# Thread: SST = SSE + SSR, proof

1. ## SST = SSE + SSR, proof

Hi,

I've been trying to figure out for a long time how to derive the starting equation of the proof. I have no idea how to come up with it. It's the third equation on the picture in the attachement.

Thank you very much for your help!

2. ## Re: SST = SSE + SSR, proof

I read into this a bit last night. I believe you can add and subtract . So, the right side of line 3 becomes: . I think you have a in place of . Then expand from here?

This is the first line of the proof. I referenced https://web.njit.edu/~wguo/Math644_2...%201_part4.pdf
Maybe we can finish the proof after fixing this small mistake?

3. ## Re: SST = SSE + SSR, proof

It is perhaps best to use the deviation form of the regression function i.e.,

.

Squaring both sides and summing over the sample yields,

because

.

As such, the various sums of squares above are:

is the total variation (TSS),

is the explained sum of squares from the regression (ESS),

is the residual sum of squares (RSS).

Thus, it follows that TSS=ESS+RSS.

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