  Astronomical data is often uncertain with errors that are heteroscedastic
(different for each data point) and covariant between different dimensions.
Assuming that a set of D-dimensional data points can be described by a (D -
1)-dimensional plane with intrinsic scatter, we derive the general likelihood
function to be maximised to recover the best fitting model. Alongside the
mathematical description, we also release the hyper-fit package for the R
statistical language (github.com/asgr/hyper.fit) and a user-friendly web
interface for online fitting (hyperfit.icrar.org). The hyper-fit package offers
access to a large number of fitting routines, includes visualisation tools, and
is fully documented in an extensive user manual. Most of the hyper-fit
functionality is accessible via the web interface. In this paper we include
applications to toy examples and to real astronomical data from the literature:
the mass-size, Tully-Fisher, Fundamental Plane, and mass-spin-morphology
relations. In most cases the hyper-fit solutions are in good agreement with
published values, but uncover more information regarding the fitted model.
