Classification of Solvents using Multivariate Statistical Methods

5 Classification of Solvents using Multivariate Statistical Methods 

In MRA, a dependent variable Y is described in terms of a series of explanatory variables Xi... X, as given in Eq. (3-14). 

It is assumed that all the explanatory variables are independent of each other and truly additive as well as relevant to the problem under study [144], MRA has been widely used to establish linear Gibbs energy (LGE) relationships [144, 149, 150], The Hammett equation is an example of the simplest form of MRA, namely bivariate statistical analysis. For applications of MRA to solvent effects on chemical reactions, see Chapter 7.7. 

The coordinates of each solvent point are (i) the factor (or principal component) scores F, and (ii) the factor (or principal component) loadings L. They give the information necessary to reconstitute the original physical properties D of any solvent according to Eq. (3-15). 

Eigenvectors and eigenvalues are the products of calculation at the beginning. They characterise the property of the square matrix (correlation or covariance) derived from the initial data matrix, and they allow calculation of the factor scores F and factor loadings L, respectively. 

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