Correlations between Empirical Parameters and Other Measurable Solvent Properties

2 CORRELATIONS BETWEEN EMPIRICAL PARAMETERS AND OTHER MEASURABLE SOLVENT PROPERTIES 

One would like to be able to understand the effects of solvents upon reactions and spectra in terms of properties of molecules or bulk solvents such as the following  

With this in view, statistical correlations have been undertaken by a number of authors, either pairwise (between two variables at a time) or between one, believed to be composite, and several others in multiple linear correlation, that is to say, seeking relationships of the form of Equation 4.1. 

The 23 parameters listed in Table 4.1 (a selection of those listed in Tables A.2a and b) were subjected to linear correlation, two at a time. The results are displayed in Table 4.2 the binary correlation coefficients r.j along with the numbers n.. of solvents for which values of both parameters were available. Values of r. below 0.2 suggest that the parameters labeled i and j were essentially independent values close to unity (lr,, l 0.9) suggest that the two measure essentially the same property. Intermediate values suggest mixing of two or more. For instance,, AN, and W 

To disentangle these cross-relationships, the statistical method of principal component analysis (PCA) (Eliasson et ah, 1982 Johnson, 1998 Malinowski and Howery, 1980 Thielemans and Massart, 1985) may be used. The purpose of PCA is to express the various properties in terms of a set of new variables, chosen to be independent of each other, that is to say, they are orthogonal. Any of the original variables can be written as a hnear combination of the orthogonal set, just as a vector in three-dimensional space can be written in terms of three base vectors, mutually at right angles. Here, then, we write for each property P . 

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