## 2 Results and Discussion
### Response Surface Model
#### 2.4.2 Correlations for Environmental Score and Economic Score  
The response surface model was developed for creating a three-dimensional relationship of related parameters. Furthermore, by developing a response surface model, the overall view of the actual response for each case predicted would be reliable for the sustainable structural design of the building. The response surface model was developed for each case that comprised of the relationship of eco-efficiency with economic factors and the environmental factors. Figures 15 and 16 shows the response surface model for a single story fly ash and blast furnace slag reinforced concrete residential houses, and Figures 17 and 18 shows the response surface model for a double story fly ash and blast furnace slag reinforced concrete residential house.  
The model developed in this study showed the suitability of the cubic relationship for fly ash double story residential houses. In contrast, the other three cases best fit was found to have a linear relationship. The different best fit was based on the overall F-value and \(p\)-value of each case calculated in the analysis using ANOVA. Linear regression is suitable to estimate the conditional mean effects of a response variable, although there are violations of the underlying assumptions in this classical linear regression [24].  
A relationship for the single story house as obtained using RSM, showed a linear relationship, which is indicated in Table 1. The three-dimensional surface relationship shows the economic score and environmental score for single story house significantly increase the eco-efficiency index level, if the optimization of the characteristic strength of concrete produced a small difference in each value because the size of floor area is small. Furthermore, in the analysis of the response surface relationship for a double story house, a cubic relationship was produced as the best fit that is suitable for this model, as shown in Figures 17 and 18. The three-dimensional surface relationship produces a cubic relationship, because of the data produced in the economic score and environmental score have significant differences that reflect the cubic relationship of the eco-efficiency index. Other than that, the  
Figure 17: Response surface graph of fly ash based concrete used for double story houses.  
Figure 18: Response surface graph of blast furnace slag based concrete used for double story houses.  
optimization of the characteristic strength of concrete found that the total material volume produced a significant difference for a few design cases, which results in a different best fit compared to single story houses. Overall, the response surface model produces a linear surface model for eco-efficiency in reinforced concrete single story houses and a cubic relationship for eco-efficiency in reinforced concrete double story houses. The slight difference between the corresponding contours is not large, which means that they are close to each other, and the loss value does not decrease that much between the contours. These flat regions will be high regions, because their color is coded in red, which indicates the error value will be high in these regions. The response surface model represents the overall performance of an economic score and an environmental score in the eco-efficiency index of the reinforced concrete structure.