Mean of residuals = 0

wenhotbabe2

New Member
Hey im having trouble proving the mean of the residuals must always be zero.
Can someone help me with this?

Thanks

LukeV

New Member
Well assuming you know how to show the sum is 0. The mean is Sum(ei) / n. Which is clearly 0.

Dragan

Super Moderator
Hey im having trouble proving the mean of the residuals must always be zero.
Can someone help me with this?

Thanks
For a simple regression it is straight forward since you can express the slope intercept form of the model as:

Yhat = b0 + b1*X
Yhat = YBar + R*(Sy/Sx)*(X - XBar)

And, the Error (E) terms are expressed as:

E=(Y - Yhat)

SumE=Sum(Y - Yhat)

SumE=Sum(Y - YBar + R*(Sy/Sx)*(X - XBar) )

SumE=SumY - SumYBar + R*(Sy/Sx)*Sum(X - XBar)

SumE=N*YBar - N*YBar + 0 = 0,

because the summation of a constant N times is N times that constant (N*YBar) and Sum(X - XBar) = 0.

Thus, as indicated above, if the sum of the error terms are zero, so will the mean.