## 3 Results
### Three Variables
#### 3.2.2 Extraction of Bioactive Components from Defatted Marigold Residue  
In Study [36], the influencing factors included \({\rm x_{1}}\), ethanol concentration, \({\rm x_{2}}\), temperature, and \({\rm x_{3}}\), time. Four responses were measured. These were \({\rm y_{TPC}}\), total phenolics (TPC), \({\rm y_{TPC}}\), total flavonoids (TFC), \({\rm y_{ABTS}}\), radical scavenging activity of ABTS, and \({\rm y_{DPPH}}\), radical scavenging activity of DPPH. The fitting models in the study were complete equations [36]. That is, all variables (\({\rm x_{1}}\), \({\rm x_{2}}\), \({\rm x_{3}}\), \({\rm x_{1}}{\rm x_{2}}\), \({\rm x_{1}}{\rm x_{3}}\), \({\rm x_{2}}{\rm x_{3}}\), \({\rm x_{1}}^{2}\), \({\rm x_{2}}^{2}\), \({\rm x_{3}}^{2}\)) were used in their models. The four responses' contour and response surface plots were plotted with these quadratic and interaction terms. The four ANOVA tables of responses that showed the three variables' effect on the responses \begin{table}
\begin{tabular}{c c c c} \hline  & **Estimated Values** & **Standard Error** & \(p\)**-Value** \\ \hline \(b_{0}\) & \(-2.980433\) & \(5.183862\) & \\ \hline \(b_{1}\) & \(0.107709\) & \(0.069684\) & \(0.1445\) \\ \hline \(b_{2}\) & \(-0.174901\) & \(0.309534\) & \(0.5810\) \\ \hline \(b_{3}\) & \(0.071086\) & \(0.037511\) & \(0.0789\) * \\ \hline \(b_{11}\) & \(-0.000427\) & \(0.000157\) & \(0.0168\) ** \\ \hline \(b_{12}\) & \(-0.001111\) & \(0.002924\) & \(0.7098\) \\ \hline \(b_{13}\) & \(-0.000500\) & \(0.000483\) & \(0.2347\) \\ \hline \(b_{22}\) & \(0.004168\) & \(0.009179\) & \(0.6567\) \\ \hline \(b_{23}\) & \(-0.00608\) & \(0.001728\) & \(0.7302\) \\ \hline \(b_{33}\) & \(-0.000135\) & \(0.000115\) & \(0.5745\) \\ \hline \end{tabular} Note.: * \(p<0.1\); **\(p<0.05\).  
\end{table} 
Table 5: Estimated regression coefficients for trypsin inhibitor activity (TIA) of extruded African breadruit–com–soy mixtures (data source: [33]). were presented in the study [36]. The \(p\)-values indicated the insignificance of some variables. With the \(p\)-values, the quadratic terms of some variables had an insignificant effect on the responses. That is, the authors did not utilize the information of \(p\)-values of some variables to evaluate the adequacy of RSM equations. The evaluation steps of the adequacy of RSM equations for the TPC and TFC responses are listed in Supplements S1 and S2. The adequate RSM equations of the four responses are  
\[1.\ \mathrm{y_{TFC}}=-80.381+3.688\mathrm{x_{1}}+0.219\mathrm{x_{1}}^{2} \tag{41}\]  
Only the \(\mathrm{x_{1}}\) variable has a significant effect on the response y. Two influential data points were found. For second data point, \(\mathrm{t_{i}}\) = 4.407, with \(\mathrm{DFFITS_{i}}\) = 5.075. For the 14 th data point, \(\mathrm{t_{i}}\) = \(-2.312\). The PRESS values of the complete and adequate equations are 3476.8 and 2083.706, respectively. The adequate equation has a better predictive ability than the complete equation. \[2.\ \mathrm{y_{TFC}}=-222.966+7.088\mathrm{x_{1}}+2.165\mathrm{x_{2}}-0.0354 \mathrm{x_{1}}^{2}-0.0272\mathrm{x_{1}}\mathrm{x_{2}} \tag{42}\]  
Two influential data points were found. For the second data point, \(\mathrm{t_{i}}\) = 2.562, with \(\mathrm{DFFITS_{i}}\) = 2.151. For the 14 th data point, \(\mathrm{t_{i}}\) = \(-2.198\). The PRESS of the complete and adequate equations was 3073.183 and 1794.138, respectively. \[3.\ \mathrm{y_{ABTS}}=-2.902+0.114\mathrm{x_{1}}+0.0102\mathrm{x_{2}}-0.000735 \mathrm{x_{1}}^{2} \tag{43}\]  
One influential data point was found. For the second run, \(\mathrm{DFFITS_{i}}\) = 2.798. The PRESS of the complete and adequate equation was 3.266 and 1.919, respectively. \[4.\ \mathrm{y_{DPPH}}=-1.254+0.0664\mathrm{x_{1}}+0.00561\mathrm{x_{2}}-0.120 \mathrm{x_{3}}-0.00511\mathrm{x_{1}}^{2}+0.00219\mathrm{x_{1}}\mathrm{x_{3}} \tag{44}\]  
Two influential data points were present. For the 2 nd and 14 th runs, the \(\mathrm{DEFITS_{i}}\) values are 2.266 and \(-2.123\), respectively.