As more data on exoplanets have been collected, some apparent correlations between planetary and stellar properties have started to emerge. However, the true nature of such correlations is often unclear as stellar properties are often interrelated. In particular, it is unresolved whether these correlations are due to the age of the system — pointing to evolution over time being an important factor — or other parameters to which the age may be related, such as stellar mass or stellar temperature. The situation is complicated further by the possibilities of selection biases, small number statistics, uncertainties in stellar age, and orbital evolution timescales that are typically much shorter than the range of observed ages. Here we develop a Bayesian statistical framework to assess the robustness of such observed correlations and to determine whether they are indeed due to evolutionary processes, are more likely to reflect different formation scenarios, or are merely coincidental. We apply this framework to the case of 2:1 resonances, where it has been proposed that systems with 2:1 resonances tend to be younger than those without, and find nearly equal support for the hypothesis of a correlation with age as for the hypothesis that the apparent trend is coincidental. We also apply this framework to the question of whether stellar obliquities are more correlated with age, more correlated with temperature, or are not related to system properties. The results very strongly favor a relation with temperature, i.e., hot stars have high obliquities and cool stars are aligned with their planetary orbits, which corroborates prior work. Finally, we examine whether the currently available hot Jupiter data truly display a trend of eccentricity due to age, and indeed find very strong support for the hypothesis that the set of known hot Jupiters show the circularization of orbital eccentricities over time.