Least Squared or Absolute Errors

It is almost impossible to escape linear regression: the act of fitting straight lines through scattered data.

The question of whether it is more appropriate to use minimization of squared or absolute error to determine the straight line, popped up yet again in a recent reviewer comment.

It feels "natural" to use least-squared error, since we have all done it so many times. However, it should be borne in mind that the popularity of this criterion usually arises from the convenience it affords, and not because it lays any special claim to uncovering the truth.

Here is a nice post (+comments), which explores the issue more fully. To nudge you to check out the post, here is a fascinating picture.