Reminder of the Directional Nature of the Product–Moment Correlation Coefficient - Metsämuuronen Jari (Academia, 2022)
Product–moment correlation coefficient (PMC), “Pearson correlation”, is usually taken as a symmetric measure of association because it produces equal estimate irrespective of how two variables in the analysis are declared. However, when the scales of the variables differ from each other, PMC is unambiguously a directional measure directed so that the variable with a wider scale (X) explains the order or response pattern in the variable with a narrower scale (g) and not in the opposite direction nor symmetrically. Hence, whenever the statistic r2 is calculated as is usually seen in the general scatterplots, this statistic is always a directional measure if the scales differ from each other; this should be kept in mind when interpreting r-squared statistics.