Correlation Coefficient

The correlation coefficient represents the relatedness of two variables, and how well the value of one can be used to predict the value of the other. The correlation coefficient r ranges between -1 and +1. A positive r values indicates that as one variable increases so does the other, and an r of +1 indicates that knowing the value of one variable allows perfect prediction of the other. A negative r values indicates that as one variable increases the other variable decreases, and an r of -1 indicates that knowing the value of one variable allows perfect prediction of the other. A correlation coefficient of 0 indicates no relationship between the variables (random scatter of the points).

To overcome the bias that a negative correlation is somehow worse than a positive correlation, the square of the correlation is often merely to indicate the strength of the relationship between the two variables. R-squared ranges from 0 to 1, and since squared values under 1 decrease rapidly, a large value of r-squared implies a very strong relationship.

This figures shows four sets of data with different correlation coefficients. Note the negative slope for the data set with the -1 correlation coefficient and the positive slope for the +1 correlation coefficient.

In satellite image analysis, the correlation matrix shows the relationship among the bands in the image.

Last revision 12/23/2017