Visualizing the Regression Lines and the Correlation Coefficient for Bivariate Discrete Random Variables Authors

Authors

• Mamunur Rashid, DePauw UniversityFollow
• Jyotirmoy Sarkar, Indiana University Purdue University Indianapolis

Document Type

Article

Publication Date

10-26-2026

Abstract

Sarkar and Rashid (2024) visualized the joint probabilities of two discrete random variables using a 2D disc plot from which they graphically obtained the conditional distributions of 𝑌 given 𝑋=𝑎, and 𝑋 given 𝑌=𝑏; and the marginal distributions of 𝑋, 𝑌, 𝑋+𝑌, 𝑋−𝑌, and 𝑐𝑋+𝑑𝑌. Sarkar and Rashid (2025) visualized the mean, mean deviation, and standard deviation of any discrete random variable using a disc plot. Here, starting with the 2D disc plot, we visualize the correlation coefficient between X and Y, and the linear regression of one variable from the other. Such visualizations help users better comprehend these concepts. Thus, this paper develops a unified geometric framework to visualize conditional means, the overall mean vector, least-squares regression lines, and the correlation coefficient, starting from the disc plot.

Recommended Citation

Sarkar, Jyotirmoy, and Rashid, Mamunur, Visualizing the Regression Lines and the Correlation Coefficient for Bivariate Discrete Random Variables, Journal of Probability and Statistical Science 24 no. 2 (2026)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.