  Astronomy is in an era where all-sky surveys are mapping the Galaxy. The
plethora of photometric, spectroscopic, asteroseismic and astrometric data
allows us to characterise the comprising stars in detail. Here we quantify to
what extent precise stellar observations reveal information about the
properties of a star, including properties that are unobserved, or even
unobservable. We analyse the diagnostic potential of classical and
asteroseismic observations for inferring stellar parameters such as age, mass
and radius from evolutionary tracks of solar-like oscillators on the lower main
sequence. We perform rank correlation tests in order to determine the capacity
of each observable quantity to probe structural components of stars and infer
their evolutionary histories. We also analyse the principal components of
classic and asteroseismic observables to highlight the degree of redundancy
present in the measured quantities and demonstrate the extent to which
information of the model parameters can be extracted. We perform multiple
regression using combinations of observable quantities in a grid of
evolutionary simulations and appraise the predictive utility of each
combination in determining the properties of stars. We identify the
combinations that are useful and provide limits to where each type of
observable quantity can reveal information about a star. We investigate the
accuracy with which targets in the upcoming TESS and PLATO missions can be
characterized. We demonstrate that the combination of observations from GAIA
and PLATO will allow us to tightly constrain stellar masses, ages and radii
with machine learning for the purposes of Galactic and planetary studies.
