## 2 Materials and Methods
### The Three Methods of Sequential Variable Selection  
Three methods for performing sequential variable selection are forward selection, stepwise regression, and backward elimination [53; 57; 58; 59; 60; 61; 62].  
1. Forward selection  
In this procedure, all variables are selected as a single regressor with a constant term, and the variable that produces the largest R\({}^{2}\) is selected as the first variable. Then, the other variables are used as candidates for the second variable in terms of the constant and the first variable. The variable of the second term that produces the largest R\({}^{2}\) is selected as the second variable. A similar procedure is used to select the third variable, and then the procedure is continued. The selected variable's partial F-value or \(p\)-value is compared with the preset value. If the t-values of this variable are less than the preselected value, the procedure ends.  
2. Stepwise regression  
This method is a modification of forward selection. Two cutoff values of the partial F-value or \(p\)-value are preset. At each step, the previously selected variables in the equation are reevaluated with their partial F-value or \(p\)-value. If these values for a variable are larger than the cutoff \(p\)-value, the variable is excluded from the equation. In this method, one variable can be entered at each stage, and another can be eliminated.  
3. Backward elimination  
The procedures for backward elimination are as follows:  
1. Fit all variables for the regression equation. Determine the t-value and \(p\)-value for each variable in this model [58].
2. Focus on the variable with the lowest observed t-values and its \(p\)-value.
3. Compare the \(p\)-value with a preselected significance level, usually \(p<0.05\).
4. Remove the variable if its \(p\)-value exceeds the preselected value [58].
5. Recompute the regression equation for the remaining variables and find the variable with the lowest t-value and highest \(p\)-value.
6. Repeat the backward elimination procedures of c, d, and e.
7. If no variable is dropped, the procedure ends. The regression model's selection consists of all remaining variables.
8. Perform the influential data point test, and the normality and constant variance tests.  
Theoretically, the final regression models of the above three procedures--forward selection, stepwise regression, and backward elimination--should be the same. However, the selected levels of significance and the collinearity among these variables influence the selection of model variables for forward and stepwise procedures.  
The disadvantage of the forward procedure is that the critical t-values are not strictly appropriate in the early stages [53]. The backward elimination procedure is recommended because this technique selects all possible explanatory variables and eliminates those of little importance to explain the variation in response y step by step [57; 61; 62; 63].  
The special feature of the RSM model is its multicollinearity. These derived variables of square variables and the interaction of variables, such as x\({}_{1}\)\({}^{2}\), x\({}_{2}\)\({}^{2}\), x\({}_{3}\)\({}^{2}\), x\({}_{1}\)x\({}_{2}\), x\({}_{1}\)x\({}_{3}\), and x\({}_{2}\)x\({}_{3}\), are prone to multicollinearity problems [56; 61; 63]. [PERSON] [64] emphasized that backward elimination is particularly useful in the collinearity problem.  
In this study, a \(t\)-test statistic is used to assess the statistical interpretation of a variable in the regression model. A detailed explanation of this procedure has been introduced [6; 63].