A data science analysis of 88 house sales reveals the limitations of Ordinary Least Squares (OLS) regression when applied to heteroscedastic data. OLS predicted $164,000 for a home selling at $219,000, missing the actual price by $55,000. The article explains that OLS models the average, assuming constant variance, which fails when data spreads as the predictor variable increases.
In the example, prediction errors were narrow at low values but widened dramatically at higher values, potentially leaving clients waiting empty-handed. Quantile Regression offers a solution by creating prediction intervals using 5th and 95th percentile models. For the case study, this approach spanned $136,000 to $227,000, successfully capturing the true $219,000 sale price.
The post demonstrates how standard regression models can mislead in forecasting decisions when variance is not constant, and how quantile methods provide a more robust alternative for handling uneven data spreads.
Source: Towards Data Science · Summarized by HeadlinesBriefing