The Minimum Absolute Deviation Trend Line

Two problems arise out of the use of the method of least squares for determining an average claim cost trend line. First, a single odd point in the data has an excessive influence on the fitted line, and second, the oldest and newest points are given excessive weight relative to intermediate points, which may result in an inordinately large change in slope when a new point is added to the data and the oldest is deleted. These problems are not unique to our trend lines, but apply to all lines fitted by the method of least squares. They are the direct result of squaring the deviations between the data and the fitted line, which is simply not as reasonable a criterion of "best fit" as the absolute value of the deviation.