  Differential privacy is a strong mathematical notion of privacy. Still, a
prominent challenge when using differential privacy in real data collection is
understanding and counteracting the accuracy loss that differential privacy
imposes. As such, the accuracy-privacy trade-off of differential privacy needs
to be balanced on a case-by-case basis. Applications in the literature tend to
focus solely on analytical accuracy bounds, not include data in error
prediction, or use arbitrary settings to measure error empirically.
  To fill the gap in the literature, we propose a novel application of factor
experiments to create data aware error predictions. Basically, factor
experiments provide a systematic approach to conducting empirical experiments.
To demonstrate our methodology in action, we conduct a case study where error
is dependent on arbitrarily complex tree structures. We first construct a tool
to simulate poll data. Next, we use our simulated data to construct a least
squares model to predict error. Last, we show how to validate the model.
Consequently, our contribution is a method for constructing error prediction
models that are data aware.
