Simple and multiple linear regression analyses are statistical methods used to investigate the link between activity/property of active compounds and the structural chemical features. One assumption of the linear regression is that the errors follow a normal distribution. This paper introduced a new approach to solving the simple linear regression in which no assumptions about the distribution of the errors are made. The proposed approach maximizes the probability of observing the event according to the random error. The use of the proposed approach is illustrated in ten classes of compounds with different activities or properties. The proposed method proved reliable and was showed to fit properly the observed data compared to the convenient approach of normal distribution of the errors.

Using reversed-phase high-performance thin-layer chromatography and a methanol-water mixture as the mobile phase, the lipophilicity of 12 new synthesized derivatives is studied. The first eight compounds have as a basic chemical structure aryliden-hydrazino-selenazoles, and the second group of the three compounds belongs to aroyl-hydrazinoselenazoles. The linear correlation between R(Mw) and the methanol-water ratios showed high values for the correlation coefficient. The chromatographic hydrophobic index is determined by using the ratio -R(Mw)/S, and the obtained values ranged between 99 and 73. A good linear correlation is obtained between R(Mw) and the slope. The log P values are calculated using ACD/Labs Software. The matrices are formed with R(Mw) and log P and are subjected to a principal component analysis (PCA). The best way to extract information from PCA is graphically, by plotting the obtained matrices. By analyzing the scores, the compounds can be grouped as follows: a group containing nine compounds, and a second one containing three compounds. Each group of compounds has the same basic chemical structure.

& Using RP-HPTLC and RP-HPLC and a methanol-water mixture as the mobile phase, eight new p-toluenesulfonyl-hydrazinothiazole and hydrazine-bis-thiazole derivatives were studied. The linear correlation between R Mw , k W and methanol=water ratios showed high values, for the correlation coefficient R 2 . The chromatographic hydrophobic index u 0 was determined by using intercept and slope, the obtained values ranging between 60 and 98. A good linear correlation was obtained between R M w, log k w , and slope. The log P values were calculated using database (Toronto, Canada). The matrices were formed with R Mw, log k w and log P and were subjected to principal component analysis (PCA). The best way to extract information from PCA was graphically, by plotting the obtained matrices. By analyzing the scores, the compounds can be grouped in two: the first group contains three compounds that have a phenyl moiety while the second group comprises other five compounds that contain: methyl, chlor-methyl, acetyl, and ethylic ester.

Selenium compounds have been proven to possess anti-inflammatory, anti-cancer, anti-bacterial and anti-viral activities. A series of fifteen synthesized hidrazinoselenazole was investigated to assess the chromatographic properties as function of structural features and the cytotoxicity as function of chromatographic properties and/or structural descriptors. The investigated chromatographic properties were retention factor, specific surface area of the solvent and chromatographic hydrophobicity index. The 3D model of the compounds was optimized using Hartree-Fock DFT/B3LYP method, 6-31+G* basis set both in vacuum and water with Spartan software (v.8). Furthermore, several quantitative structure-activity relationship (QSAR) descriptors were calculated with Spartan and Dragon (v. 5.5) software. Full search approach was used to construct simple and multiple linear regression models. No reliable model was identified for specific surface area of the solvent. The models with higher performances in estimation and prediction for retention factor and chromatographic hydrophobicity index proved the ones with Dragon descriptors and molecules optimized in water (retention factor: rloo2 (loo = leave-one-out analysis) = 0.9244; rtr2 (tr = training set) = 0.9652; rts2 (ts = test set) = 0.9606; chromatographic hydrophobicity index: rloo2 = 0.9489; rtr2 = 0.9592; rts2 = 0.9669). The cytotoxicity proved related neither to chromatographic properties nor with compounds� structural characteristics.