In the previous section, we learned that the coefficient of correlation between two quantitative variables X and Y provides information on the existence of a linear relation between the two variables. This index, however, does not allow determining whether it is X that affects Y, if it is Y that affects X, or whether both X and Y are consequences of a phenomenon that affects both of them. Only more knowledge of the problem under study can allow some hypothesis of the dependence of one variable on another.
If a correlation between two variables is not found, it does not necessarily imply that they are independent, because they might have a nonlinear relationship.
Calculating correlation and covariance is a useful way to investigate whether there exists a linear relationship between variables, without the need to assume or fit a specific model...
