## 3 Response Models
### Model Fitting  
Statistical regression models were fitted to the data for each CCD: Full, Fractioned A, Fractioned B and Small (Table 2). Design-Expert software (Stat-Ease, Inc., Minneapolis, MN \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **D-Flow** & **T-Funnel** & **F24h** & **Rc,24h** \\  & **[mm]** & **[s]** & **[MPa]** & **[MPa]** \\ \hline \hline \multicolumn{5}{c}{Fractionated B CCD} \\ \hline Min & 339.50 & 13.56 & 11.03 & 59.31 \\ Max & 348.00 & 14.74 & 12.08 & 62.17 \\ Average & 342.92 & 14.27 & 11.55 & 60.36 \\ Std Dev & 3.46 & 0.41 & 0.48 & 1.04 \\ CV (\%) & 1.01\% & 2.84\% & 4.17\% & 1.72\% \\ \hline \hline \multicolumn{5}{c}{Fractionated B CCD} \\ \hline Min & 168.00 & 6.94 & 9.43 & 48.92 \\ Max & 398.00 & 79.63 & 12.11 & 78.42 \\ Average & 322.42 & 19.59 & 11.08 & 61.58 \\ Std Dev & 53.42 & 17.55 & 2.82 & 6.26 \\ CV (\%) & 16.57\% & 89.59\% & 25.49\% & 10.17\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary statistics for Fractionated B CCD. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **D-Flow** & **T-Funnel** & **F24h** & **Rc,24h** \\  & **[mm]** & **[s]** & **[MPa]** & **[MPa]** \\ \hline \hline \multicolumn{5}{c}{Small Ci points} \\ \hline Min & 339.50 & 13.77 & 11.28 & 59.31 \\ Max & 348.00 & 14.98 & 12.29 & 62.10 \\ Average & 343.90 & 14.43 & 11.88 & 60.44 \\ Std Dev & 4.08 & 0.48 & 0.38 & 1.09 \\ CV (\%) & 1.19\% & 3.33\% & 3.22\% & 1.80\% \\ \hline \hline \multicolumn{5}{c}{Small CCD} \\ \hline Min & 168.00 & 6.91 & 9.43 & 48.92 \\ Max & 398.00 & 79.63 & 12.79 & 78.42 \\ Average & 322.71 & 21.37 & 11.19 & 61.27 \\ Std Dev & 56.15 & 19.11 & 3.15 & 6.20 \\ CV (\%) & 17.40\% & 89.43\% & 28.16\% & 10.11\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary statistics for Small CCD. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **D-Flow** & **T-Funnel** & **F24h** & **Rc,24h** \\  & **[mm]** & **[s]** & **[MPa]** & **[MPa]** \\ \hline \hline \multicolumn{5}{c}{Fractionated A Ci points} \\ \hline Min & 339.50 & 13.77 & 11.28 & 59.31 \\ Max & 348.00 & 14.98 & 12.29 & 62.17 \\ Average & 343.42 & 14.425 & 11.88 & 60.73 \\ Std Dev & 3.84 & 0.43 & 0.34 & 1.20 \\ CV (\%) & 1.12\% & 2.98\% & 2.88\% & 1.98\% \\ \hline \hline \multicolumn{5}{c}{Fractionated A CCD} \\ \hline Min & 168.00 & 6.91 & 9.43 & 48.92 \\ Max & 398.00 & 114.06 & 12.79 & 78.42 \\ Average & 321.66 & 23.69 & 11.27 & 61.58 \\ Std Dev & 53.11 & 24.15 & 2.88 & 6.18 \\ CV (\%) & 16.51\% & 101.92\% & 25.59\% & 10.04\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary statistics for Fractionated A CCD. 55413-2561, USA--Design-Expert(r) Software, version 13.0.9.0 64-bit; Serial Number 0964-0841-3719-3394) was used to interpret the model graphically, fit an operating regression analysis and ANOVA, support the analyses of the results for each response variable by examining the summary plots of the data, and validate the model by checking the residuals for trends and outliers, autocorrelations, leverage points, and violations of the statistical assumption of the regression method. This methodology can be found in the literature, e.g., [17], in more detail. The central composite design applied allows us to estimate a full quadratic model as described in Equation (1). \[Y=\beta_{0}+\sum_{i=1}^{k}\beta_{i}X_{i}+\sum_{i=1}^{k}\beta_{ii}X_{i}^{2}+\sum _{i<j}\beta_{ij}X_{i}X_{j}+\varepsilon \tag{1}\]  
where \(Y\) is the response variable; \(X_{i}\) corresponds to the \(i\)th design variable considered; the letter \(\beta\) is applied for the model parameters (\(\beta_{0}\) is the independent term, \(\beta_{i}\) means the linear effect of \(X_{i}\), \(\beta_{ii}\) is the quadratic effect of \(X_{i}\) and \(\beta_{ij}\) is the linear-by-linear interaction between \(X_{i}\) and \(X_{j}\)); and \(\varepsilon\) regards the fitting error. Multilinear regression analysis may assess the model parameters (\(\beta_{0}\), \(\beta_{i}\), \(\beta_{ij}\)). In the sequence of the analysis, some of the terms in Equation (1) may be considered as not significant.