Correlation Coefficient

The Correlation Coefficient, or r value, is the mathematical measure of the correlation between two variables, or how close the points on a scatterplot are to the line of best fit as determined by linear regression.

Values of r range from -1 to 1. Values of r closer to -1 and 1 represent data points very close to the best fit line, either with a negative slope (for negative r values) or with a positive slope (positive r). Values of r closer to 0 represent data points farther from the line (and more cloud-like in appearance).

We typically calculate r using technology. Almost no one does it by hand. Seriously, use a graphing calculator or spreadsheet or website to do it for you. If the r-value for data relating annual salary to days of vacation per year is 0.94, we can expect the scatterplot of the data to be a set of points in a nearly perfect line from the lower left of the plot to the upper right. We can also assume there’s a very strong correlation between those two variables. The one variable doesn’t have to cause the other to change, but they are correlated...somehow.