# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 3 Results and Discussion
### Correlations Between Rheology and Other Parameters  
#### 3.3.1. Putting Correlations  
The Shapiro-Wilk test, using the (scipy.stats) Python library, evaluated the normality of the variables before the correlation analysis. The results revealed that most variables did not significantly vary from normality (\(p\)-value \(>\) 0.05), validating the application of [PERSON]'s correlation. Figure 6 presents a heatmap depicting the correlation matrix among \(G^{*}/\sin\!\delta\), chemical indices (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\)), thermal residue, and various other parameters (such as mix type: \"field, plant, or lab,\" ABR by RAP or RAS, total AC, and age of the mix). The numerical value and hue within each cell of the map represent [PERSON]'s correlation coefficient between the two variables on the x- and y-axes. The right-hand scale of the figure displays weak to very weak correlations in white or light grey, strong positive correlations close to 1 in red, and strong negative correlations close to \(-1\) in blue. The absolute value of [PERSON]'s critical correlation (0.26) was computed using a sample size of 60 and a significance level of 0.05. This indicates that \(|\,\mathrm{r}\,|>\) 0.26 signifies the [PERSON] correlation coefficient is statistically significant at the 0.05 level with \(n=60\). A strong, significant negative correlation was observed between \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\): binders with increased aging exhibited higher aging indices \(I_{CO}+I_{SO}\) and reduced total aliphatic compounds compared to aromatics (lower \(I_{CC}+I_{CH}\)). Moderate, significant positive and negative correlations were assigned between \(G^{*}/\sin\!\delta\) and \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\), respectively. The addition of aged materials from RAP/RAS increased the  
Figure 6: Heatmap of rutting parameter. aging indices and promoted the conversion of aliphatic compounds to aromatics, suggesting that the binder had greater stiffness. Moderate, significant positive and negative correlations were observed between \(G^{\star}\)/sin\(\delta\) and ABR by RAS and ABR by RAP, respectively. A moderately significant negative correlation was identified between the ABR by RAP and \(G^{\star}\)/sin\(\delta\), indicating that an increase in the RAP binder replacement diminishes the rutting resistance. This result can be attributed to the utilization of a softer virgin binder in high-RAP-content mixes, which can counteract the stiffening influence of the aged RAP binder. In addition, the variability in the RAP binders from different sources can lead to variations in the stiffness and performance of the extracted binder [5; 7]. Weak correlations were noted between \(G^{\star}\)/sin\(\delta\) and the remaining parameters, that is, mix type, total AC, mix's age, and thermal residue content. A linear regression relationship exists between \(G^{\star}\)/sin\(\delta\) and other variables, as represented in Equation (9). Figure 7 illustrates the correlation between the measured and predicted \(G^{\star}\)/sin\(\delta\) values of the 60 extracted binders using the linear model established by regression analysis. The data points clustered around a line, which represented an ideal fit for the data, as shown in Figure 7, with a 1:1 slope. The R\({}^{2}\), which shows the extent to which the variability in the data are explained, was 0.66, and the R, which shows the predictive reliability of the \(G^{\star}\)/sin\(\delta\) values, was 0.81. The standard error ratio (Se/Sy) was 0.58, indicating a moderate level of predictive error associated with variability among the samples. The chemical indices (\(I_{CO}+I_{SO}\)) and (\(I_{CC}+I_{CH}\)) interaction and the percentage of residue combined with the mix's age were the most significant variables discovered in the linear analysis. Thus, this reflects the importance of chemical and thermal analyses in predicting the rutting parameters of the binders. The subsequent equation illustrates a linear model between \(G^{\star}\)/sin\(\delta\) and the other parameters:  
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