## 5 Principal Component Regression Analysis
### Analysis of Principal Component Through Sensitivity Analysis for Unconfined Compressive Strength  
Principal component regression analysis reveals significant insights into relationships between soil properties and unconfined compressive strength. PC1 accounts for approximately 78% of total variance, while PC2 contributes 17%, collectively explaining nearly 95% of variance (Figure 18). This high cumulative explanation indicates that PCR effectively captures essential relationships while substantially reducing dimensionality. The regression coefficients reveal each component's influence on UCS prediction. PC1's substantial negative coefficient (\(-\)170.70) indicates that variables loading heavily on this component exhibit strong inverse relationships with soil strength. This aligns with geotechnical principles where void ratio and porosity negatively impact UCS by creating matrix discontinuities that compromise structural integrity. PC2's positive coefficient (21.24) indicates that variables with high loadings contribute positively to UCS development through secondary or interaction effects. PC1's dominance confirms that primary UCS determinants include lime content, cement content, and pre-consolidation stress--properties enhancing soil strength through particle binding, cementitious reactions, and densification processes. The substantial variance explanation demonstrates that these properties collectively define a primary variation axis strongly predicting UCS behavior in stabilized soil systems. This sensitivity analysis provides a quantitative framework for understanding the relative importance of different soil properties in determining UCS, offering insights for optimizing stabilizer formulations. The high cumulative variance explanation validates the PCR approach  
Figure 17: Scatter plot comparing actual versus predicted UCS values for curing times, with PCR line showing model fit quality: (**a**). A 7-day curing time. (**b**). A 14-day curing time. (**c**). A 28-day curing time. Different color dots on the plot represent the data points with variation of samples. for developing predictive models while maintaining the interpretability of underlying mechanisms governing soil strength enhancement. Analysis of Principal Component Loadings in Soil Stabilization  
Principal component loadings extraction reveals how individual geotechnical parameters contribute to the principal components, enabling the interpretation of soil mechanical behavior in response to stabilization treatments. The primary component (PC1), accounting for 46% of total variance, exhibits strong positive loadings for void ratio (0.462), porosity (0.463), and compression index (0.462), with substantial negative loadings for pre-consolidation stress (\(-\)0.439) and compressibility modulus (\(-\)0.407). This pattern characterizes PC1 as a fundamental contrast axis between soil compressibility and strength characteristics, capturing the inverse relationship between void spaces and mechanical strength consistent with geotechnical principles. The secondary component (PC2), explaining 20% of variance, shows pronounced negative loading for compressibility modulus (\(-\)0.909) with moderate positive loading for pre-consolidation stress (0.263). This component differentiates between these strength parameters, suggesting they represent distinct aspects of soil mechanical behavior not perfectly correlated. The tertiary component (PC3), contributing 15% of variance, is characterized by strong negative loading for pre-consolidation stress (\(-\)0.859), indicating that certain pre-consolidation behavior aspects warrant dedicated representation, potentially reflecting complex stress history dependencies not captured by PC1. Higher-order components exhibit specialized patterns, with PC4 influenced by porosity (\(-\)0.828) and compression index (0.407), while PC5 shows associations with void ratio (\(-\)0.714) and compression index (0.700).