## 3 Response Models
### Discussion of Fitted Models Obtained  
Tables 11 and 12 present the estimates of the model coefficients in coded values and denote the relative effect of the different input parameters on each response. It is well known that higher values indicate the higher influence of the design variable in the response. We recall that for each model, the three most significant parameters are typed in bold in Tables 11 and 12, and the most significant term is also underlined. A positive coefficient means that the response (or transformed response) variable will increase if the  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**E24h Response Models**} & \multicolumn{6}{c}{**Rc,24h Response Models**} \\ \hline  & **Full** & **Fractioned A** & **Fractioned B** & **Small** & **Full** & **Fractioned A** & **Fractioned B** & **Small** \\ \hline
**Model Terms** & \begin{tabular}{c} **F24h** \\ **[MPa]** \\ \end{tabular} & \begin{tabular}{c} **F24h [MPa]** \\ \end{tabular} & \
\begin{tabular}{c} **F24h [MPa]** \\ \end{tabular} &
\begin{tabular}{c} **F24h** \\given mixture parameter increases and vice versa. The results in Tables 11 and 12 clearly show that Vs/Vm presented the strongest (negative) effect in the response in terms of the fresh state properties D-flow and T-funnel, followed by the Vw/Vp, representing the second strongest (positive) effect. Comparing the models of each CCD, it can be perceived that the main significant factors are the same among them. For T-funnel, the three main effects are the same.  
Concerning the mechanical properties, the strongest effect is that of Vw/Vc, which is also a negative effect, as expected. By increasing the water content (Vw), the mechanical performance decreases. Vw/Vp also has a significant effect on F,24h and Rc,24h in the majority of the models. It can be noted that Vfs/Vs presents a significant negative effect on the compressive strength at 24 h.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Full** & **Fractioned A** & **Fractioned B** & **Small** \\ \hline \multirow{6}{*}{D-flow} & Only two results & & & \\  & predicted by the & & & Five results \\  & model showed & All results & All the results & showed \\  & differences & predicted by the & predicted by the & differences \\  & between 5\% and & model showed & model showed & between 5\% and \\  & 10\%. The others & discrepancies of & discrepancies of & 10\%. The others \\  & presented results & less than 5\%. & less than 5\%. & presented results \\  & with differences of & & & \\  & less than 5\%. & & & \\ \hline \hline \end{tabular}
\end{table}
Table 13: Summary—predicted versus measured (laboratory test) values for different designs.  
Figure 5: Box plot: Difference between predicted and measured values for Fraction A, Fraction B, Full and Small plans (\({}^{\circ}\) represent extreme difference values; \(\ast\) represent outlier values).  
Given the analyses presented in Table 13 and taking into account the actions developed to fit the statistics models, it can be seen that, among the designs studied, the fractioned plans were the ones that represented a good compromise between the cost of experimentation and usefulness of the statistical model obtained. Among the analysed variables, the compressive strength (Rc,24h) followed by the slump flow (D-flow) were the ones that obtained the most accurate predictions.