A multivariate statistical regression technique is proposed to address underlying nonlinear correlations among the predictor variables, as well as between the predictor variables and the response variable. The method is based on a neural network architecture that preserves the orthogonality properties of the principal component analysis (PCA) approach. Applications to a synthetic dataset and a benchmark example demonstrate the key features of the method, and another example shows the utility of the method in using process measurements to predict the shelf-life stability characteristics of a pharmaceutical product.