Abstract
Some important problems in the application of multiple regression analysis (MRA) to the study of quantitative structure-activity relationships (QSAR) are the effect of so-called collinearity among the explaining variables on MRA and the chance correlation. In order to reduce these effects on MRA we have here employed a combination of principal component analysis (PCA) and MRA. Firstly all the explaining variables (xi) are normalized to the zero mean and one variance (x'i), then converted to zero correlation coefficient by using the technique of PCA. Principal component scores pertinent to each principal component (Zm) were next calculated, and MRA was carried out with a linear combination of Zm's. Important Zm's can easily be identified by applying the character of zero correlation coefficient among the variables. The above multiple regression equation is rewritten as a linear combination of x'i or xi by using the transformation matrix between Zm and x'i. This type of equation also seems to be useful for the purpose of predicting new drug structures. Actual calculation results are presented for some drug series. Finally, classification of the explaining variables was done by focusing on the factor loading values of the variables.
