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Thread: Proving the SST = SSE + SSR

  1. #1
    Nov 2010

    Proving the SST = SSE + SSR

    I need help with this last part of this proof. This is my first time using the forums so I'm not sure how to write all the symbols but I will make it as clear as possible:

    SST = SUM [(yi-yavg)^2]
    SST = SUM [(yi-yavg + yi hat - yi hat)^2]

    This ends up afters foiling:

    SST = SSE + SSR + 2SUM[(yi hat - yavg)(yi - y hat)]

    I can't figure out how to show that the last term is zero. My professor says to use

    y hat = B0+B1*Xi

    B0 = yavg -Bi*xavg


    B1 = SUM [ ((xi - xavg)*(yi-yavg))/((xi-xavg)^2)]

    but I can't get it to work out. I get

    Which leads me to

    SUM[ xi * ( yi - yavg + SUM[ ((xi - xavg)*(yi-yavg))/((xi-xavg)^2)] * (xavg - xi)]

    Maybe I am forgeting a trick for dealing with nested summation..

    Help! and Thanks in advance!
    Last edited by Seda1; Nov 9th 2010 at 09:30 AM.
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