This chapter outlines regression-and projection-based approaches useful for QSAR analysis in predictive toxicology. The methods discussed and exemplified are: multiple linear regression (MLR), principal component analysis (PCA), principal component regression (PCR), and partial least squares projections to latent structures (PLS). Two QSAR data sets, drawn from the fields of environmental toxicology and drug design, are worked out in detail, showing the benefits of these methods. PCA is useful when overviewing a data set and
exploring relationships among compounds and relationships among variables. MLR, PCR, and PLS are used for establishing the QSARs. Additionally, the concept of statistical molecular design is considered, which is an essential ingredient for selecting an informative training set of compounds for QSAR calibration.