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. 2025 Aug 22;15:30831. doi: 10.1038/s41598-025-99971-0

Table 5.

ANOVA and fit statistics comparing linear, two-factor interaction (2FI), and quadratic polynomial models.

Reponses dry density (/) Cohesion (kN/m2) internal friction angle (°) compressibility coefficient Cc (/) Swelling coefficient Cg (/)
Model tested (1) Linear polynomials
R2 0.9628 0.9594 0.9774 0.9662 0.9988
Adjusted R2 0.9594 0.9558 0.9754 0.9631 0.9986
Predicted R2 0.9433 0.9397 0.9705 0.9537 0.9983
Model F value 284.36 260.25 476.35 314.23 8852.15
Model P value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
Model remarks Significant Significant Significant Significant Significant
Model tested (2) Two-factor interaction (2FI)
R2 0.9979 0.9869 0.9775 0.9789 0.9988
Adjusted R2 0.9975 0.9843 0.9730 0.9746 0.9986
Predicted R2 0.9958 0.9796 0.9607 0.9632 0.9982
Model F value 2394.83 377.17 217.47 231.64 4282.00
Model P value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
Model remarks Significant Significant Significant Significant Significant
Model tested (3) Quadratic polynomials
Standard deviation 0.0031 0.9482 0.7020 0.0014 0.0004
Mean 1.66 31.69 14.81 0.1470 0.0399
R2 0.9979 0.9869 0.9775 0.9789 0.9988
Adjusted R2 0.9975 0.9843 0.9730 0.9746 0.9986
Predicted R2 0.9958 0.9796 0.9607 0.9632 0.9982
Adequate precision 125.8695 50.1427 38.6144 39.5951 171.3478
Model F value 2394.83 377.17 217.47 231.64 4282.00
Model P value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
Model remarks Significant Significant Significant Significant Significant
model adopted Quadratic Quadratic Quadratic Quadratic Quadratic

R2 coefficient of determination, MSE mean square error, ANOVA analysis of variance.