  Starting from a well defined local Lagrangian, we analyze the renormalization
group equations in terms of the two different arbitrary scales associated with
the regularization procedure and with the physical renormalization of the bare
parameters, respectively. We apply our formalism to the minimal subtraction
scheme using dimensional regularization. We first argue that the relevant
regularization scale in this case should be dimensionless. By relating bare and
renormalized parameters to physical observables, we calculate the coefficients
of the renormalization group equation up to two loop order in the $\phi^4$
theory. We show that the usual assumption, considering the bare parameters to
be independent of the regularization scale, is not a direct consequence of any
physical argument. The coefficients that we find in our two-loop calculation
are identical to the standard practice. We finally comment on the decoupling
properties of the renormalized coupling constant.
