## 2 Materials and Methods
### Establishment of the Model  
Once the regression equation is established, contour and 3D surface plots can be generated using commercial software programs, allowing researchers to easily visualize the optimization using these figures. Suppose the selection of the regression equation is inappropriate. In that case, these contour and 3D surface plots are inappropriate, so the conclusions and suggestions regarding the effect of the dependent variable (factors and levels) are meaningless.  
Three methods for performing sequential variable selection are forward selection, stepwise regression, and backward elimination. These methods are illustrated in detail [17; 18; 39; 40; 41; 42; 43; 47].  
For the forward selection procedure, all variables are selected as regressors and enter the model with a constant term. The variable that produces the largest R-squared value is selected first, and the resulting equation is referred to as the first equation. The other variables are considered as the second variable of the first equation. The variable that produces the largest R-squared value in the second analysis is selected as the second variable. The selection of variables continues in this way. For each procedure, the \(p\)-value of the selected variable is compared with the preset value. If the \(p\)-value of the selected variable is greater than the preset value, the procedure ends.  
Stepwise regression is an improvement on forward selection. Variables that were deleted in the previous stage can be re-entered in the selection procedure. The selection procedure is the same as forward regression.  
Backward elimination procedures are used to fit all variables for the regression equation and determine the \(p\)-value for each variable in the model. The variable with the lowest observed \(t\)-value and its corresponding \(p\)-value are compared with a preselected significance level, usually \(p<0.05\). If its \(p\)-value exceeds the preselected value, the variable is removed. The remaining variables are recalculated, and the variable with the lowest \(t\)-value and \(p\)-value is identified to compare its \(p\)-value with a value of \(p<0.05\). The above backward elimination procedures are repeated until no variable is dropped, and the procedure ends. The selection of the regression model consists of all remaining variables.  
The problem with forward and stepwise methods is that the critical \(t\)-values they set are not appropriate in the early stages [17]. Since there are fewer variables in the early stages, the standard values of the estimates are usually overestimated, and the \(p\)-values of the variables may be too significant, thus preventing important variables from entering the model. Therefore, forward and stepwise models often underestimate. [PERSON] and [PERSON] [42] recommend the use of backward elimination because this method can select all possible explanatory variables as early as possible and eliminate those that are not important in explaining the response variation. Backward elimination is recommended because it considers the effects of all candidate variables [41; 43; 48].  
In the backward elimination procedure, a \(t\)-test statistic for a variable is used to calculate its \(p\)-value, which is then used to assess the statistical interpretation of the variable in the regression model [14; 48].