## 4 Results and Discussion
### Predictive Model Performance and Interpretation
[32] conducted a comparative study on fly ash-slag geopolymer mixtures and observed that GBR predictions showed minimal residual bias across both strength and emission targets, particularly evident in predicted vs. actual plots, where GBR consistently aligned with the identity line. The statistical robustness of GBR models under repeated validation has also been confirmed by [PERSON] et al. [61], who employed bootstrapping and cross-validation approaches to assess uncertainty and robustness. [PERSON] et al. [62] recommended visual residual analysis and calibration plotting as essential tools in verifying whether machine learning predictions maintain both bias-free behavior and variance homogeneity--criteria clearly satisfied in our GBR-based model. To ensure the statistical calibration of the GBR model, residuals from the test set were further analyzed using a Q-Q plot, as shown in Figure 4. The residuals align closely with the reference line of normality, suggesting no significant skew or kurtosis. This confirms that the GBR model satisfies normality assumptions and does not suffer from heteroskedastic errors [63]. Additionally, a calibration curve was plotted using binned prediction intervals (Figure 5). The GBR model aligns well with the ideal diagonal, particularly in the central prediction ranges. Slight deviations at high predicted values (>90 th percentile) suggest marginal underestimation in rare, high-cost scenarios, which is common in ensemble models and can be corrected via post-calibration methods. The use of Q-Q plots and calibration curves further reinforces the statistical integrity of the GBR model. This methodology is in alignment with recommendations by [PERSON] et al. [64], who emphasized the use of Q-Q plots for diagnosing distributional bias in regression models applied to infrastructure prediction tasks. The reliability of the GBR model is further supported by the calibration curve, which exhibits near-ideal alignment throughout most of the prediction range [65]. Figure 4: Q–Q plot for GBR residuals: (**a**) cost prediction, (**b**) CO2 emission. To further validate generalization capacity, stratified performance analysis was conducted by dividing Transport Distances (x\({}_{1}\)) into three operational bins: short (5-50 km), medium (51-150 km), and long (>150 km). Across all bins, GBR consistently maintained low RMSE (<6.1 USD/m\({}^{3}\)) and high a20 (>85%), affirming robustness across variable input regimes. This finding aligns with the results reported by [PERSON] et al. [66], who demonstrated that boosting algorithms maintained stable error margins across different transportation. Furthermore, [PERSON] et al. [67] highlighted that stratified validation is crucial for ensuring model applicability in real-world infrastructure design scenarios. The observed robustness of the GBR model in our study supports these assertions and suggests its utility in policy-relevant modeling, where operational heterogeneity is high. Comparable conclusions were drawn by [PERSON] et al. [68], who highlights the importance of incorporating the spatial and temporal variability of biomass yield and quality into supply chain planning to achieve sustainable and cost-effective production. Finally, [PERSON] et al. [69] demonstrate that the importance of uncertainty and price analysis in evaluating the transition to a circular economy for a regional building materials industry. The GBR model's consistent performance across all transport intervals confirms its viability in such heterogeneous and region-sensitive applications. Notably, the GBR model also demonstrates favorable behavior in the tail regions of the data--where traditional models like RFR or linear regression often fail to generalize--by preserving low bias even under extreme values of transport distance or grid emission intensity.