Multiple linear regression, solvent effects

Using a multiple linear regression computer program, a set of substituent parameters was calculated for a number of the most commonly occurring groups. The calculated substituent effects allow a prediction of the chemical shifts of the exterior and central carbon atoms of the allene with standard deviations of l.Sand 2.3 ppm, respectively Although most compounds were measured as neat liquids, for a number of compounds duplicatel measurements were obtained in various solvents. 

Numerous authors have devised multiple linear regression approaches to the eorrelation of solvent effects, the intent being to widen the applieability of the eorrelation and to develop insight into the moleeular factors controlling the eorrelated proeess. For example, Zilian treated polarity as a eombination of effeets measured by molar refraction, AN, and DN. Koppel and Palm write... 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

In contrast to points (l)-(3) of discussion, the effect of ion association on the conductivity of concentrated solutions is proven only with difficulty. Previously published reviews refer mainly to the permittivity of the solvent or quote some theoretical expressions for association constants which only take permittivity and distance parameters into account. Ue and Mori [212] in a recent publication tried a multiple linear regression based Eq. (62)... 

Equations containing a number of solvent parameters in linear or multiple linear regression and expressing the effect of the solvent on the rate of the reaction or the thermodynamic equilibrium constant. See Ej Values Kamlet-Taft Solvent Parameter Koppel-Palm Solvent Parameter Z Value... 

Correlations with Reactivity Results. In addition to the correlations described previously, we have used the scale, alone or in combination with the 7T scale (in which case all correlations have been by the method of multiple linear regression analysis) to rationalize solvent effects on many additional types of properties and reactivity parameters. Representative examples are as follows. 

Heats of Transfer of the Et4N l Ion Pair. The AG c terms from methanol into nonprotic solvents for the tetraethylammonium iodide ion pair (30), reported by Abraham (44b), were discussed earlier in connection with the tt and d parameters. When results in the 18 protic and nonprotic aliphatic solvents (1,2,7,11,16,18,25,28,29,32,50,101,102,103,104,105,111,112) are considered together, the effects of type-A hydrogen bonding by HBD solvents to iodide become evident. The multiple linear regression equation becomes. 

Here, however, the high r value for Equation 137o masks an important contribution of solvent polarity to medium effects on Ls. Multiple linear regression analysis (ex solvents 70,75 for which tc values are not yet known) leads to... 

The procedure for parameterization of solvent electrophilicity has been criticized, mainly because it was found that the use of t(30) instead of E in the multiple regression treatment of solvent effects is often quite successful see reference [15, 116] for examples. It has been shown that values of t(30) and E are linearly correlated, at least for solvents with an t(30) value of greater than ca. 40 kcal/mol [178]. This calls into question the value of Koppel and Palm s division of t(30) into pure electrophilicity effects and non-specific effects by means of Eq. (7-51). 

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