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 characterize 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 analyze 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 analyze 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 GALA and PLATO will allow us to tightly constrain stellar masses, ages, and radii with machine learning for the purposes of Galactic and planetary studies.