Highly Collinear Descriptors The Problem That Is Not

Finally, a word on that collinear descriptors...add nothing to mechanistic interpretation of QSAR or QSPR, in fact they detract from it. This is apolitical statement. 

Consider the following illustration Let us start with a simple regression (that is, a regression using one independent variable) for molar refraction or refractivity of octanes. Molar refractivity, MR, is a measure of the total polarizability of a mole of a substance and depends on the temperature, the index of refraction, and the pressure. It is defined as 

But here is a great surprise If one decides to use both useless descriptors, one obtains a very respectable regression equation  

We repeat, for the third time, that the orthogonalization of molecular descriptors was introduced into structure-property-activity studies about 25 years ago [7,20-28] and has only occasionally been used since then [29-41]. It is still today not widely known, not recognized as indispensible in QSAR and QSPR modeling if people want to interpret their models in terms of descriptors used in the construction of the regression equation. Repeating the same message three times deliberately is 

FIGURE 5.1 Schematic representation of the structure space in the case of two vectors spanning the space but individually not pointing to the property considered. 

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