## 4 Discussion  
This study collected 16 papers related to the application of RSM models in three engineering fields. This literature dataset was used to evaluate the adequacy of RSM equations. The evaluation of the adequate RSM model was completed through a complete regression analysis. This analysis calculated the coefficients for all variables, tested the significant effect of each variable, verified the assumptions, and identified influential data points in the regression analysis. It was found that only one paper reported an equation that could fully and correctly express the relationship between the response and the influencing factors [28]. The common issues with the application of RSM in three engineering fields, as identified in the study, are listed in Table 7.  
Most papers adopted the full model and then used it to create contour plots and 3D response surface plots, allowing for the observation of the optimization of these variables. In the literature, ANOVA tables typically include the coefficient value of variable parameters, the \(t\)-value, and the \(p\)-value for each variable. However, this information was not used by some researchers [24; 25; 26; 27; 30; 32; 33; 34; 38] to evaluate the adequacy of equations. One study did not report the RSM model [36]. The contour and response surface plots were produced with the full equation. One study completely deleted unwanted variables after the first regression calculation [29]. When the ANOVA table of regression results indicated that the \(p\)-values of some variables were greater than 0.05, these variables were deleted simultaneously [29]. The equation was proposed using the coefficient values of the remaining variables. However, the full equations were still used to yield the contour and response surface plots for this study [29]. This method is unreasonable for model building. Two studies employed sequential models to investigate the significant effects of linear, interaction, and quadratic terms on the response [31; 37]. The \(p\)-values of some combinations (linear + interaction, linear + square terms) indicated that these combinations did not \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Issue** & **Literature** \\ \hline
1. & The full model was used to generate contour plots and three-dimensional response surface plots, which were then used to optimize these variables. However, the coefficient values, \(t\)-values, and \(p\)-values for each variable in the ANOVA table were not used. \\
2. & The contour plots and three-dimensional response surface plots with the full equation were proposed, but the RSM model was not reported. \\
3. & All variables with \(p\)-values higher than the preselected value (usually \(p<0.05\)) were deleted at once. \\
4. & The ANOVA table of the sequential model was used and all variables were included in the linear or squared term directly, without conducting significance testing for each variable. \\
5. & Datasets did not pass the normality test. \\
6. & Datasets did not pass the constant variance test. \\
7. & Influential data points were found. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Common issues with the applications of RSM in the literature. significantly affect the response. However, full equations were still used to produce contour and response surface plots. If the RSM models are not full equations, the curved contour and 3D surface response plots produced using the full equations are inappropriate. The performance of the optimization conditions of these variables by these plots is meaningless. Some datasets failed the normality test [25; 27; 29], and others failed the constant variance test [25; 37; 38]. These datasets need to be transformed to align with the assumptions of regression analysis. [PERSON] et al. [50] emphasized that departures from the homogenous assumption will induce seriously incorrect results and require remedying this violation. [PERSON] et al. [35] used the logarithmic transformation of the response to perform the regression analysis.