## 3 Results
### Two Variables
#### 3.1.2 Compressive Strength of Rubberized Concrete  
In Study [30], the experimental design was a CCD with 13 runs. The influencing factors included x\({}_{1}\) BCBP in %, and x\({}_{2}\) WTR in %. The two responses are \(y_{\rm 7D}\) (7-day compressive strength) and \(y_{\rm 2 BD}\) (28-day compressive strength). The reported RSM equations for y\({}_{1}\) and y\({}_{2}\) are the complete equation; the independent variables involved are x\({}_{1}\), x\({}_{2}\), x\({}_{1}\)\({}^{2}\), x\({}_{2}\)\({}^{2}\), and x\({}_{1}\)x\({}_{2}\)[30]. In the study, the contour and response surface plots of 7-day and 28-day compressive strength are curved distributions. The ANOVA table in the study for 7-day results showed that the \(p\)-values of x\({}_{1}\)\({}^{2}\) and x\({}_{1}\)x\({}_{2}\) were higher than \(p\) < 0.05. The ANOVA table for 28-day results indicated that the \(p\)-values of the x\({}_{1}\), x\({}_{1}\)x\({}_{2}\), x\({}_{1}\)\({}^{2}\), and x\({}_{2}\)\({}^{2}\) variables were higher than the  
Figure 1: The contour plots for the complete and adequate equations of the yORAC response. The difference in the contour curves indicates the effect of the RSM equation on the relationship between response and influential variables. (**a**). Complete equation. (**b**). Adequate equation. cutoff value (\(p<0.05\)). Despite the higher \(p\)-value indicated in the ANOVA table presented in the study, the complete equations are still selected and used to produce contour and response surface plots [30]. The procedure to evaluate the adequate equation of the y\({}_{1}\) response (7-day compression) is listed as follows:  
\[1.\ \mathrm{y}_{7\mathrm{D}}=25.310+0.458\mathrm{x}_{1}+0.130\mathrm{x}_{2}-0. 0183\mathrm{x}_{1}^{2}-0.0272\mathrm{x}_{2}^{2}-0.00401\mathrm{x}_{1}\mathrm{x }_{2} \tag{25}\]  
\[\mathrm{(1.267)}\ \ \ \mathrm{(1.437)}\ \ \ \mathrm{(-0.287)}\ \ \ \mathrm{(-6.834)}\ \ \ \mathrm{(-0.303)}\]  
\[\mathrm{R}^{2}=0.979,\ \mathrm{R}^{2}_{\mathrm{adj}}=0.964,\ \mathrm{s}=0.664,\ \mathrm{PRESS}=12.070\]  
The normality test is passed (\(p=0.522\)), and the constant variance test is passed (\(p=0.220\)). The x\({}_{1}\)\({}^{2}\) variable had the smallest t-value, and its \(p\)-value was higher than the cutoff value (\(p<0.05\)). The variable was deleted. The results of the recalculation are  
\[2.\ \mathrm{y}_{7\mathrm{D}}=25.352+0.549\mathrm{x}_{1}+0.121\mathrm{x}_{2}-0. 0268\mathrm{x}_{1}^{2}-0.00401\mathrm{x}_{1}\mathrm{x}_{2} \tag{26}\]  
\[\mathrm{(3.417)}\ \ \ \mathrm{(1.512)}\ \ \ \mathrm{(-7.730)}\ \ \ \mathrm{(-0.322)}\]  
\[\mathrm{R}^{2}=0.978,\ \mathrm{R}^{2}_{\mathrm{adj}}=0.968,\ \mathrm{s}=0.623,\ \mathrm{PRESS}=7.751\]  
The x\({}_{1}\)x\({}_{2}\) variable had the smallest t-value, and its \(p\)-value was larger than the cutoff value (\(p<0.05\)). The variable was deleted. The new equation is  
\[3.\ \mathrm{y}_{7\mathrm{D}}=25.452+0.509\mathrm{x}_{1}+0.111\mathrm{x}_{2}-0. 0268\mathrm{x}_{1}^{2} \tag{27}\]  
\[\mathrm{(5.277)}\ \ \ \mathrm{(1.586)}\ \ \ \mathrm{(-8.147)}\]  
\[\mathrm{R}^{2}=0.978,\ \mathrm{R}^{2}_{\mathrm{adj}}=0.971,\ \mathrm{s}=0.591,\ \mathrm{PRESS}=5.636\]  
The normality test is passed (\(p=0.652\)), and the constant variance test is passed (\(p=0.236\)). No influential data point was found. The adequate equation showed that x\({}_{1}\) has a curvilinear relationship with the response, and the quadratic equation x\({}_{2}\) variable has a linear relationship with response y\({}_{7\mathrm{D}}\). Compared with PRESS, the predictive ability of the adequate equation (PRESS = 5.636) is significantly improved over that of the complete equation (PRESS = 12.070). Figure 2 shows the contour plots produced with complete or adequate equations. The distribution of each figure presents different results. When researchers use visual methods to conduct their experiments and observe the variables' effect on the response, inadequate RSM equations will induce incorrect conclusions.