  Scaling relations are very useful tools for estimating unknown stellar
quantities. Within this framework, eclipsing binaries are ideal for this goal
because their mass and radius are known with a very good level of accuracy,
leading to improved constraints on the models. We aim to provide empirical
relations for the mass and radius as function of luminosity, metallicity, and
age. We investigate, in particular, the impact of metallicity and age on those
relations. We used a multi-dimensional fit approach based on the data from
DEBCat, an updated catalogue of eclipsing binary observations such as mass,
radius, luminosity, effective temperature, gravity, and metallicity. We used
the {PARAM web interface for the Bayesian estimation of stellar parameters,
along with} the stellar evolutionary code MESA to estimate the binary age,
assuming a coeval hypothesis for both members. We derived the mass and
radius-luminosity-metallicity-age relations using 56 stars, {with metallicity
and mass in the range -0.34<[Fe/H]<0.27 and 0.66<M/M{_\odot}<1.8}. With that,
the observed mass and radius are reproduced with an accuracy of 3.5% and 5.9%,
respectively, which is consistent with the other results in literature. We
conclude that including the age in such relations increases the quality of the
fit, particularly in terms of the mass, as compared to the radius. On the other
hand, as other authors have noted, we observed an higher dispersion on the mass
relation than in that of the radius. We propose that this is due to a stellar
age effect.
