A scatter plot shows the relationship between two continuous variables x and y. If the relationship is linear or if the two variables have a bivariate normal distribution, then the least squares regression lines of y on x and x on y can predict one variable as a linear function of the other. These two regression lines suffice to identify the mean vector, the coefficient of determination, Pearson’s product moment correlation coefficient, and the ratio of the standard deviations (SD). So does a coverage ellipse! Additionally, we answer: In which direction must the points be projected to maximize (or minimize) the SD of the projections?
Rashid, M., Sarkar, J. "Visualizing Bivariate Data: What’s Your Point of View?" Journal of Probability and Statistical Science 19(1), 83-95, Feb. 2021