Application of Multivariate Adaptive Regression Splines (MARSplines) for Predicting Hansen Solubility Parameters Based on 1D and 2D Molecular Descriptors Computed from SMILES String

Table 2

MARSplines p(25, 3) model regression factors along with their weights.

Factor	ai ± SD	Mathematical relationships
F0	3.0017 ± 0.2777
F1	13.0874 ± 1.3342	max(0; IC0-1.14332)
F2	−9.0702 ± 2.4982	max(0; 1.14332-IC0)
F3	18.0918 ± 1.7520	max(0; PetitjeanNumber-0.46154)
F4	−0.8421 ± 0.2724	max(0; 60.09146-AATS2m)·F1
F5	−25.2410 ± 3.4481	max(0; 0.75379-GATS2e)·F1
F6	51.6379 ± 5.0897	F5·max(0; AATSC5i-0.48388)
F7	73.5427 ± 8.2229	F5·max(0; 0.48388-AATSC5i)
F8	8.5172 ± 0.8475	max(0; MLFER_S-0.54800)
F9	−0.1257 ± 0.0262	max(0; ZMIC2-16.19833)
F10	0.7386 ± 0.0940	max(0; 16.19833-ZMIC2)
F11	−20.5206 ± 3.2197	F8·max(0; MATS1v + 0.17725)
F12	−16.5968 ± 2.2740	F8·max(0; −0.17725-MATS1v)
F13	−28.6245 ± 4.1609	max(0; GATS5m-0.54611)·max(0; GATS2e-0.75379)·F1
F14	−48.3050 ± 7.0216	max(0; 0.54611-GATS5m)·max(0; GATS2e-0.75379)·F1
F15	67.3423 ± 17.0712	max(0; −0.26841-ATSC5e)·max(0; 0.46154-PetitjeanNumber)
F16	4.7141 ± 1.0570	max(0; 60.09146-AATS2m)·max(0; mindssC + 0.24537)·F1
F17	2.0457 ± 0.4563	max(0; 60.09146-AATS2m)·max(0; −0.24537-mindssC)·F1
F18	82.5944 ± 16.2082	max(0; GATS2e-0.75379)·max(0; GATS1e-0.84779)·F1
F19	116.1381 ± 25.4572	max(0; GATS2e-0.75379)·max(0; 0.84779-GATS1e)·F1

Model statistics: fitting criteria: N = 130, R² = 0.954, R²_adj = 0.945, F = 122.2, and LOF = 3.533; internal validation criteria: LMO (30%), Q²_loo = 0.935, RMSE = 1.771, and MAE = 1.247.