We present results from an experiment aimed at using logs of interactions with a visual analytics application to better understand how interactions lead to insight generation. We performed an insight-based user study of a visual analytics application and ran post hoc quantitative analyses of participants' measured insight metrics and interaction logs. The quantitative analyses identified features of interaction that were correlated with insight characteristics, and we confirmed these findings using a qualitative analysis of video captured during the user study. Results of the experiment include design guidelines for the visual analytics application aimed at supporting insight generation. Furthermore, we demonstrated an analysis method using interaction logs that identified which interaction patterns led to insights, going beyond insight-based evaluations that only quantify insight characteristics. We also discuss choices and pitfalls encountered when applying this analysis method, such as the benefits and costs of applying an abstraction framework to application-specific actions before further analysis. Our method can be applied to evaluations of other visualization tools to inform the design of insight-promoting interactions and to better understand analyst behaviors.