In the era of big data, along with machine learning and databases, visualization has become critical to managing complex and overwhelming data problems. Vision science has been a foundation of data visualization for decades. As the systems that use visualization become more complex, advances in vision science are needed to provide fundamental theory to visualization researchers and practitioners to address emerging challenges. In this paper, we present our work on modeling the perception of correlation in bivariate visualizations using the Weber’s Law. These Weber models can be applied to definitively compare and evaluate the effectiveness of these visualizations. We further demonstrate that the reason for this finding is that people approximate correlation using visual features that are known to follow the Weber’s Law. These findings have multiple implications. One practical implication is that results like these can guide practitioners in choosing the appropriate visualization. In the context of big data, this result can lead to perceptually-driven computational techniques. For instance, it could be used for quickly sampling from big data in a way that preserves important data features, which can lead to better computational performance, a less overwhelming user experience, and more fluid interaction.