## 3 Results
### Regression Model for 28-Day Compressive Strength  
The regression analysis seemed to suggest that quadratic models were the most promising candidates. However, upon ANOVA analysis, the quadratic model was found to be nonsignificant, as the \(p\)-value was 0.2889 and therefore under the recommended threshold of 0.05. Among the terms examined, only A\({}^{2}\) exhibited statistical significance, with a \(p\)-value of 0.0252, while all the other terms (A, B, C, D, AB, AD, BC, BD, CD, B\({}^{2}\), C\({}^{2}\), and D\({}^{2}\)) were found to be not significant. Moreover, the predicted R\({}^{2}\) was found to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Model & 227.36 & 75.79 & 37.54 & \(<\)0.0001 \\ A–w/c & 215.95 & 215.95 & 106.96 & \(<\)0.0001 \\ C—w/p & 10.42 & 10.42 & 5.16 & 0.0316 \\ D—g/m & 0.9928 & 0.9928 & 0.4917 & 0.4894 \\ Residual & 52.49 & 2.02 & & \\ Lack of Fit & 35.04 & 1.67 & 0.4778 & 0.8934 \\ Pure Error & 17.46 & 3.49 & & \\ Cor Total & 279.86 & - & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Fitting results for compressive strength results after 24 h of curing. Figure 6: Regression model for compressive strength after 24 h of curing: (**a**) Normal Plot of Residuals and (**b**) Predicted versus Actual. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **Intercept** & **A—w/c** & **C—w/p** & **D—s/m** \\ \hline Coefficient Estimate & 58.44 & \(-\)3.00 & \(-\)0.6589 & 0.2034 \\ Standard Error & 0.2594 & 0.290 & 0.2900 & 0.2900 \\
95\% CI Low & 57.91 & \(-\)3.60 & \(-\)1.26 & \(-\)0.3928 \\
95\% CI High & 58.97 & \(-\)2.40 & \(-\)0.0628 & 0.7996 \\ VIF & - & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Coefficients in terms of coded factors—compressive strength after 24 h of curing. be \(-0.8825\), with an adjusted R\({}^{2}\) of 0.1506. This substantial discrepancy suggests that the quadratic model's efficacy was low. Graphic diagnosis was conducted and revealed a potential outlier at Std 18, Run 20, which was clearly shown by the distribution in the Predicted versus Actual plot, the Residual versus Predicted plot, the Residual versus Factor plot, and the Cook's distance relationships (not show here for the sake clarity). This data point exceeded the DEFFITS limit and was consequently excluded from subsequent analysis. Still, these results suggested that the quadratic model could be reduced (by removing some terms) to enhance its significance. Table 10 shows the fitting results for the regression model compressive strength after removing the terms B, C, AB, AC, AD, BC, BD, CD, B\({}^{2}\), C\({}^{2}\), and D\({}^{2}\). The likelihood of such a high F-value occurring due to noise was only 0.15%. Therefore, the quadratic model was directionally reduced to address the presence of insignificant terms and to ensure statistical significance. The significant terms A, D, and A\({}^{2}\) were retained. The newly built model had a nonsignificant lack of fit, with an 82.97% probability that misfit could be attributable to noise. The predicted R\({}^{2}\) value of 30.89% exhibited reasonable agreement with the adjusted R\({}^{2}\) value of 39.95%, with a difference of less than 20%. Adequate precision was measured, with a value of 9.366, which indicates that the signal was sufficiently strong and the model was well-suited to describe the design space. Table 11 presents the estimated coefficients for compressive strength after 28 days of curing, which all lay within the 95% confidence interval. The variance inflation factor (VIF) for the factors A and A\({}^{2}\) was 1.14, thereby indicating multicollinearity, while the variable D had a VIF of 1.0, thereby demonstrating orthogonality. Figure 7a shows the normal plot of the residuals for the compressive strength model after excluding the data point Std 18, Run 20. One can observe that the data points appear distributed across a line, but a fully linear distribution is not entirely perceived.