## 3 Results
### Three Variables
#### 3.2.4 The Adequate Equations of the RSM in the Other Literature
 } & Biodiesel & \multirow{4}{*}{\(y_{\text{TM}}\) (biodiesel  yield ) + complete \(x_{2}\): oil ratio \(x_{3}\): catalyst  loading} & \multirow{4}{*}{Curved surface} & \multirow{4}{*}{\(y_{\text{TM}}\) = \(f(x_{2},x_{2})\)} & \multirow{4}{*}{Passed} & \multirow{4}{*}{Passed} & \multirow{4}{*}{no} \\  & & & & & & & \\ \hline \multirow{4}{*}{\ \begin{tabular}{c} [PERSON] et al. [43] \\ \end{tabular}  } & Cryoprotcants & \multirow{4}{*}{\(y_{\text{TAC}}\) = \(f(x_{1},x_{2},x_{3})\) \\  & for direct vat set \\ \cline{1-1}  & starless & & & & & \\ \cline{1-1}  & \(x_{1}\): skin milk & \(y_{\text{TAC}}\) = complete \(y_{\text{TAC}}\) & \multirow{4}{*}{Curved surface} & \multirow{4}{*}{\(y_{\text{TAC}}\) = \(f(x_{1},x_{2},x_{3})\), \(x_{1}{}^{2},x_{3}{}^{2}\)} & \multirow{4}{*}{Passed} & \multirow{4}{*}{Passed} & \multirow{4}{*}{\(2 nd,3 rd,6 th,7 th,11 th} \\ \cline{1-1}  & \(x_{2}\): sucrose & & & & & \\ \cline{1-1}  & \(y_{\text{TAC}}\) - L-proline or  glycerol & \multirow{4}{*}{Curved surface} & \multirow{4}{*}{\(y_{\text{TAC}}\) = \(f(x_{1},x_{2},x_{3})\), \(x_{1}{}^{2},x_{2}{}^{2},x_{3}{}^{2}\)} & \multirow{4}{*}{Passed} & \multirow{4}{*}{Passed} & \multirow{4}{*}{\(2 nd,3 rd,6 th,7 th,10 th,11 th} \\ \cline{1-1}  & \(y_{\text{TAC}}\) = & & & & & \\ \hline \multirow{4}{*}{ \begin{tabular}{c} [PERSON] et al. [44] \\ \end{tabular}  } & Antioxidant & \multirow{4}{*}{\(y_{\text{TAC}}\) = \(y_{\text{TAC}}\) = \(y_{\text{TAC}}\) = \(f(y_{\text{TAC}},y_{2})\), \(y_{\text{TAC}}\) = \(y_{\text{TACan appropriate equation. The influential data points were found for three responses. The normality test was failed for the y\({}_{3}\) response. [PERSON] et al. [41] studied the factors affecting piper nigrum microcapsules with spray drying. The results of ANOVA and the statistics of the model were presented in a table in the study [41]. The F-values and \(p\)-values showed that six variables did not significantly affect the response. However, the complete equation was reported in the study. The results of the modern regression showed that the x\({}_{1}\) term did not have a quadratic form with a response. The constant variance test was failed (\(p=0.644\)). The transformation of y\({}_{\text{EFF}}\) could be performed for the recalculation of the RSM models. [PERSON] et al. [42] reported on optimizing biodiesel production from wastes. The authors proposed complete equations involving all variables and produced curve contour and response surface plots. The regression results of our study showed that only the x\({}_{2}\) variable affected the response. Two variables, x\({}_{1}\) and x\({}_{3}\), did not significantly influence the response. In a study of cryoprotectants for direct vat set starters in Sichuan paocai, [PERSON] et al. [43] used RSM to determine the optimization. The two responses were y\({}_{\text{SICC}}\) (_L. plantarum_ SICC) and y\({}_{\text{Y61}}\) (_B. subtilis_ Y61). The ANOVA table and the \(p\)-values for each coefficient were listed in the study [43]. The \(p\)-values of some parameters indicated an insignificant effect on the response. However, the complete models were proposed and used to produce a curved relationship for contour and response surface plots. The results of modern regression analysis indicated that the influence factors for y\({}_{\text{SICC}}\) were x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), x\({}_{2}\)x\({}_{3}\), x\({}_{1}\)\({}^{2}\), and x\({}_{3}\)\({}^{2}\). The variable x\({}_{2}\) only has a linear relationship with y\({}_{\text{SICC}}\). Influence factors for y\({}_{\text{Y61}}\) were x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), x\({}_{2}\)x\({}_{3}\), x\({}_{1}\)\({}^{2}\), x\({}_{2}\)\({}^{2}\), and x\({}_{3}\)\({}^{2}\). There was no interaction effect on y\({}_{\text{Y61}}\) for the x\({}_{1}\)x\({}_{2}\) and x\({}_{1}\)x\({}_{3}\) terms. [PERSON] and [PERSON] [44] reported the optimization of antioxidants and cellulose from walnut husks. The reported y\({}_{\text{TAC}}\) equation was a complete model.