## 3 Results
### Semiconductor Manufacturing
\begin{split}\text{y}_{SR}=1.988+0.501x_{1}-0.0440x_{2}-0.172x_{3 }+0.235{x_{1}}^{2}+0.0101{x_{2}}^{2}\\ (<0.001)\ (0.464)\ (0.027)\ (0.084)\ (0.931)\\ +0.223{x_{3}}^{2}+0.0711x_{1}x_{2}-0.128x_{1}x_{2}+0.00125x_{2}x_{3} \\ (0.098)\ (0.302)\ (0.095)\ (0.985)\\ R^{2}=0.958,\ \text{R}^{2}_{\text{adj}}=0.882,\ \text{s}=0.172, \ \text{PRESS = 1.299}\end{split}  \tag{11}\] \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multirow{2}{*}{**Source**} & **Reported Equations** & **Contour Response Plot** & **Adequate Equations** & **Normality Test** & **Constant Variance Test** & **Influential Data** \\ \hline [PERSON] et al. [23] & Not reported & Curve surface & \(\text{y}_{\text{SR}}=\text{f}(x_{1},\,x_{3},\,x_{1}x_{3},\,x_{1}^{2},\) \(x_{3}^{2})\) & Passed & Passed & 2, 15 \\ \hline [PERSON] et al. [24] & Full models & Curve surface & \(\text{y}_{\text{SR}}=\text{f}(x_{1},\,x_{2},\,x_{3},\,x_{1}x_{3},\) \(x_{2}^{2},\,x_{3}^{2})\) & Passed & Passed & 4, 6, 7, 12 \\ \[PERSON] et al. [25] & Full models & Curve surface & \(\text{y}_{\text{VHT}}=\text{f}(x_{1},\,x_{2},\,x_{3},\,x_{1}x_{2},\) \(x_{2}^{2},\,x_{3}^{2})\) & Passed & Passed & 5, 13, 17 \\  & & & \(\text{y}_{\text{VHT}}=\text{f}(x_{1},\,x_{2},\,x_{3},\,x_{1}x_{2},\) \(x_{2}^{2},\,x_{3}^{2},\) \(x_{1}^{2},\,x_{3}^{2},\) \(x_{1}x_{2})\) & Failed & Passed & 13 \\ \hline [PERSON] et al. [26] & \(\text{y}_{\text{W}}=\text{full}\) model & Curve surface & \(\text{y}_{\text{W}}=\text{f}(x_{2})\) & Passed & Passed & 12, 14 \\  & \(\text{y}_{\text{Oside}}=\text{full}\) model & & \(\text{y}_{\text{Oside}}=\text{(}x_{1},\,x_{3})\) & Passed & Passed & no \\ \hline [PERSON] and [PERSON] [27] & Full model & Curve surface & \(\text{y}_{\text{VV}}=\text{f}(x_{1},\,x_{2},\,x_{3},\,x_{4},\) \(x_{1}x_{3},\,x_{3}^{2})\) & Failed & Passed & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the evaluation of adequate RSM equations for semiconductor manufacturing. The adequate equation was evaluated with the regression technique of backward elimination:  
\[ \begin{split}\text{y}_{\text{SR}}=1.991+0.501x_{1}-0.172x_{3}+0.238{x _{1}}^{2}+0.225{x_{3}}^{2}-0.128x_{1}x_{2}\\ (<\!0.001)\;(0.007)\;(0.030)\;(0.037)\;(0.044)\\ R^{2}=0.941,\text{R}^{2}_{\text{adj}}=0.909,\text{s}=0.154,\text{ PRESS}=0.646\end{split}  \tag{12}\]  
The normality and constant variance tests are passed. Two influential data points are found, the 7 th and 15 th data points. In this study [23], the authors used the full equation to produce the curved surface plots. However, the adequate equation indicated that the \(x_{2}\) variable (platen speed) did not significantly affect the response, surface roughness. With the complete regression technique, the adequate RSM equation could help researchers to find the optimal condition. Figure 1 indicates the contour plots for the complete and adequate equations. The difference between the two equations resulted in a difference in the distribution of curves between the two figures. The contour and response surface plots produced with the full equation were presented in the study [23]. The incorrect RSM equation could induce incorrect results of observation. [PERSON] et al. [24] investigated the polishing factors affecting surface roughness using a Box-Behnken design. The polishing factors were \(x_{1}\), pressure; \(x_{2}\), wheel speed; and \(x_{3}\), process time. The authors proposed the full equation as the best equation and found that the \(R^{2}\) was 0.974 for this equation. This full equation produced contour and response surface plots. The full equation proposed by the authors is  
\[ \begin{split}\text{y}_{\text{SR}}=9.465-24.850x_{1}-0.163x_{2}-0.2 78x_{3}+46.375{x_{1}}^{2}+0.00309{x_{2}}^{2}\\ (<\!0.001)\;(0.006)\;(0.011)\;(0.001)\;(0.008)\\ +0.00815{x_{3}}^{2}-0.0325{x_{1}}{x_{2}}+0.425{x_{1}}{x_{3}}+0.00 0150x_{2}x_{3}\\ (0.038)\;(0.661)\;(0.029)\;(0.919)\\ \text{R}^{2}=0.974,\text{R}^{2}_{\text{adj}}=0.928,\text{s}=0.140, \text{PRESS}=1.559\end{split}