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

Table 1

Regression factors along with their weights defining the d(25, 2) MARSplines model in Eq. (4).

Factor	ai ± SD	Mathematical relationships
F0	16.6638 ± 0.1485
F1	0.0092 ± 0.0015	max(0; ATSC1v + 144.0547)
F2	0.0648 ± 0.0050	max(0; −6.51036-ATSC1i)
F3	−0.0002 ± 0.0001	F1·max(0; SsOH-7.94125)
F4	0.0015 ± 0.0001	F1·max(0; 7.94125-SsOH)
F5	1.5234 ± 0.3405	max(0; AATS2e-7.54442)
F6	−3.4184 ± 0.3990	max(0; 7.54442-AATS2e)
F7	−1.2270 ± 0.2402	F5·max(0; minHCsats-4.17191)
F8	−6.0944 ± 0.5530	F5·max(0; 4.17191-minHCsats)
F9	0.2519 ± 0.0682	max(0; AATS2p-1.25641)
F10	−6.6966 ± 1.3720	max(0; 1.25641-AATS2p)
F11	−0.0192 ± 0.0036	max(0; ATS4m-2039.674)·F10
F12	0.0021 ± 0.0006	max(0; 2039.6739-ATS4m)·F10
F13	1.5646 ± 0.2463	max(0; nHBDon_Lipinski-2.00000)·F5
F14	0.3218 ± 0.1429	max(0; 2.00000-nHBDon_Lipinski)·F5
F15	0.0208 ± 0.0037	max(0; −144.0547-ATSC1v)·max(0; VE3_Dzi + 1.57191)
F16	−0.1155 ± 0.0211	max(0; ATSC1i + 6.51036)·max(0; 1.00111-GATS6c)
F17	−0.0008 ± 0.0002	F1·max(0; ATSC3p + 0.63792)
F18	−0.0031 ± 0.0006	F1·max(0; −0.63792-ATSC3p)
F19	0.2626 ± 0.0721	max(0; 0.00000-AATSC6v)·max(0; AATS2p-1.25641)

Model statistics: fitting criteria: N = 130, R² = 0.947, R²_adj = 0.938, F = 103.39, and LOF = 0.368; internal validation criteria: LMO (30%), Q²_loo = 0.860, RMSE = 0.697, and MAE = 0.431.