Thursday
April 24, 2014

Homework Help: statistics

Posted by statstudent on Wednesday, August 29, 2007 at 12:15pm.

I'm trying to work through the proof for
SST = SSM + SSE

MEAN = ∑(X)/N

SST = ∑((x - MEAN)^2)
= ∑(x^2 - 2 * x1 * MEAN + MEAN^2)
= ∑(x^2) - 2 * MEAN * ∑(x) + N * MEAN^2
= ∑(x^2) - 2 * ∑(x)^2/N + ∑(x)^2/N
= ∑(x^2) - ∑(x)^2/N

SSM = ∑((MODEL - MEAN)^2)
= ∑(MODEL^2 - 2 * MODEL * MEAN + MEAN^2)
= ∑(MODEL^2) - 2 * MEAN * ∑(MODEL) + N * MEAN^2
= ∑(MODEL^2) - 2 * MEAN * ∑(MODEL) + N * MEAN^2
= ∑(MODEL^2) - 2/N * ∑(x) * ∑(MODEL) + ∑(x)^2/N

SSE = ∑((x - MODEL)^2)
= ∑(x^2 - 2 * x * MODEL + MODEL^2)
= ∑(x^2) - 2 * ∑(x * MODEL) + ∑(MODEL^2)

SST = SSM + SSE
∑(x^2) - ∑(x)^2/N = ∑(MODEL^2) - 2/N * ∑(x) * ∑(MODEL) + ∑(x)^2/N + ∑(x^2) - 2 * ∑(x * MODEL) + ∑(MODEL^2)
2 * ∑(MODEL^2) - 2/N * ∑(x) * ∑(MODEL) + 2 * ∑(x)^2/N + - 2 * ∑(x * MODEL) = 0
∑(MODEL^2) - 1/N * ∑(x) * ∑(MODEL) + ∑(x)^2/N + - ∑(x * MODEL) = 0

I can't complete the proof. What am I missing? Thanks!

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