## 2 Materials and Methods
### The Criteria for the Evaluation of RSM Equations  
1. R-squared The R\({}^{2}\) value is called the coefficient of determination. An R\({}^{2}\) value near 1.0 shows that the equation is very good at determining the relationship between the response and the independent variables. 2. Adjustable R\({}^{2}\) The adjusted R\({}^{2}\) considers the effect of the number of independent variables. Like R\({}^{2}\), an R\({}^{2}\)\({}_{\rm adj}\) value closer to 1.0 indicates a regression equation's good descriptive ability. 3. Standard error of the estimated value, s The s value indicates the actual variability in the equation with the data distribution between the response and independent variables. 4. t-value The t-value of the variables is called the t-statistic. It is used to test the null hypothesis that the coefficients of independent variables are zero. A large t-value of the independent variable reveals that the coefficient is not zero and is valid. That is, the variable is effective. 5. _p_-value The _p_-value of a variable coefficient is calculated from its t-value. The _p_-value serves as the probability of being incorrect to determine whether the variable coefficient is not zero. A smaller _p_-value represents a greater probability of the validity of the variable. 6. PRESS, the Predicted Residual Error Sum of Squares This statistic is used to evaluate the predictive ability of the regression model. The calculation of PRESS is explained as follows: To calculate the PRESS value of a regression model, for n samples, the first dataset (y\({}_{1}\)) is removed, and the remaining n-1 datasets are used to calculate the regression equation. Then the first data point is substituted into this equation to find the predictive value \(\hat{y}_{1,-1}\). The predictive error is called the first PRESS residual. In other words, the predictive error for dataset 1 is \(e_{-1,-1}\). The next step is to take out the second dataset, 2, and return the data x\({}_{1}\) to this dataset. The second regression equation is computed with datasets without the dataset y\({}_{2}\). The y\({}_{2}\) dataset is substituted in Equation (2) to calculate the predictive value, and the predictive error for dataset 2 is \(e_{2,-2}\) The procedure is repeated n times for all data and produces a set of n PRESS residuals (\(e_{1,-1}\), \(e_{2,-2}\), \(\ldots\), \(e_{n,-n}\)). The PRESS statistic is calculated as the sum of the squares of the n PRESS residuals. A lower PRESS value of an RSM equation indicates that this equation has better predictive ability. 7. Normality test The normality test assesses whether the datasets are normally distributed. The regression analysis technique assumes that residuals are normally distributed about the regression line. In this study, the normality test technique used is the Kolmogorov-Smirnov method. The _p_-value calculated with this method is compared with the preset value (_p_ = 0.05). Failure of the normality test reveals the inadequacy of the regression model. 8. Constant variance test This test evaluates the constant variance of the dependent variable (response) in its population source. This study uses the Spearman Rank correlation method, and the _p_-value calculated by this method assesses the assumption of constant variance. The cutoff value is \(p\) = 0.05. The partial F-value or \(p\)-value is used to help the researcher conclude whether a significant effect of the linear, square, and integration term significantly affects the y response. The trick to misusing these methods is to test the linear, interaction, and square terms with the F-value or \(p\)-value.