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4 Tutorials that teach Positive and Negative Correlations
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Positive and Negative Correlations
Common Core: 8.SP.1 S.ID.8

Positive and Negative Correlations

Author: Ryan Backman
Description:

Determine a given scenario as having a positive or negative correlation.

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Hi. This tutorial covers Positive and Negative Correlations. So recall that correlation coefficient measures the direction and strength of a linear association. So both direction and strength are important. So hopefully, you have a little bit of experience calculating the correlation coefficient. Now, we're going to look at how to interpret that value, and direction and strength are both important things to comment on.

So the direction of a linear association can either be positive or negative. A positive association will increase from left to right. A negative association will decrease from left to right. So a positive association is going to look more like that. A negative association is going to look more like that. OK?

Now, the strength of a linear association can either be near 0, moderate, or strong. OK? So let's look at just rules of rules of thumb that help you interpret that value of r, once you have it. So generally, if you get an r value between negative 1 and negative 0.8, including both of those values, what we do is we call that a strong negative association. So the direction is negative, and the strength is strong. OK? What that will mean is that we're going to decrease from left to right, and those points on your scatter plot are going to be pretty tightly clustered around a straight line.

A moderate negative association is generally between negative 0.8 and negative 0.5, not including the negative 0.8. So if we had something exactly negative 0.8 for an r value, that would be considered a strong negative association. So moderate negative association, again, it's going to decrease from left to right, but it's going to be moderate. So the points will not be as tightly clustered around that line.

Now, anything really between negative 0.5 and positive 0.5, if we don't really have a very strong association in either the positive direction or the negative direction, what we can say is that's just a relatively 0 association. OK? It's just very weak, no real association in the positive or negative direction. So what we can do is called that relatively 0. Now, if we go 0.5 to 0.8-- we can see that there's some symmetry going on here-- we have a moderate positive association. 0.8 to 1, we have a strong positive association, and again, that boundary point at 0.8 is going to go in the strong category.

All right. So positive correlation, it's a type of correlation present when two variables have a correlation coefficient generally greater than or equal to 0.5. So I wrote generally there, because again, those breakdowns of the r value is just a rule of thumb. A negative correlation, a type of correlation present when two variables have a correlation coefficient generally less than or equal to negative 0.5. And relatively 0 correlation, the type of correlation present when two variables have a correlation coefficient between negative 0.5 and positive 0.5. I put exclusive, because we're not going to include those values.

All right. So let's take a look at some scatter plots now. OK. Notice, we have the x-axis as all of the horizontal axes, and y-axes are vertical. So we can see in this first scatter plot, we have a strong negative association. We can see it's decreasing from left to right, and those points are really tightly clustered around that straight line there. OK?

If we go to r equals negative 0.5, this is just barely a moderate negative association. So again, it's decreasing from left to right, but now we do have a little more scatter around that line. OK. If we look at r equals 0, notice we just have a big cloud of points, no association in either direction, positive or negative. OK?

If we look at this one, we have r equals 0.5. Again, this would be a moderate positive association. r equals 0.9, strong positive association, so tightly clustered around that line. And r equals 1, also a strong positive association. Sometimes, we even call this a perfect positive association, because everything's right in line there. OK?

So again, it's important when you're interpreting r that it is a linear relationship. OK? A non-linear relationship, those are associations between two variables that can be better modeled with a curve than a line. The use of the term correlation and calculation of the correlation coefficient should not be applied to non-linear relationships.

So if we had, say, a scatter plot, and the data comes out, where we can see that there is a pretty significant curve there, we might not want to use the word correlation or calculate r in this case. Because it seems like that association would be better modeled with a curve rather than a line. This has been the tutorial on Positive and Negative Correlations. Thanks for watching.

Terms to Know
Negative Correlation

The type of correlation present when two variables have a correlation coefficient generally less than or equal to -0.5.

Non-linear Relationships

Associations between two variables that can be modeled better with a curve than a line.

Positive Correlation

The type of correlation present when two variables have a correlation coefficient generally greater than or equal to 0.5.

Relative Zero Correlation

The type of correlation present when two variables have a correlation coefficient generally between -0.5 and 0.5.