Application of linear statistical models of earthquake magnitude versus fault length in estimating maximum expectable earthquakes

Correlation or linear regression estimates of earthquake magnitude from data on historical magnitude and length of surface rupture should be based upon the correct regression. For example, the regression of magnitude on the logarithm of the length of surface rupture L can be used to estimate magnitude, but the regression of log L on magnitude cannot. Regression estimates are most probable values, and estimates of maximum values require consideration of one-sided confidence limits.