Source: Correlation Examples; Public Domain: http://en.wikipedia.org/w/index.php?title=File:Correlation_examples2.svg&page=1
This tutorial covers positive and negative correlations. With a positive correlation, your r is positive. And then the other piece is that it's not near 0. Something like 0.1, it would be a positive correlation. But because it's near 0, it's not a very strong one. So we wouldn't necessarily call that positive.
On the other hand, negative correlation, you can guess it, r is going to be negative. And then again, r is not near 0. A value like negative 0.1 is going to be very close to 0. So it's not a very strong correlation anyways. So even though it's a negative number, we might not necessarily say that it's a negative correlation.
And then as a quick review, this r that we're talking about, that r is just a measure of the strength of the linear association. So again, it's only talking about linear associations. We could have non-linear relationships. So the variables have a relationship. It's just not linear. It could make a curve. It could make a circle, anything like that that's not going to approximate a line. Even though they have some sort of relationship, the r is probably going to come up as close to 0 because r is only telling us how well it fits a line.
Now we could have relatively 0 correlation. And that means that the variables don't have much association. And it's that they don't have much linear association. So again, r is only talking about later. So if you get something that's relatively 0 like that 0.1 I talked about a moment ago or the negative 0.1, we're going to say that's relatively 0 correlation.
So this here shows us some positive and negative correlations. Here we have positive 1, positive 1, positive 1, positive 1. So they're all making pretty positive, straight, nicely compacted lines. We have positive 0.8. That's a little bit more diffuse. Positive 0.4. That's much more diffuse.
On the other hand, we have some negative. We have negative 1, negative 1, negative 1, negative 1. Even though the lines have different pitches or different angles, different slopes, they're still all negative 1. It's a nice, tight line. The data is very closely associated. And then we have negative 0.8, which is a bit more diffuse, and negative 0.4, which is much more diffuse.
Down the bottom row here, we have sets of correlations that are 0 or relatively 0. And again, they can have a relationship. It's just a non-linear relationship. So this set of data has some sort of relationship that makes this W curve. Here, this data has some sort of relationship that has it make a U. This data has some sort of association or relationship. It forms a circle. But because it's 0-- sorry. Because it's non-linear, it's going to come up with an r of 0 or very close to 0. This has been your tutorial on positive and negative correlations.
The type of correlation present when two variables have a positive correlation coefficient that is not near 0.
The type of correlation present when two variables have a negative correlation coefficient that is not near 0.
Relative Zero Correlation
The type of correlation present when two variables have a correlation coefficient that is close to 0.
Associations between two variables that can be modeled better with a curve than a line
Source: Images, Public Domain: http://en.wikipedia.org/w/index.php?title=File:Correlation_examples2.svg&page=1