Multiple regression analysis with optimal molecular descriptors

We consider construction of optimal molecular descriptors to be used for multiple regression analysis of several properties of alcohols. The descriptors are obtained by considering shorter paths with variable weight x for carbon-oxygen bond in alcohol. In particular we consider as molecular descriptors paths of length 1, 2 and 3. The multiple regression analysis of the following molecular properties was examined: - log S (S = solubility), CSA (cavity surface area), log P (P = octanol/water partition), and log gamma (gamma = infinite solution activity coefficient). By minimizing the standard error of the regression for each property we found optimal variable weight.