  Existing work on differentially private linear regression typically assumes
that end users can precisely set data bounds or algorithmic hyperparameters.
End users often struggle to meet these requirements without directly examining
the data (and violating privacy). Recent work has attempted to develop
solutions that shift these burdens from users to algorithms, but they struggle
to provide utility as the feature dimension grows. This work extends these
algorithms to higher-dimensional problems by introducing a differentially
private feature selection method based on Kendall rank correlation. We prove a
utility guarantee for the setting where features are normally distributed and
conduct experiments across 25 datasets. We find that adding this private
feature selection step before regression significantly broadens the
applicability of ``plug-and-play'' private linear regression algorithms at
little additional cost to privacy, computation, or decision-making by the end
user.
