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(7.2) Measuring Correlation

In the previous section, you used words such as strong, weak, positive, and negative to describe correlation.
However, there is also a numerical value that describes the strength and sign of the correlation.

It is called the Pearson's product-moment and is usually denoted with the letter .


In the Desmos window above, the value of corr(x1,y1) is the value of r.

When there is perfect positive correlation between two variables, r=
Drag the data points so that they form a descending line.

When there is perfect negative correlation between two variables, r=
Drag the data points so that they are scattered with no apparent trend.

When there appears to be no correlation between two variables, the value of r is close to

Here are some other values of r and their scatter diagrams.


r=0.9

r=0.4

r=−0.3

r=−0.65

When r=0.9, there is a linear correlation between the two variables.
When r=0.4, there is a linear correlation between the two variables.
When r=−0.3, there is a linear correlation between the two variables.
When r=−0.65, there is a linear correlation between the two variables.
This table summarizes how the value of r describes the correlation.
Pearson's correlation
coefficient (r)		 Correlation
0≤r≤0.25 no / very weak
0.25<r≤0.50 weak
0.5<r≤0.75 moderate
0.75<r<1.00 strong
r=1.00