Quantile Regression with Q1/Q3 Anchoring: A Robust Alternative for Outlier-Resistant Modeling

Outliers introduce considerable difficulties in statistical modeling and regression analysis by skewing parameter estimates and reducing model reliability. To mitigate these effects, we introduce an enhanced Quantile Regression (QR) framework that strategically incorporates the 25th (Q1) and 75th (Q3) percentiles of the target variable. By emphasizing these robust statistical markers, our approach effectively minimizes the influence of extreme values while preserving the underlying data structure. Through comprehensive evaluations across multiple datasets, including Iris, Fish, Advertising Budget and Sales, and Geyser, we demonstrate that this method consistently delivers stable and accurate predictions. The experimental results further highlight the superior resilience of QR compared to conventional Linear Regression (LR), particularly in handling datasets affected by noise and outliers.