Why Do We Square Errors in Least Squares Regression?

[likephysics]

You must have used it couple of times while solving an engineering problem. For example in line fitting, why do we have to square?
Can't we just pass the line thru the max number of points. Can someone explain.
Thanks in advance.

 

[FredGarvin]

The whole point is to minimize the error between the regression line and the individual datum points. The term "least squares" comes from the fact that you are taking the sum of the squared error terms. The terms are squared so that the error, either positive or negative, becomes a positive term (it needs to be positive because you are looking at the ditance from a point to a line).

 

[Mentz114]

The LS estimators of the parameters a and b in the line y = a.x + b are also the best unbiased estimators if x and y are assumed to have proper values with a normally distributed errors. See the ' Gauss-Markov theorem'. If you have a large number of of readings for x and y then the normal error distribution condition can be relaxed.