[R] regression problem

[Gabor Grothendieck]

 <pnick <at> virgilio.it> writes:

> 
> i need to know how to estimate a linear regression whose coefficients sum
> to zero
> 


Transform the model:

y = Xb + error

to

y = XPb + error 

where P is the projection onto the orthogonal complement of the vector 1.
Solve this regression for b and then Pb will be your desired coefficients.
In R this would be:

n <- ncol(X)
P <- diag(n)-matrix(1,n,n)/n
z <- lm(y ~.-1, data=(X%*%P))
b <- coef(z)
b[is.na(b)] <- 0
P %*% b