# Diagnosing Heteroskedasticity and Resolving Multicollinearity Paradoxes in Physicochemical Property Prediction

arXiv: https://arxiv.org/abs/2512.24643 · HTML: https://mlsanity.com/paper/2512.24643/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 5 of 5)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Scrutinizing XAI using linear ground-truth data with suppressor variables](https://mlsanity.com/paper/2111.07473/) (2021)
- [Benchmarking Pretrained Molecular Embedding Models For Molecular Representation Learning](https://mlsanity.com/paper/2508.06199/) (2025)
- [Transformers for molecular property prediction: Domain adaptation efficiently improves performance](https://mlsanity.com/paper/2503.03360/) (2025)

## Abstract (arXiv)

Lipophilicity (logP) prediction remains central to drug discovery, yet linear regression models for this task frequently violate statistical assumptions in ways that invalidate their reported performance metrics. We analyzed 426,850 bioactive molecules from a rigorously curated intersection of PubChem, ChEMBL, and eMolecules databases, revealing severe heteroskedasticity in linear models predicting computed logP values (XLOGP3): residual variance increases 4.2-fold in lipophilic regions (logP greater than 5) compared to balanced regions (logP 2 to 4). Classical remediation strategies (Weighted Least Squares and Box-Cox transformation) failed to resolve this violation (Breusch-Pagan p-value less than 0.0001 for all variants). Tree-based ensemble methods (Random Forest R-squared of 0.764, XGBoost R-squared of 0.765) proved inherently robust to heteroskedasticity while delivering superior predictive performance. SHAP analysis resolved a critical multicollinearity paradox: despite a weak bivariate correlation of 0.146, molecular weight emerged as the single most important predictor (mean absolute SHAP value of 0.573), with its effect suppressed in simple correlations by confounding with topological polar surface area (TPSA). These findings demonstrate that standard linear models face fundamental challenges for computed lipophilicity prediction and provide a principled framework for interpreting ensemble models in QSAR applications.