  We model the binding energies of rovibrational levels of the RbYb molecule
using experimental data from two-color photoassociation spectroscopy in
mixtures of ultracold $^{87}$Rb with various Yb isotopes. The model uses a
theoretical potential based on state-of-the-art \emph{ab initio} potentials,
further improved by least-squares fitting to the experimental data. We have
fixed the number of bound states supported by the potential curve, so that the
model is mass scaled, that is, it accurately describes the bound state energies
for all measured isotopic combinations. Such a model enables an accurate
prediction of the s-wave scattering lengths of all isotopic combinations of the
RbYb system. The reduced mass range is broad enough to cover the full
scattering lengths range from $-\infty$ to $+\infty$. For example, the
$^{87}$Rb$^{174}$Yb system is characterized by a large positive scattering
length of $+880(120)$~a.u., while $^{87}$Rb$^{173}$Yb has $a=-626(88)$~a.u.. On
the other hand $^{87}$Rb$^{170}$Yb has a very small scattering length of
$-14.5(1.8)$~a.u. confirmed by the pair's extremely low thermalization rate.
For isotopic combinations including $^{85}$Rb the variation of the interspecies
scattering lengths is much smoother ranging from $+39.0(1.6)$ a.u. for
$^{85}$Rb$^{176}$Yb to $+230(10)$ a.u. in the case of $^{85}$Rb$^{168}$Yb.
Hyperfine corrections to these scattering lengths are also given. We further
complement the fitted potential with interaction parameters calculated from
alternative methods. The recommended value of the van der Waals coefficient is
$C_6$=2837(13)~a.u. and is in agreement and more precise than the current
state-of-the-art theoretical predictions (S. G. Porsev, M. S. Safronova, A.
Derevianko, and C.W. Clark, arXiv:1307.2654 (2013)).
