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!