Utilizing Model Residuals to Identify Rental Properties of Interest: The
  Price Anomaly Score (PAS) and Its Application to Real-time Data in Manhattan
Youssef Sultan Jackson C. Rafter Huyen T. Nguyen
Understanding whether a property is priced fairly hinders buyers and sellers
since they usually do not have an objective viewpoint of the price distribution
for the overall market of their interest. Drawing from data collected of all
possible available properties for rent in Manhattan as of September 2023, this
paper aims to strengthen our understanding of model residuals; specifically on
machine learning models which generalize for a majority of the distribution of
a well-proportioned dataset. Most models generally perceive deviations from
predicted values as mere inaccuracies, however this paper proposes a different
vantage point: when generalizing to at least 75\% of the data-set, the
remaining deviations reveal significant insights. To harness these insights, we
introduce the Price Anomaly Score (PAS), a metric capable of capturing
boundaries between irregularly predicted prices. By combining relative pricing
discrepancies with statistical significance, the Price Anomaly Score (PAS)
offers a multifaceted view of rental valuations. This metric allows experts to
identify overpriced or underpriced properties within a dataset by aggregating
PAS values, then fine-tuning upper and lower boundaries to any threshold to set
indicators of choice.