Variables, indicator

In cement chemists notation, where subscripts x andj indicate variable unknown quantities. 

The Kd(X) values thus obtained (Table 3) were analyzed by the multivariant technique using such parameters as n, a0, Bt, Ibmch, and Ihb, where Bj is a STERIMOL parameter showing the minimum width of substituents from an axis connecting the a-atom of the substituents and the rest of molecule, and Ibrnch, an indicator variable representing the number of branches in a substituent. 

This is an inverted parabolic relation in terms of ttx (calculated hydrophobic parameter of the substituents), which suggests that activity of these compounds first decreases as the hydrophobicity of substituents increases and after a certain point (inversion point ttx = 0.67), activity begins to increase. This may correspond to an allosteric reaction [54]. The indicator variable I is assigned the value of 1 and 0 for the presence and absence of N(CH3)2 substituent at the X position. Its positive coefficient suggests that the presence of a N(CH3)2 substituent at X position, increases the activity. REC is the relative effective concentration i.e., concentration relative to topotecan, whose value is arbitrarily assumed as 1, that is able to produce the same cleavage on the plasmid DNA in the presence of human topo I. 

The indicator variable I is assigned the value of 1 for the presence of amide derivatives and 0 for the esters. Its negative coefficient suggests that esters would be preferred over amides for this data set. nx is the calculated hydrophobic parameter of the X-substituents. Its positive coefficient suggests that the highly hydrophobic X-substituents would be preferred. 

MRx is the calculated molar refractivity of X-substituents, whereas I is an indicator variable taking the value of 1 and 0 for the presence and absence of a phenyl ring in the X-substituents. The negative sign of MRx brings out a steric effect for the X-substituents that do not appear to reach a hydrophobic surface for ttx (calculated hydrophobicity of X-substituents), r = 0.470. The indicator variable (I) with positive coefficient suggests that the presence of a phenyl ring in the X-substituents would be favorable. 

Dearden,. C., Ghafourian, T. Hydrogen bonding parameters for QSAR comparison of indicator variables, hydrogen bond counts, molecular orbital and other parameters. J. Chem. Inf. Comput. Sci. 1999, 39, 231-235. 

Aqueous solubility is selected to demonstrate the E-state application in QSPR studies. Huuskonen et al. modeled the aqueous solubihty of 734 diverse organic compounds with multiple linear regression (MLR) and artificial neural network (ANN) approaches [27]. The set of structural descriptors comprised 31 E-state atomic indices, and three indicator variables for pyridine, ahphatic hydrocarbons and aromatic hydrocarbons, respectively. The dataset of734 chemicals was divided into a training set ( =675), a vahdation set (n=38) and a test set (n=21). A comparison of the MLR results (training, r =0.94, s=0.58 vahdation r =0.84, s=0.67 test, r =0.80, s=0.87) and the ANN results (training, r =0.96, s=0.51 vahdation r =0.85, s=0.62 tesL r =0.84, s=0.75) indicates a smah improvement for the neural network model with five hidden neurons. These QSPR models may be used for a fast and rehable computahon of the aqueous solubihty for diverse orgarhc compounds. 

Polynomial regression with indicator variables is another recommended statistical method for analysis of fish-mercury data. This procedure, described by Tremblay et al. (1998), allows rigorous statistical comparison of mercury-to-length relations among years and is considered superior to simple hnear regression and analysis of covariance for analysis of data on mercury-length relations in fish. 

Tremblay G, Legendre P, Doyon J-F, Verdon R, Schetagne R. 1998. The use of polynomial regression analysis with indicator variables for interpretation of mercury in fish data. Biogeochemistry 40 189-201. 

Table 37.3 shows the complete table of eight indicator variables for 10 triply substituted tetracyclines [31 ] that have been tested for bacteriostatic activity (1/Z), which is defined here as the ratio of the number of colonies grown with a substituted and with the unsubstituted tetracycline. In this application we have three substitution positions, labelled U, V and W. The number of substituents at the three sites equals 2,3 and 3, respectively. Arbitrarily, we chose the compound with substituents H, NOj and NO2 at the sites U, V and W as the reference compound. This leads to a reduction of the number of indicator variables from eight to five, as shown in Table 37.4. The solution of the Free-Wilson model can be obtained directly by means of multiple regression ...

In the above expression the indicator variable I(X) takes the value 0 or 1, depending upon the absence or presence of the substituent X in a particular compound. The overall result of the regression is not significant at the 0.05 level of probability. This may be due to the unfavorable proportion of the number of compounds to the number of parameters in the regression equation (10 to 6). Only the indicator variable for substituent NHj at position W in the tetracycline molecule reaches significance (p = 0.02). This can be confirmed by looking at Table 37.4... 

RP-HPLC-k correlation including MCI related to non-dispersive intermolecular interactions, hydrogen-bonding indicator variable, Hong et al. 1996)... 

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