Sum of the residuals in multiple linear regression

**kingwinner** · Jun 20th 2009, 12:21 PM

In my textbook, the following results are proved in the context of SIMPLE linear regression:
∑e_i = 0
∑(e_i)(Y_i hat)= 0

I tried to modify the proofs to mutliple linear regression, but I am unable to do so, so I am puzzled...

Are these results also true in MULTIPLE linear regression?

Thanks!

[also under discussion in Talk Stats forum]

**matheagle** · Jun 20th 2009, 06:17 PM

Nope, As I've posted before.
The sum of the residuals equals 0 iff you have a constant term in your model.
That means you have the column vector of all ones in your design matrix.

For example in the simple model $Y_i=mX_i+\epsilon$
we won't necessarily have the residuals sum to zero.

I just ran that model in JMP with the 3 points (1,1), (2,5) and (3,8).

The Least Squares fit is $\hat Y=5x/2$ .

My residuals are 1.5,0,-.5 and my SSE is 2.5 as JMP confirms.
Note these residuals do not sum to zero.

YOU seem to be comparing my comments to those at another forum,
do they agree with me for the most part?

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