We consider the problem of maintaining the data-structures of a partition-based regression procedure in a setting where the training
data arrives sequentially over time. We prove that it is possible to maintain such a structure in time $Oparen{log n}$ at any time step $n$ while achieving a nearly-optimal regression rate of $tilde{O}(n^{-2/(2+d)})$
in terms of the unknown metric dimension $d$. Finally we prove a new regression lower-bound which is independent of a given data size, and hence is more appropriate for the streaming setting.