Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help me understand Least squares regression

  1. Apr 3, 2008 #1
    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.
  2. jcsd
  3. Apr 4, 2008 #2


    User Avatar
    Science Advisor

    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).
  4. Apr 5, 2008 #3


    User Avatar
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook