## 3 Results and Discussion
### Model Development and Statistical Analysis
#### 3.2.2 Statistical Analysis  
Lack of fit test, test for significance of coefficients of the quadratic model, and the individual model terms were performed to ascertain the model's accuracy. Commonly, grounded on the F or \(p\)-values at 95% confidence level, the significant factors are determined. ANOVA for the hydraulic conductivity quadratic model was performed, and the findings are presented in Table 5.  
Statistical Analysis for Response Surface Quadratic Model for Hydraulic Conductivity  
Table 5 shows that the model is statistically significant. The F and \(p\)-values are respectively 274.17 and \(<\)0.0001. There is only a chance of 0.01% probability that an F-value of this magnitude will occur due to noise. Only when the \(p\)-values are \(<\)0.05 are the model terms significant. In this case, A, B, C, AB, A\({}^{2}\), B\({}^{2}\), and C\({}^{2}\) are significant model terms. Other model terms with \(p\)-values \(>\) 0.05 are insignificant. Adequate precision, obtained by comparing the range of the predicted value to the average prediction error at the design \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{1}{c}{**Source**} & \multicolumn{1}{c}{**Sum of Squares**} & \multicolumn{1}{c}{**DF**} & \multicolumn{1}{c}{**Mean Square**} & \multicolumn{1}{c}{**F-Value**} & \multicolumn{1}{c}{**\(p\)-Value**} & \multicolumn{1}{c}{**Remark**} \\ \hline Model & 3.062 \(\times\) 10\({}^{-19}\) & 9 & 3.420 \(\times\) 10\({}^{-20}\) & 274.17 & \(<\)0.0001 & significant \\ A-Olivine content & 7.230 \(\times\) 10\({}^{-20}\) & 1 & 7.230 \(\times\) 10\({}^{-20}\) & 582.66 & \(<\)0.0001 & significant \\ B-Carbonation time & 1.729 \(\times\) 10\({}^{-19}\) & 1 & 1.729 \(\times\) 10\({}^{-19}\) & 1393.50 & \(<\)0.0001 & significant \\ C-Carbonation pressure & 2.381 \(\times\) 10\({}^{-21}\) & 1 & 2.381 \(\times\) 10\({}^{-21}\) & 19.19 & 0.0072 & significant \\ AB & 1.656 \(\times\) 10\({}^{-20}\) & 1 & 1.656 \(\times\) 10\({}^{-20}\) & 133.50 & \(<\)0.0001 & significant \\ AC & 4.687 \(\times\) 10\({}^{-22}\) & 1 & 4.687 \(\times\) 10\({}^{-22}\) & 3.78 & 0.1096 & \\ BC & 7.480 \(\times\) 10\({}^{-22}\) & 1 & 7.480 \(\times\) 10\({}^{-22}\) & 6.03 & 0.0576 & \\ A\({}^{2}\) & 9.930 \(\times\) 10\({}^{-21}\) & 1 & 9.930 \(\times\) 10\({}^{-21}\) & 80.03 & 0.0003 & Significant \\ B\({}^{2}\) & 2.792 \(\times\) 10\({}^{-20}\) & 1 & 2.792 \(\times\) 10\({}^{-20}\) & 225.02 & \(<\)0.0001 & significant \\ C\({}^{2}\) & 8.378 \(\times\) 10\({}^{-21}\) & 1 & 8.378 \(\times\) 10\({}^{-21}\) & 67.52 & 0.0004 & significant \\ Residual & 6.204 \(\times\) 10\({}^{-22}\) & 5 & 1.241 \(\times\) 10\({}^{-22}\) & & & \\ Lack of Fit & 6.203 \(\times\) 10\({}^{-22}\) & 3 & 2.068 \(\times\) 10\({}^{-22}\) & 3264.51 & 0.0003 & significant \\ Pure Error & 1.267 \(\times\) 10\({}^{-25}\) & 2 & 6.333 \(\times\) 10\({}^{-26}\) & & & \\ Correlation Total & 3.068 \(\times\) 10\({}^{-19}\) & 14 & R\({}^{2}\) & 0.9980 & & \\ \hline Standard deviation & 1.114 \(\times\) 10\({}^{-11}\) & & Adjusted R\({}^{2}\) & 0.9943 & \\ \hline PRESS & 9.924 \(\times\) 10\({}^{-21}\) & & Predicted R\({}^{2}\) & 0.9677 & \\ \hline C.V. (\%) & 5.86 & & & & & \\ \hline \multicolumn{1}{c}{DF = Degree of Freedom; PRESS = Predicted residual sum of squares; CV = Coefficient of variation.} \\ \end{tabular}
\end{table} 
Table 5: ANOVA for response surface quadratic model for hydraulic conductivity. points, indicates the signal to noise ratio. Normally, a ratio greater than 4 is optimal. The ratio of 53.2329 suggests an adequate signal in this case. Hence, the model can be used to navigate the design space. The determination coefficient (R\({}^{2}\)) gives a measure of the model's precision. The model's R\({}^{2}\)-value of 0.9980 is close to 1. This implies that 99.80% sample variance is due to the independent variables, and only about 0.2% of the total variation cannot be explained by the model. Therefore, the model's general ability and accuracy are sound.