Results 1 to 3 of 3

Math Help - deriving the formula for the least square estimates

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    2

    deriving the formula for the least square estimates

    when deriving the formula for the least squares estimates of veta0 and veta1 from the following population model:

    yt=veta0+veta1(xt-xbar)+ut

    do you have to do anything different seeing as its normally just Xt not Xt-Xbar.

    What im thinking is that you do the normal process for deriving the least sqaure estimates, however wasnt sure because of the Xt minus Xbar

    also I dont know how to insert symbols and formula hence what I have written, I hope its understandable
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by nickpatto View Post
    when deriving the formula for the least squares estimates of veta0 and veta1 from the following population model:

    yt=veta0+veta1(xt-xbar)+ut

    do you have to do anything different seeing as its normally just Xt not Xt-Xbar.

    What im thinking is that you do the normal process for deriving the least sqaure estimates, however wasnt sure because of the Xt minus Xbar

    also I dont know how to insert symbols and formula hence what I have written, I hope its understandable
    Rewrite your model as:

    yt=veta1*xt+c+ut

    with c=veta0-veta1*xbar, now do the regression.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2010
    Posts
    2

    deriving the estimates

    Hi thanks for that but I need to derive the formula for the estimates veta0 and veta1.

    The normal formula when the regression is Yi=veta0+veta1Xi+ui is the following:

    the intercept estimate (veta0) is

    veta0=Ybar-veta1xbar

    and the slope intercept (veta1)

    veta1= sum of(xi-xbar)(yi-ybar)/sum of (xi-xbar)squared

    Whats confusing me is that the regression model i have been given is

    yt=veta0+veta1(xt-xbar)+ut

    the fact that its not just Xi after veta1 is confusing me, I dont know if i can just use the formulas for the estimates that i used about or because its xt-xbar do i need to do something different when deriving my forumlas for my estimates?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Deriving the Least Squares Estimates
    Posted in the Advanced Statistics Forum
    Replies: 17
    Last Post: May 28th 2011, 11:04 PM
  2. var/covar of Linear Lease Square estimates
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 29th 2010, 05:23 PM
  3. deriving the formula
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 10th 2009, 06:56 AM
  4. [SOLVED] Deriving a square root under a square
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 29th 2007, 07:21 AM
  5. Deriving a square root under a square
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 28th 2007, 07:31 PM

Search Tags


/mathhelpforum @mathhelpforum