## 6 Results and Discussion
### Descriptive Statistics of the Experimental Dataset Variables
#### 6.1.7 Density vs. UCS  
* A strong positive correlation (r \(\approx\) 0.80) indicates that denser rocks resist compressive loading more effectively, making density one of the most predictive features for UCS (bottom-right scatter).  
These pairwise patterns confirm the expected geomechanical interdependencies--moisture and porosity weaken the rock, whereas density enhances strength--and validate the selection of these four variables as primary inputs for subsequent machine learning models.  
Figure 11 presents the pairwise Pearson correlation coefficients between moisture content (%), interconnected porosity (%), real density (g/cm\({}^{3}\)), and uniaxial compressive strength (UCS, MPa). The color-coded matrix, with overlaid coefficient values, highlights the following key relationships:  
* Water Content vs. Porosity (r = 0.992): A near-perfect positive correlation indicates that specimens with higher moisture content exhibit increased interconnected porosity, reflecting the pore network's enhanced fluid-retention capacity.
* Moisture Content vs. Real Density (r = -0.861): A strong inverse relationship indicates that specimens retaining more moisture exhibit lower density, consistent with increased pore volume reducing the mass per unit volume.
* Moisture Content vs. UCS (r = -0.649): A moderate inverse correlation indicates that higher moisture content typically reduces compressive strength, although additional factors also influence UCS variability.
* Porosity vs. Density (r = -0.805): Porosity and density are strongly inversely related, confirming that an increased void fraction corresponds to reduced material compactness.
* Porosity vs. UCS (r = -0.568): A moderate negative correlation indicates that increased porosity compromises compressive strength, underscoring pore structure as a primary weakening mechanism.
* Density vs. UCS (r = 0.929): A robust positive correlation indicates denser rocks resist compressive loading more effectively, making real density the most predictive univariate feature for UCS.  
These findings validate the anticipated geomechanical interdependencies and support the inclusion of all four variables in our multivariate predictive models.  
On the other hand, Figure 12 shows a parallel coordinate plot with four vertical axes--water content (%), interconnected porosity (%), real density (g/cm\({}^{3}\)), and uniaxial compressive strength (UCS, MPa) simultaneously mapping each sample's values to highlight multidimensional relationships and sample heterogeneity.  
* _High-strength subset (rightmost lines):_ Samples with UCS > 45 MPa (the upper bundle on the right axis) consistently correspond to high real density (2.5-2.7 g/cm\({}^{3}\)) and low moisture content (3-6%) and porosity (9-15%), reaffirming that dense, low-porosity rocks exhibit superior compressive resistance.
* _Low-strength subset:_ Samples with UCS < 25 MPa align with lower real density (1.9-2.2 g/cm\({}^{3}\)) and elevated moisture content (8-14%) and porosity (18-28%), highlighting how increased pore volume and moisture compromise compressive strength.
* _Intermediate cluster:_ The majority of samples fall within mid-range values--moisture content 5-8%, porosity 12-18%, real density 2.3-2.5 g/cm\({}^{3}\), and UCS 30-45 MPa--reflecting the dataset's central tendency and confirming these intervals as representative for model training.
* _Outliers:_ A few lines diverge sharply, such as one sample with exceptionally high porosity (>25%) yet moderate UCS (\(\sim\)30 MPa), suggesting localized lithological variations or measurement anomalies worth further geological investigation.  
Overall, the parallel coordinate plot visually confirms the inverse relationship between moisture content/porosity and density/UCS, clearly delineating distinct strength-density-porosity regimes that inform feature selection and stratified modeling strategies in our subsequent machine learning workflows.  
Figure 11: Pearson correlation coefficient heatmap for rock properties.