In the previous chapter, 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, or 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 a variable on another.
Note
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 a linear relationship exists between variables, without having to assume or fit a specific model to our data. It can happen that two variables have a small or no linear correlation, meaning a strong nonlinear relationship...