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

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.