What Is Correlation?
Correlation is a relationship between variables. by looking at the correlation we can get an idea of how strong this relationship is and what type of relationship exists between our variable. One feature of a correlation is its direction. By looking at whether or not a correlation coefficient has a positive or negative sign, we can tell what is happening between the variables.
Also when we take a look at a graph of the correlation, we can quickly see what direction or correlation is there. For example a positive correlation occurs when both variables are increasing or decreasing at the same time. our dataset will fall in an upward sloping direction when we have a positive correlation so if we have a dataset that has points that look like in this picture.
You can see that if we draw a line through this data going in an upward sloping direction. What this tells us is that as our variable X increases our variable Y is also increasing.
Now a negative correlation is when our variables are going in opposite directions meaning that as one variable increases the other decreases this gives us a negative correlation. In this case our dataset will fall in a downward sloping direction. So if we need have a dataset looks like this and we draw the line that best fits the dataset you can see it is going down.
Now what this means is that as our values for X increased as we move along the x-axis our values for y are decreasing so we can see here that our variables are going in opposite direction as one is increasing in this case are x values, then y is decreasing.
Now if our dataset doesn't seem to follow either one of these predictable patterns that it may be described as having no correlation. No correlation means there's no discernible pattern that can be detected between the variables meaning that no relationship exist.
This can happen in two different cases:
- The first one when our dataset appears to be scattered where it has no real pattern so let's say for example we had a dataset that looks like this. Now we draw a line through this like we did for the positive and negative correlation, we would really have a straight line this would be the best fit. if we ever see this type of dataset or we can draw straight horizontal line then that means that there's no real relationship between X and Y.
- We could also have a dataset that would go the in both opposite directions as well. This means that it's not a reliable linear relationship we can see here that when X is really low or when it's really high, y is low. We can see that drawing a best fit line to our dataset here does not lead to a sloping line or signifying a direction.
A positive correlation if signified by a positive sign and both of the variables are going in the same direction this can be from 0 to +1. A negative correlation means that our correlation is from 0 to -1 or has a negative sign and our variables are going in opposite directions. No correlation will be close to zero so we'll have no sign. It means there's no discernible relationship between the variables.
Another feature up of a correlation is it strength. The closer the number is to one regardless of the sign of the direction whether it's positive or negative the stronger the correlation is.
Although we would have to look up the critical r or correlation coefficient which is affected by the sample size to determine whether or not the correlation is large enough to be significant, We can get a basic idea of the strength by simply look at the correlation coefficient itself.
When r equals to (+ or -) 0.8 or higher, it is typically referred to as a strong correlation and r equals to you (+ or -) 0.5 to 2.8 is considered a medium correlation but r equals to you (+ or -) 0.4 or lower is usually referred to as a week correlation.
For example a strong positive correlation would fit a straight or would be very close to that straight line so very similar to this.
If we had a dataset like this where the best fit line it goes right through the middle, then that would be a very strong positive correlation the closer those dots -the points in our dataset- to that line the stronger the relationship the stronger correlation the greater that number will be to 1. For a weak positive correlation dataset will have an upward sloping direction.
You can see here that our points are spread out more they're not packed greatly around the line that we have here with the best fitting line so this would represent a weaker correlation.
Overall remember that correlations tell us about our relationship between variables how strong the relationship is and in what direction those variables are going however we cannot infere causality or say that one variable is impacting or affecting the other