# Generalized R-squared for Detecting Dependence

arXiv: https://arxiv.org/abs/1604.02736 · HTML: https://mlsanity.com/paper/1604.02736/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2016.

## Built on by (most cited first, 3 of 3)

- [A survey of some recent developments in measures of association](https://mlsanity.com/paper/2211.04702/) (2022)
- [Kernel Integrated R2: A Measure of Dependence](https://mlsanity.com/paper/2602.22985/) (2026)
- [A Comparative Analysis of Machine Learning Models for Long and Short-Term Forecasting of the Egyptian Stock Market: A Focus on EGX30](https://mlsanity.com/paper/2607.14391/) (2026)

## Abstract (arXiv)

Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimates are among the most powerful test statistics compared with several state-of-the-art methods.