## 5 Principal Component Regression Analysis
### Principal Component Regression Sensitivity Analysis for Unconfined Compressive Strength  
The principal component regression sensitivity analysis quantifies the relative influence of soil properties on UCS, revealing a clear hierarchical structure across principal  
Figure 18: Scree plot for the principal component regression sensitivity analysis for unconfined compressive strength. components (Figure 19). PC1 (compressibility characteristics) exhibits the strongest impact with a regression coefficient of 0.72. Through loadings on void ratio, porosity, and compression index, this component directly influences soil matrix structure and compressive resistance. The positive coefficient confirms that reduced compressibility enhances UCS, supporting the established inverse relationship between void spaces and soil strength. PC2 (stiffness parameters) shows moderate importance (coefficient = 0.51), representing the contrast between compressibility modulus and pre-consolidation stress. This indicates that increased soil stiffness contributes positively to UCS development, though less significantly than fundamental compressibility properties. PC3 (pre-consolidation stress) demonstrates negative influence (coefficient = \(-\)0.32), suggesting that stress history effects interact with stabilization processes in ways that do not translate to proportional strength increases. This counterintuitive finding warrants further investigation. PC4 and PC5 show negligible influence, indicating that once primary compressibility effects are captured in PC1, subtle variations in porosity and void ratio become irrelevant to UCS prediction. The established hierarchy (compressibility > stiffness > stress history > minor variations) provides clear guidance for optimizing soil stabilization formulations, enabling engineers to focus on controlling primary compressibility characteristics while recognizing the limited value of fine-tuning secondary property variations. Table 3 presents a principal component regression analysis of factors influencing soil settlement, showing how various soil properties contribute to settlement variance. PC1 (soil compressibility) accounts for the largest portion of variance (46%) with a high coefficient (0.72), indicating it has the highest sensitivity ranking. PC2 (modulus vs. pre-consolidation stress) contributes 20% of the variance with moderate sensitivity, while PC3-PC5 have progressively decreasing impacts on soil settlement behavior. This analysis helps geotechnical engineers prioritize the most influential parameters when modeling and predicting soil settlement. UCS increases with lime and cement but shows diminishing returns beyond 20-30% lime. For cross-validation, the PCR performance varies (\(R^{2}\) = 0.86), suggesting a fit model. Figure 19: PCR sensitivity analysis for unconfined compressive strength (UCS). The color of the bar sticks represent the variation of PC’s. The principal component regression (PCR) sensitivity analysis conducted in this study, which identified soil compressibility (PC1, \(\beta\) = 0.72, 46% variance) as the dominant factor influencing unconfined compressive strength (UCS), demonstrates both consistency and contrast with alternative methodologies reported in the literature. When compared to studies employing multivariate adaptive regression splines (MARS) for UCS prediction [66], PCR offers a more interpretable hierarchical variable structure, though MARS may capture nonlinear interactions unobserved in linear PCR frameworks. For instance, [PERSON] et al. achieved predictive accuracy with MARS but did not quantify parameter sensitivity hierarchies [26], which PCR explicitly resolves through regression coefficients and variance decomposition. Support vector regression (SVR) has shown superior predictive performance (R\({}^{2}\) > 0.90) in some geomechanical studies [66], potentially surpassing this study's PCR model (R\({}^{2}\) = 0.86).