The term “correlation” is one that is often used in economics. A correlation exists when two variables change in ways that are related to one another. Correlations can be positive or negative. A positive correlation exists when an increase in one variable and an increase in the other variable tend to occur together. A negative correlation exists when an increase in one variable is typically observed along with a decrease in the other variable. Please note that correlation does not imply causation. That is, the fact that variable A and variable B both increase does not necessarily mean that one of those has caused the other to rise.
In the case of rain and umbrellas, it is likely that a positive correlation will exist. If a particular area gets more rain than another area, it stands to reason that its people will need more protection from rain. Umbrellas provide protection from rain. Therefore, it makes sense that more umbrellas would be sold in the place with more rain.
In this case, there will be a positive correlation and we can imagine that there is causation as well since we can infer that the rain causes people to need umbrellas.