Correlation Coefficient

Not everybody will be aware of what a correlation coefficient is, and simply put, it measures the strength of a linear relationship between two things. So what is a linear relationship? Again, simply put, if one goes up, so does the other one; in a straight line. If one goes up and the other one goes down, that can be linear relationship too; just in the opposite direction.

A short way of noting a correlation coefficient is rxy and you will see that used throughout the rest of this blog article.

The rxy is a number between 1 and -1. A positive number indicates the strength of a linear relationship when both are going up. A negative number indicates the strength of a linear relationship when one is going up and the other is going down. The closer the number is to zero, the less evidence there is of a linear relationship. The closer the number is to one or negative one, the more evidence there is of a linear relationship.

Why is a correlation coefficient important? It is important because we like to try and predict things. The stronger the evidence of a linear relationship there is, the more confident we feel about using one to predict another.

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A perfect example

Take, for example, a spring and weight compression; that is a linear relationship. If you were to compress a "perfect" 100lb spring with 100, 200, 300, 400, etc. lbs, then it would compress 1in, 2in, 3in, 4in, etc. If you were to graph that, and draw a line between those points, it would look like this

So, in this case, if you wanted to "predict" the amount of compression by how much weight you put on the spring, you would be very confident. You already know exactly how much it would compress.

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A less than perfect example

Say the spring is getting older and it just does not spring like it should. It might look like this instead ...

If you were to try and draw a straight line, it does not line up so nicely anymore. It still kind of looks like a straight line though. In this case, I would think that the data "fits" that line pretty well and I can still estimate how much the spring would compress given the amount of weight I put on it. Maybe not perfectly, but I should be in the ballpark.

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Time for a new spring, really

Say your spring looked like this ...

Personally, I would not even try to use the weight to estimate the amount of compression of this spring.

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How do you measure that?

So how would you get some sort of measurement around how well does the data "fit" a perfectly straight line. That is where a correlation coefficient comes in. So, for the first example, if you were to calculate the rxy it would be 1.0; for a perfect fit. The second example comes in around .925, which is pretty intuitive since it looks close. The third one comes in at .399, ouch!

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In the tool

So when you use a Scatter Graph in the tool, it will automatically calculate the rxy for you. Say for example, I wanted to see how well right rear tire pressure "predicts" lap time, then it would look something like below. With an rxy of -.729, that looks like pretty good evidence. I would feel pretty confident in putting more air in my right rear tire on the next race day and know that I will get a better lap time out of that car.

Another thing to note, the more data points you collect the better your estimates will be. Always record your sessions and make sure to capture all the data points you want to analyze.