 Correlation describes the degree of relationship between two variables. Let's call them A and B. A positive correlation means that when variable A increases, so does variable B. If variable A decreases, so does variable B. A negative correlation means that as one variable increases, the other decreases. And these are describing our linear relationship. So when we talk about Pearson's R or Spearman's Rho, we're talking about the line that best describes our data. Let's look at an example of a high positive correlation. On the x-axis is the waiting time between eruptions of the old faithful geyser. It's a geyser in one of America's national parks. On the y-axis is the duration of each eruption. And as you can see, the longer the waiting time is, the longer the subsequent eruption is going to be. If we draw the line that best fits this data, we'll see that we have a very high correlation, 0.91, where that absolute maximum is 1.0. The maximum negative correlation, by the way, is negative 1. And we have 272 data points here. The next graph shows a very low negative correlation of negative 0.17. On the x-axis is the temperature at various times during two days. And on the y-axis is the dew point. So they're related, but just barely. One thing that's important to notice is that this correlation coefficient, again, is for a linear relationship. And not all relationships are linear. Here, for example, on the x-axis is the time of day. And on the y-axis is the temperature and degrees. Even though it turns out that a straight line does fit this data fairly well with a R of 0.62, it's very clear from the graph that the relationship is not really linear. Moral of the story, whenever you get your data, always graph it first before you start doing the correlation coefficient. The most important thing to know about correlation is that correlation is necessary but not sufficient for causation. By necessary, I mean if A causes B, they have to at least be related. If A and B aren't related, then there's absolutely no way that one can cause the other. By not sufficient, I mean just because A and B are related does not automatically mean that A causes B or B causes A. For example, every time the minute hand of my watch hits the 12, the bell in the tower across town goes off. Now does that mean that my watch is causing the bell to go off, or that the bell is causing the minute hand on my watch to move? Of course not. It just so happens that we both have our clocks set to the same time. So again, just because things are related does not mean that one causes the other. It's only your first clue that that might be the case.