In this paper, we describe how two multivariate statistical techniques can be used to investigate how different structures within the brain vary statistically relative to each other. The first of these techniques is canonical correlation analysis which extracts and quantifies correlated behaviour between two sets of vector variables. The second technique is partial least squares regression which determines the best factors within a first set of vector variables for predicting a vector variable from a second set. We applied these techniques to 178 sets of 3D MR images of the brain to quantify and predict correlated behaviour between 18 sub-cortical structures. Pairwise canonical correlation analysis of the structures gave correlation coefficients between 0.51 and 0.67, with adjacent structures possessing the strongest correlations. Pairwise predictions of the structures using partial least squares regression produced an overall sum squared error of 4.26 mm2, compared with an error of 6.75 mm2 produced when using the mean shape as the prediction. We also indicate how the correlation strengths between structures can be used to inform a hierarchical scheme in which partial least squares regression is combined with a model fitting algorithm to further improve prediction accuracy.