Hansch best equation

Eqs. 63 — 68 reveal a typical dilemma in Hansch analysis while eqs. 65 — 68 are significantly better than eq. 63 and are based on more reasonable assumptions than eq. 64, which one of them is the best equation On the basis of the correlation coefficients r (the crutches of a QSAR beginner), eq. 67 is to be preferred eq. 66 seems to be the best one if the standard deviation s, a much better criterion, is considered. The differences in the correlation coefficients r and in the standard deviations s of eqs. 65—68 are rather small. However, if one applies the principle of parsimony, eqs. 66 and 67 should be omitted because too many parameters are included for such a small data set. 

LINEST is a function that is included in almost every spreadsheet software, including Microsoft Excel, OpenOffice.org Calc, and Google Docs Spreadsheet. LINEST accepts a table of values for a dependent variable (experimental activity) and any number of independent variables (such as parameters for use in a Hansch equation). LINEST then outputs the best-fit coefficients for the independent variables and certain statistical parameters for the regression. While Excel s Regression option in the Data Analysis tool is more user friendly, LINEST is much more widely available. 

The activity of 1,1jl-trifluoro 3-mercapto substituted phenyl propan-2-ones was not simply correlated with MR alone, therefore, a combination of Hammett a constant, Taft steric parameter (Eg) and Hansch hydrophobic constant (x) was included in the regression analysis. "Equation 36" was found to be of the best fit for compounds substituted in the meta and para positions. 

We chose 60 compounds with pl50 values ranging from 7.1 to 4.9 and subjected them to regression analysis using several physicochemical parameters (Table I). The 60 compounds contained variations in six positions of the basic structure. Quantitative structure-activity correlations with as many individual uncouplers in one equation have not yet been published. As far as we know, the Hansch approach has been applied to uncouplers of oxidative phosphorylation only twice first in 1965 by Hansch and co-workers to phenols and recently by Muraoka and Terada to N-phenylanthranilic acids. From Muraoka s data we recalculated the correlation with w and o- and obtained an equation which gave the best fit (last equation, Figure 3). 

In a manner similar to that outlined above for Foxtail without surfactant, the TFMS compounds were separated into two groups consisting of only meta- or only para-substituted derivatives, and the corresponding data gathered in each herbicidal test series for the three weed types (in the presence and absence of Tween 80) were fitted to the Hansch equation. 4-SCH3 and 3-SCH3 data points were omitted from all the fits (see below). The H-substituted parent compound was omitted when the TFMS compounds were separated into two groups (see above). For comparison with Equations 10-18, the final best-fit correlation equations obtained for Foxtail in the presence of 0.1% Tween 80 are tabulated below. 

Comparisons similar to those outlined in Equations 28-31 were likewise undertaken for the remaining cases (Foxtail with Tween 80 present Wild Mustard with and without Tween 80 present Cheat Grass without Tween 80 present). The statistical parameters for the final best-fit Hansch correlations for each case are listed in Table IX. 

On the basis of the statistical data in Table IX, the parent TFMS herbicide is obviously more correctly placed with the 4-substituted series members than with the 3-TFMS compounds. Finally, Table X lists, for comparative purposes, the best-fitting equational and statistical parameters for Hansch correlations of the herbicidal data for 4-substituted series members in which the parent compound has been included. These equations should be compared with those in Table XI. 

Optimum Correlation Equations. Table XI gives the final best-fit Hansch relationships which mathematically describe the pre-emergence herbicidal activity of the 3- and 4-substituted TFMS compounds under all conditions examined in this study. The results and conclusions reached... 

In view of the data presented, both questions can now be answered in the affirmative. The best-fit Hansch relationships in Table XI can be used to predict and to explain variations in TFMS grass and broadleaf activity. Furthermore, the appropriate equations in Table XI can be used... 

Mathematical analysis of the extrathermodynamic relationships exemplified by Hansch and Free-Wilson equations is done by the statistical method of regression analysis, the least-squares fit. With the aid of computers the best fit of a large amount of data to the... 

Charton s intermolecular force equation (IMF) is the best model covering all physicochemical and physicobiochemical events (97), but it is not in general use. Hansch (98), Fujita (99) and Verloop (100) all use internally consistent variations in their own research. By any consistent approach, accidental correlations are of little concern in the analysis of statistically large (n>30) sets of well measured binding data. Even smaller sets can reliably extract the major mechanistic components provided overdescription is not attempted (less than 4 data points/variable). 

Quantitative structure-activity relationships, based on the Hansch-Fujita approach (7), were analyzed for 13 compounds related to ch1 orf1uazuron (Figure 2), In the best correlation obtained (Equation 2), the only term needed to determine larvicidal activity log (I/LC90) against Spodoptera 1 i t u r a (common cutworm) is tt and the straight line obtained shows that substituents having larger 71 values show enhanced activity,... 

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