Results 1 to 2 of 2

Math Help - Sum of the residuals in multiple linear regression

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    404

    Sum of the residuals in multiple linear regression

    In my textbook, the following results are proved in the context of SIMPLE linear regression:
    ∑e_i = 0
    ∑(e_i)(Y_i hat)= 0

    I tried to modify the proofs to mutliple linear regression, but I am unable to do so, so I am puzzled...

    Are these results also true in MULTIPLE linear regression?

    Thanks!

    [also under discussion in Talk Stats forum]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Nope, As I've posted before.
    The sum of the residuals equals 0 iff you have a constant term in your model.
    That means you have the column vector of all ones in your design matrix.

    For example in the simple model Y_i=mX_i+\epsilon
    we won't necessarily have the residuals sum to zero.

    I just ran that model in JMP with the 3 points (1,1), (2,5) and (3,8).

    The Least Squares fit is \hat Y=5x/2.

    My residuals are 1.5,0,-.5 and my SSE is 2.5 as JMP confirms.
    Note these residuals do not sum to zero.


    YOU seem to be comparing my comments to those at another forum,
    do they agree with me for the most part?
    Last edited by matheagle; June 20th 2009 at 07:36 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multiple linear regression calculation
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 12th 2010, 02:47 PM
  2. Regression fundamentals (linear, non linear, simple, multiple)
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: November 12th 2009, 07:47 AM
  3. Regression SS in multiple linear regression
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: June 20th 2009, 01:23 PM
  4. Multiple Linear Regression
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 27th 2008, 10:12 AM
  5. Multiple Linear Regression
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 11th 2008, 03:01 AM

Search Tags


/mathhelpforum @mathhelpforum