## 2 Results and Discussion
### Validation of the Eco-Efficiency Index  
The regression analysis was conducted for the validation and checking the reliability of the data obtained from the simulations. Table 3 shows the summary of all analytical results, as obtained using linear regression for calculating the eco-efficiency index for single story and double story residential houses. All results showed that the data is significant; there is a minimum possibility of errors, which was required to satisfy the requirements for each analysis. Hence, the simulation was done accurately, and the data produced was reliable for this study. The F-value of 10.51 was determined for fly ash concrete applied in the single story houses; it implies that the model is significant. It estimated that there is only a 0.11% chance that the F-value could be affected by the noise. Similarly, when a \(p\)-value of less than 0.0500 indicates that the model terms are significant. In this case, B is a significant model term. The predicted R\({}^{2}\) of 0.4605 was found in a good agreement with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**House Type** & \multicolumn{2}{c}{**Single**} & \multicolumn{2}{c}{**Double**} \\ \hline
**Analysis** & **FA** & **BFS** & **FA** & **BFS** \\ \hline F-Value & 10.51 & 5891.61 & 227.95 & 23.84 \\ \(p\)-Value & 0.0011 & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 \\ Std. Dev & 0.0017 & 0.0001 & 0.0026 & 0.0021 \\ Mean & \(-\)0.0489 & 0.0127 & \(-\)0.0473 & 0.0167 \\ CV\% & 3.45 & 0.6295 & 5.52 & 12.26 \\ R\({}^{2}\) & 0.5530 & 0.9986 & 0.9951 & 0.9555 \\ \hline Best Fit & Linear & Linear & Cubic & Cubic \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Regression analysis results. adjusted R\({}^{2}\) of 0.5004, where the difference was obtained less than 0.2. The ratio of 10.054 indicates an adequate signal. An F-value of 227.95 was estimated for fly ash concrete used in the double story houses, which showed that the model is significant. There is only a 0.01% chance that an F-value could be affected due to noise. \(p\)-values less than 0.0500 indicate that the model terms are significant. In this case, A, B, AB, A\({}^{2}\), A\({}^{2}\)B, AB\({}^{2}\), A\({}^{3}\) are the significant model terms. The ratio of 68.419 indicates an adequate signal. This model can be used to navigate the design space. The F-value of 5891.61, as estimated for blast furnace slag concrete based single story houses, implies that the model is significant. There is only a 0.01% chance that the F-value could be affected due to noise. \(p\)-values less than 0.0500 indicate that the model terms are significant. In this case, B is a significant model term. The predicted R\({}^{2}\) of 0.9978 is in reasonable agreement with the adjusted R\({}^{2}\) of 0.998. That is, the difference is less than 0.2. The ratio of 222.975 indicates an adequate signal. The F-value of 23.84 for BFS based concrete used in the double story houses implies that the model is significant. There is only a 0.01% chance that the F-value could be due to noise. \(p\)-values less than 0.0500 indicate model terms are significant. In this case, A, AB, A\({}^{2}\), A\({}^{2}\)B, A\({}^{3}\) are significant model terms. The lack of fit F-value of 935.88 implies that the lack of fit is significant. There is only a 2.54% chance that a lack of fit F-value could be due to noise. The ratio of 18.786 indicates an adequate signal. In the overall analysis, the \(p\)-values of each case are significant because the values are less than 0.1000. Adequate precision measures the signal to noise ratio where the average ratio greater than four is desirable. This model can be used to navigate the design space. Further verification is essential to ensure the reliability of the data regarding the method used and the analysis of results. The different best fit that obtained in this study verified the model found to have different patterns, although the fundamental analysis used in this study is the same. Clarification of the best fit was developed in the overall relationship of the subject studied in this research.