The white matter contains long-range connections between different brain regions and the organization of these connections holds important implications for brain function in health and disease. Tractometry uses diffusion-weighted magnetic resonance imaging (dMRI) to quantify tissue properties along the trajectories of these connections. Statistical inference from tractometry usually either averages these quantities along the length of each fiber bundle or computes regression models separately for each point along every one of the bundles. These approaches are limited in their sensitivity, in the former case, or in their statistical power, in the latter. We developed a method based on the sparse group lasso (SGL) that takes into account tissue properties along all of the bundles and selects informative features by enforcing both global and bundle-level sparsity. We demonstrate the performance of the method in two settings: i) in a classification setting, patients with amyotrophic lateral sclerosis (ALS) are accurately distinguished from matched controls. Furthermore, SGL identifies the corticospinal tract as important for this classification, correctly finding the parts of the white matter known to be affected by the disease. ii) In a regression setting, SGL accurately predicts "brain age." In this case, the weights are distributed throughout the white matter indicating that many different regions of the white matter change over the lifespan. Thus, SGL leverages the multivariate relationships between diffusion properties in multiple bundles to make accurate phenotypic predictions while simultaneously discovering the most relevant features of the white matter.