## 4 Discussion
However, the response \(y_{\text{D}}\) of their datasets did not violate the normality assumption, as determined by the Kolmogorov-Smirnov method in our study. The implementation of remedial measures for heteroscedasticity in regression analysis includes transforming the dependent variable, such as log transformation, log(\(y\)); square root, (\(y^{0.5}\)), and Box-Cox transformation; using weighted least squares (WLS); considering segmenting the data; and using generalized least squares (GLS) [51; 52; 53]. Influential data points are usually found in the datasets of the examined literature. These data points may be the source of experimental error or indicate the need for further study of other forms of RSM models. The treatment of influential points in regression analysis involves identifying whether these points are due to a pure data entry error or a valid data point that is an extreme value [54; 55]. If an influential point is due to a mistake (e.g., experimental error or sampling error), it can be corrected or removed. Valid data points with extreme values can be transformed to reduce their influence, or robust regression can be used [54; 55]. [PERSON] et al. [3] reported the integration of computer technology in RSM. They described the high-performance computing used to calculate the models and visualize the results, which helped the researchers understand the relationships between influencing variables and responses. Graphical visualization helped the researchers interpret results and make decisions [3]. However, the effect of adequate RSM models on graphical visualization was not considered. The challenges of RSM include limitations in modeling nonlinear systems, sensitivity to experimental error, model interpretability, and model validation [3]. The nonlinear systems of an RSM experiment can be evaluated with nonlinear regression. The criteria for evaluating linear regression can also be applied to a nonlinear system. Some advanced modeling techniques, such as machine learning, neural networks, and support vector machines, can be applied and incorporated into the regression analysis technique. The experimental error can be further studied and quantified by checking the criteria of influential data points. The model's interpretability problems can be addressed by incorporating the criteria of regression analysis. The PRESS criterion introduced in this study can be used as the model validation criterion to assess the predictive ability of other RSM models. Sample size is an essential criterion for ensuring the power of statistical techniques. Researchers have proposed simple sample size equations to evaluate the required sample size (\(n\)) for multiple regression models. These criteria can be applied in the calculation of RSM models. [PERSON] [56] proposed this equation: \(n\geq 2p+20\). [PERSON]'s equation is \(n\geq 8p+50\)[57]. The calculation equation used by [PERSON] and [PERSON] is \(n\geq 5p+20\)[58]. In these equations, \(n\) is the required number of samples, and \(p\) is the number of parameters in the RSM models. With these equations, the sampling numbers are not great enough for the RSM equations in most studied. The solution method is to increase the replicates at each run. The study used sixteen published studies to evaluate the adequacy of the RSM equation. The 16 papers used in this study employed the following commercial regression analysis software: Design Expert (10 papers), Minitab (2 papers), and MOODE (1 paper). Three papers did not report the software used. The three commercial software packages provide detailed analyses of regression calculations, including regression coefficients, \(t\)-values, and ANOVA tables. However, most users struggle to utilize the calculation results of these programs. Ten papers, accounting for 62.5% of the total literature analyzed, utilized Design Expert software. However, only one study [28] reported the appropriate equation.