约束最小二乘回归 - Matlab或R.

Question

I'm doing a least-square regression on some data, the function has the form

y ~ a + b*x

and I want the regression line to pass through a specific point P(x,y) (which is not the origin). How can I do that?

I'm using the lm command in R and the basic fitting GUI in Matlab. I think that I could use the constrOptim command (in R) or translate the origin into the point P, but I'm wondering if there's a specific command to do that.

I only need the solution for one of these programs, then I can use the coefficients in the other one.

Answer 1

Just center the data appropriately and force the regression through the 'origin':

lm(y ~ I(x-x0)-1, offset=rep(y0,nrow(dat)) data=dat)

You might then need to adjust the intercept coefficient accordingly.

edited : offset needs to be a vector of the correct length. Another way to do this would be:

set.seed(1)
d <- data.frame(x=1:10,y=rnorm(10,mean=1:10,sd=0.1))
x0 <- 3
y0 <- 3
(lm1 <- lm(y ~ I(x-x0)-1, offset=y0, data=data.frame(d,y0)))

This gives a slope of 1.005. The intercept would be coef(lm1)*(-y0/x0) , I think.