A correlation of zero between two quantitative variables indicates what?

A correlation of zero between two quantitative variables indicates that there is no linear association between them. This means that changes in one variable do not predict changes in the other variable in a linear manner. Essentially, when the correlation coefficient is zero, it suggests that the relationship between the two variables does not follow a straight-line pattern, even though they could still have some form of non-linear relationship.

It's important to note that correlation measures only linear relationships, so a correlation of zero does not imply that there is no relationship at all; it purely indicates the absence of any linear trend. Therefore, while there may be other types of associations present, such as quadratic or exponential, those would not be captured by the correlation coefficient, reinforcing that the proper interpretation of a zero correlation is a lack of linearity.