statstudent

Where can I find a proof for: SST = SSM + SSE

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) = ∑(MOD...

I have a simple set of 10 data points My ten Data Points 2 3 3 4 5 8 9 11 11 13 (mean = 6.9) My prediction nodel predicts the following values for the ten data points (listed in same order) 2 3 4 5 6 7 9 10 11 12 I calculate SST = SIGMA (VALUE - MEAN)^2 =...

Wow. That's right, but how do you get from SST = ∑((x - MEAN)^2) to this SST = ∑(x^2) - (∑(x))^2/N ? The former is the definition I'm used to. The latter is what you used in your simple proof. I tested it out and they are equal, but can you prove that?

Got it... SST = ∑((x - MEAN)^2) = ∑(x^2 - 2 * x1 * MEAN + MEAN^2) = ∑(x^2) - 2 * MEAN * ∑(x) + N * MEAN^2 MEAN = ∑(x)/N = ∑(x^2) - 2 * ∑(x)^2/N + ∑(x)^2/N = ∑(x^2) - ∑(x)^2/N Awesome! Thanks!

OK, SST makes sense, but I can't see how to derive your SSM or SSE formulas: I get this: SSM = ∑((MODEL - MEAN)^2) = ∑(MODEL^2 - 2 * MODEL * MEAN + MEAN^2) = ∑(MODEL^2) - 2 * MEAN * SIGMA(MODEL) + N * MEAN^2 SSE = ∑((X - MODEL)^2) = ∑(X^2 - 2 * X * MODEL...

I don't follow this: <<X>^2> = <X^2> Of course, if k is constant and x is variable: <kx> = k<x> <k> = k <k^2> = k^2 but... <x^2> != <x>^2

I don't follow this at all: <(X - m + m - <X>)^2> = <(X-m)^2> + <(m - <X>)^2> + 2 <X-m><m-<X>> Trying to follow your logic, for the left side: <(X - m + m - <X>)^2> = <(X - <X>)^2> = <x^2> - <x>^2 = SST For SSM + SSE: <(x - m>^2> + <(m - <x>)^2> = <x^2 -...