{3}\) variable is \(>\)0.05. However, the authors proposed the full equation, which was used to produce the surface plots [34]. The adequate equation, evaluated using complete regression analysis, is \(y_{phenol\;yield}\) = f(\(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{1}\)\({}^{2}\), \(x_{2}\)\({}^{2}\), \(x_{3}\)\({}^{2}\)). The interaction terms (\(x_{1}x_{2}\), \(x_{1}x_{3}\), \(x_{2}x_{3}\)) are excluded in this equation. That is, the full equation is inappropriate. [PERSON] et al. [35] investigated the optimization of deposition variables to synthesize upright ZnO rod arrays with large diameters. There were four influencing factors: \(x_{1}\), the concentration of Zn\({}^{+2}\); \(x_{2}\), reaction temperature; \(x_{3}\), reaction time; and \(x_{4}\), the molar ratio of Zn\({}^{+2}\). The response was \(y_{D}\) diameter. The authors used the logarithm transform for the response. The form of their proposal equation is  
\[\text{Log}\;(y_{D}+0.5)=\text{f}\;(x_{1},x_{2},x_{3},x_{4},x_{3}\text{${}^{2} $},x_{1}x_{2},x_{2}x_{3},x_{2}x_{4},x_{3}x_{4}). \tag{34}\]  
Both tests are passed for the \(y\) response using the normality and constant variance tests, so it is not necessary to transform the response \(y\) into a logarithmic form. The adequate equation calculated by complete regression analysis in our study is  
\[ \begin{split} y_{D}=1.182-57.722x_{1}-0.0289x_{2}+0.288x_{3}+0.00 265x_{4}-0.00822x_{3}\text{${}^{2}$}+0.778x_{1}x_{2}\\ -0.0000299x_{2}x_{4}-0.0000643x_{3}x_{4}\\ R^{2}=0.86,R^{2}_{\text{adj}}=0.797,\text{s}=0.169,\text{ PRESS}=1.18\end{split}  \tag{35}\]  
[PERSON] et al. [36] reported the optimization of nanosized zinc oxide synthesis conditions using electrospinning. Three influencing factors were applied: voltage; \(x_{2}\), distance; and \(x_{3}\), calcination temperature, and the response, \(y\), was zinc oxide. The authors did not propose the empirical equation; instead, surface plots of the curve were presented [36]. The full equation evaluated by complete regression with the datasets in the literature is  
\[