Correlation of graph-theoretical parameters with biological activity

Ośmialowski and Kaliszan calculated graph-theoretical indices for substituted isonicotinic hydrazides and used simple and multiple regression to search (unsuccessfully) for correlations with biological activity. The present paper describes successful searches for correlation in the same data set using principal component analysis (PCA) with multivariate outlier testing and also using stepwise multiple regression. Following PCA, correlation with biological activity always appeared in the second principal component, not the first, that is, after projection of the data points into the (n - 1)-space orthogonal to the first principal component axis. In that space, the principal component score was a more accurate predictor of biological activity than were equations provided by multiple regression or stepwise multiple regression using the underlying variables. A multivariate outlier test identified one observation as discordant, and removing that observation improved prediction further.