Table 13 Regression analysis for entropies of TIs based on best predictors.
Property\(\sim \mathcal {I}_{TI}\) | Models | Regression Equations | \(R^{2}\) | RMSE | F-test | p-value | SE | MPE | MAE |
|---|---|---|---|---|---|---|---|---|---|
BP\(\sim \mathcal {I}_{ESO}\) | Linear | \(-359.745 +295.132(\mathcal {I}_{ESO})\) | 0.829 | 50.627 | 82.16 | \(6.40\times 10^{-8}\) | 11.615 | \(-\)0.008 | 42.083 |
Quadratic | \(248.307 -108.530(\mathcal {I}_{ESO}) +65.798(\mathcal {I}_{ESO})^2\) | 0.836 | 49.528 | 40.759 | \(5.25\times 10^{-7}\) | 11.362 | \(-\)0.009 | 41.275 | |
Cubic | \(-3718.492 +3947.831(\mathcal {I}_{ESO}) -1297.071(\mathcal {I}_{ESO})^2 +150.648(\mathcal {I}_{ESO})^3\) | 0.839 | 49.028 | 26.098 | \(3.34\times 10^{-6}\) | 11.248 | \(-\)0.009 | 40.708 | |
MR\(\sim \mathcal {I}_{BSO_1}\) | Linear | \(-166.030 +81.553(\mathcal {I}_{BSO_1})\) | 0.912 | 9.412 | 291.868 | \(2.42\times 10^{-16}\) | 1.718 | \(-\)0.002 | 7.729 |
Quadratic | \(246.893 -183.330(\mathcal {I}_{BSO_1}) +41.797(\mathcal {I}_{BSO_1})^2\) | 0.959 | 6.435 | 316.406 | \(1.82\times 10^{-19}\) | 1.175 | \(-\)0.004 | 4.696 | |
Cubic | \(545.895 -476.522(\mathcal {I}_{BSO_1}) +136.343(\mathcal {I}_{BSO_1})^2 -10.040(\mathcal {I}_{BSO_1})^3\) | 0.96 | 6.397 | 205.674 | \(3.17\times 10^{-18}\) | 1.168 | \(-\)0.004 | 4.755 | |
HAC\(\sim \mathcal {I}_{BSO_1}\) | Linear | \(-43.942 +21.698(\mathcal {I}_{BSO_1})\) | 0.944 | 1.974 | 469.631 | \(4.89\times 10^{-19}\) | 0.36 | 0.003 | 1.533 |
HAC\(\sim \mathcal {I}_{ESO}\) | Quadratic | \(65.787 -48.751(\mathcal {I}_{ESO}) +11.148(\mathcal {I}_{ESO})^2\) | 0.991 | 0.796 | 1462.179 | \(3.01\times 10^{-28}\) | 0.145 | \(-\)0.001 | 0.663 |
Cubic | \(-2.910 +19.355(\mathcal {I}_{ESO}) -11.033(\mathcal {I}_{ESO})^2 +2.377(\mathcal {I}_{ESO})^3\) | 0.991 | 0.777 | 986.073 | \(6.95\times 10^{-27}\) | 0.142 | \(-\)0.001 | 0.623 | |
EM\(\sim \mathcal {I}_{BSO_1}\) | Linear | \(-492.960 +267.074(\mathcal {I}_{BSO_1})\) | 0.879 | 37.007 | 202.463 | \(2.42\times 10^{-14}\) | 6.756 | \(-\)0.004 | 31.053 |
EM \(\sim \mathcal {I}_{mRSO}\) | Quadratic | \(1371.757 -931.093(\mathcal {I}_{mRSO}) +189.373(\mathcal {I}_{mRSO})^2\) | 0.961 | 21.01 | 331.244 | \(1.01\times 10^{-19}\) | 3.836 | \(-\)0.003 | 17.492 |
Cubic | \(914.052 -479.734(\mathcal {I}_{mRSO}) +43.112(\mathcal {I}_{mRSO})^2 +15.597(\mathcal {I}_{mRSO})^3\) | 0.961 | 20.981 | 213.252 | \(2.02\times 10^{-18}\) | 3.831 | \(-\)0.003 | 17.404 | |
FP\(\sim \mathcal {I}_{BSO_2}\) | Linear | \(-275.920 +181.563(\mathcal {I}_{BSO_2})\) | 0.839 | 29.753 | 88.799 | \(3.67\times 10^{-8}\) | 6.826 | \(-\)0.012 | 24.407 |
FP\(\sim \mathcal {I}_{ESO}\) | Quadratic | \(92.301 -59.096(\mathcal {I}_{ESO}) +39.021(\mathcal {I}_{ESO})^2\) | 0.846 | 29.114 | 43.996 | \(3.14\times 10^{-7}\) | 6.679 | \(-\)0.013 | 23.833 |
Cubic | \(-1950.495 +2029.823(\mathcal {I}_{ESO}) -662.821(\mathcal {I}_{ESO})^2 +77.580(\mathcal {I}_{ESO})^3\) | 0.849 | 28.889 | 28.006 | \(2.15\times 10^{-6}\) | 6.628 | \(-\)0.012 | 23.374 | |
P\(\sim \mathcal {I}_{BSO_1}\) | Linear | \(-65.790 +32.319(\mathcal {I}_{BSO_1})\) | 0.912 | 3.738 | 290.547 | \(2.56\times 10^{-16}\) | 0.683 | \(-\)0.002 | 3.07 |
Quadratic | \(98.047 -72.780(\mathcal {I}_{BSO_1})+16.584(\mathcal {I}_{BSO_1})^2\) | 0.959 | 2.559 | 314.253 | \(1.99\times 10^{-19}\) | 0.467 | \(-\)0.004 | 1.866 | |
Cubic | \(220.946 -193.290(\mathcal {I}_{BSO_1})+55.445(\mathcal {I}_{BSO_1})^2 -4.127(\mathcal {I}_{BSO_1})^3\) | 0.959 | 2.543 | 204.45 | \(3.41\times 10^{-18}\) | 0.464 | \(-\)0.004 | 1.89 |
