Autocorrelation

Understanding correlation

Correlation is a measure of the linear relationship between two numeric variables. In other words, it tells us how much two variables are related. A correlation coefficient is a number between $-1$ and $+1$ , and it gives not only the measure of how strong that relationship is but also the direction it leans toward.

For example, if the correlation coefficient between two variables is $0.8$, it means those variables are strongly related and that when one of them goes up, the other one tends to go up too. We could think of average temperature and ice cream sales as an example.

On the other hand, if the correlation coefficient is $-0.8$, it also means those variables are strongly related, but when one of them goes up, the other one usually goes down. An example of that case could be average temperature and coat sales.

Finally, if the correlation coefficient is zero (or close to zero), there is not much of a relationship between those two variables. An example could be average temperature and laptop sales.

If we plotted observations as dots in a plane where $x$ represents one of the variables and $y$ represents the other (a type of graph called scatterplot), different correlation coefficients would yield different shapes.