What does a Pearson correlation coefficient of 0 show about a linear relationship?

A Pearson correlation coefficient of 0 indicates that there is no linear relationship between the two variables being analyzed.1

While this coefficient serves as a measure of association, it specifically quantifies the strength of a linear connection. A value of 0 signifies that the variables do not follow a linear pattern, though it does not necessarily mean there is no relationship of any kind—only that no linear one exists. It is also important to note that correlation does not imply causation, and researchers must carefully distinguish between independent and dependent variables to draw meaningful conclusions from their data.1