# Math Help - Sst=ssr+sse

1. ## Sst=ssr+sse

Hello,
I am stuck proving the following:

For simple linear regression prove that
SST=SSR+SSE
where
$SSE = \sum(Y_i-\hat{Y}_i)^2$
$SSR = \sum(\hat{Y}_i-\bar{Y})^2$
$SST = \sum(Y_i-\bar{Y})^2$

Here's what I have so far,

$(Y_i-\bar{Y})^2=(Y_i-\hat{Y}_i+\hat{Y}_i-\bar{Y})^2=((Y_i-\hat{Y}_i)+(\hat{Y}_i-\bar{Y}))^2=$
$(Y_i-\hat{Y}_i)^2-2(Y_i-\hat{Y}_i)(\hat{Y}_i-\bar{Y})+(\hat{Y}_i-\bar{Y})^2
$

So, $
SST=\sum(Y_i-\bar{Y})^2=\sum{(Y_i-\hat{Y}_i)^2}-2\sum{(Y_i-\hat{Y}_i)(\hat{Y}_i-\bar{Y})}+\sum{(\hat{Y}_i-\bar{Y})^2}=$

$SSE-2\sum{(Y_i-\hat{Y}_i)(\hat{Y}_i-\bar{Y})}+SSR$

Thanks in advance.

2. start with SSTotal and add and subtract Y hat's
Then do the square and the intermediate term drops out.