Is it possible to determine a rotation speed (Vr) using other known V-Speeds?
From FAR 23.51 that covers normal, utility, acrobatic, and commuter category airplanes:


  For multiengine landplanes, VR,
  must not be less than the greater of
  1.05 VMC; or 1.10 VS1


So 110% of the Vs of a particular configuration works. (Do not use for flight.)




Note from @Pondlife: 23.51 has been superseded with 23.2115 and the quoted definition is no longer there.
Related: What makes V1 one or two knots less than Vr on this performance table?