## 4 Results and Discussion
### Compressive Strength
#### Regression Function:  
Based on the experimental results, the regression model is constructed depending on the researcher's choice to ensure the model's appropriateness. In this research, to build the regression function based on the provided context, constructing a multiple regression model that takes into account the compressive strength (Y1), the influencing factors (GO, fly ash (FA), and days (t)), and their interaction terms was necessary. Y1 = \(\beta_{0}+\beta_{1}\)t + \(\beta_{2}\)FA + \(\beta_{3}\)GO + \(\beta_{4}\)t\({}^{2}\) + \(\beta_{5}\)FA\({}^{2}\) + \(\beta_{6}\)GO\({}^{2}\) + \(\beta_{7}\)(t-FA) + \(\beta_{8}\)(t-GO) + \(\beta_{9}\)(FA-GO) + \(\epsilon\)  
where Y1 = compressive strength (MPa); t = time (in days); FA = fly ash content (in %); GO = graphene oxide content (in %); \(\beta_{0}\), \(\beta_{1}\), \(\beta_{2}\),..., \(\beta_{9}\) = regression coefficients; \(\epsilon\) = error term. The regression equation for the compressive strength of mortar was expressed as shown in Equation (1) below with statistically significant variables, such as a \(p\) value < 0.05, R-sq = 99.43%, and R-sq(adj) = 99.39%. Y1 = 5.889 + 351.3 GO + 0.5128 FA + 5.0089 t - 5319 GO\({}^{2}\) - 0.020838 FA\({}^{2}\) - 0.12128 t\({}^{2}\)  
\[\hskip 14.226378 pt- 0.765\,\mathrm{GO}\times\mathrm{FA}+2.026\,\mathrm{GO}\times \mathrm{t}-0.002487\,\mathrm{FA}\times\mathrm{t}\]  
Regression Equation (1) revealed the following observations:  
* The most significant positive influencing factor on the compressive strength of mortar was the content of GO with a considerable influence weight of (+351.3), which means that under the condition that other variables did not change, if the compressive strength of mortar includes 0.01% GO, the strength of mortar increases by 3.513 MPa. * Similarly, other factors that had a significant influence on the compressive strength of mortar include FA content and time (days) with influence weights of (+0.5128) and (+5.0089), respectively. Compressive strength changes significantly over time, which is true for all types of cement mortar in general. Here, when the time increases by 1 day, the strength of the mortar will also be increased on average by 5.0089 MPa. Meanwhile, if FA (fly ash) increases by 1%, the strength also increases by 0.5128 MPa. Figure 8: DoE on compressive strength of hardened cement paste. * Interestingly, when these independent variables are of higher order, specifically of the second order in Equation (1), the influence weights are all negative. However, if these terms are removed, the equation has a relatively low \(R\) value and some variables will not be statistically significant. Thus, the regression Equation (1) also clearly showed the influence of the factors and their content according to the quantitative method. Furthermore, Table 5 shows that the compressive strength of hardened mortar changes clearly over time, and the growth rate at each time was also different. What is also noteworthy is that in the early stage (3 days), the growth level was relatively high for mortar samples with GO, reaching the highest value of about 37.2%. In comparison, at 7 and 28 days, it only came to about 28.79% and 26.81%, respectively, compared to the control sample, which did not have GO and fly ash in the mixture. Thanks to the presence of oxygen-rich functional groups on the surface, GO accelerates the hydration process of cement and also helps form crystals, so the compressive strength of the mortar is higher and develops strongly at the beginning. Additionally, compared to the strength at 28 days, at 3 days, the strength ranged from 38.5% to 44.3% depending on the proportions of graphene oxide (GO) and fly ash (FA) in the mix. By 7 days, the compressive strength has noticeably increased, ranging from 69.66% to 71.37%. However, the compositions that achieved the fastest and slowest rate of strength gain did not have the same proportions in the mix. * For mortar samples containing GO, the strength change is also apparent depending on the GO content and fly ash content used.