TITLE: Method of Least Squares-Why is it preferred?
QUESTION [6 upvotes]: Possible Duplicate:
Why do we use a Least Squares fit? 

To find the normal equations for derivation of the regression line we use the method of least squares, We want to make the error smallest for each individual,so we may take summation of mod of the error term for each individual instead of taking the summation of the square of the errors of the individuals. Why is the former method used for regression and not the second one?

REPLY [2 votes]: In addition to all the reasons given in the other answers, consider that in comparison to the sum of absolute values of errors, the sum of squared errors gives greater weight to large errors and less weight to small errors. This is because
$$x^2 > |x| ~~ \text{if} ~~ 1 < |x| < \infty,\\
x^2 < |x| ~~ \text{if} ~~ 0 < |x| < 1.$$
This affects the fitting of the regression line in ways that some might
consider more desirable.