  One approach to tackle regression in nonstandard spaces is Fr\'echet
regression, where the value of the regression function at each point is
estimated via a Fr\'echet mean calculated from an estimated objective function.
A second approach is geodesic regression, which builds upon fitting geodesics
to observations by a least squares method. We compare these two approaches by
using them to transform three of the most important regression estimators in
statistics - linear regression, local linear regression, and trigonometric
projection estimator - to settings where responses live in a metric space. The
resulting procedures consist of known estimators as well as new methods. We
investigate their rates of convergence in general settings and compare their
performance in a simulation study on the sphere.
