**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*