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In statistics, correlation coefficient is used to determine the relationship between two variables. Not only that, but correlation coefficient also tells how strong or weak their relationship is and the direction in which their linearity is. The linearity and its direction is easily seen through scatterplots on the graph.
In this article, we will see how to interpret correlation coefficient in detail.
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The below Correlation coefficient is denoted by r and the value of r is always between +1 and -1. To have a reference to judge our r value, given below is the list of r values and what your correlation coefficient tells you if it is close to any of those:
r value | What it tells about the relation |
Exact -1 | Perfect downhill slope giving negative linear relationship |
-0.70 | Strong downhill slope with negative linear relationship |
-0.50 | Moderate downhill slope and negative relationship |
-0.30 | Weak downhill negative linear relationship |
0 | No relationship |
0.30 | Weak uphill positive linear relationship |
0.50 | Moderate uphill slope with positive relationship |
0.70 | Strong uphill positive linear relationship |
Exact +1 | Perfect uphill slope with positive linear relationship |
It is a perfect uphill with all the scatterplots on the line of best fit. So we can say it is a perfect positive linear relationship.
It shows a downhill but the scatterplots are scattered away from the line. It shows a not so strong linear relationship. So we can say it is a moderate negative relationship.
It shows a strong uphill pattern but is not as perfect as figure 1. As +0.85 is close to +0.70, we can say the correlation is a strong positive linear relationship.
We can see the scatterplots are far away from each other and the data does not make any sense. As the correlation is +0.15 which is close to 0, we can say that there is no relationship between the variables.
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When you see a scatterplot with points being plot far away from each other, it is advisable to not bother looking for a relationship in the variables. The graph itself tells that there is no linear relation there and you don’t have to worry about still finding the correlation for it.
When it comes to “no relationship”, there might be cases like above, where there is no relationship visible on the graph. But the other possibility can be that there is no “linear” relationship. Meaning, it might be the case that the scatterplot is in such a way that the line of best fit is a curve, like so:
The first figure shows a strong positive relationship and the second figure shows a strong negative relationship.
When it comes to the closeness of the correlations to the values shown in the table, the problem comes when the value is in between the determined r values. Like, you might get +0.45 and rush to make it a perfect positive linear relationship because you think it is close enough to +1. Just to avoid this, researchers wait till the correlation is above +0.5 or -0.5 to take it as a perfect linear relationship. But it is better to be ready for all the imperfections when you are measuring real-world data.
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