# Standard error of the intercept in orthogonal regression

I want to perform a univariate regression but with substantial measurement error in both $x$ and $y$. I therefore want to try orthogonal regression with R. The best answer to my question so far have been this: How to perform orthogonal regression (total least squares) via PCA?

However, what I need is to pick out the intercept for the regression and its standard error. I'm not sure if/how this can be done via the PCA approach.

I suggest to use package deming. Here is an example of Deming regression using the package:

library(deming)
fit.lm <- lm(aes ~ aas, data=arsenate)

fit.deming <- deming(aes ~ aas, data=arsenate, stdpat = c(1, 0, 1, 0))
print(fit.deming)
#Call:
#deming(formula = aes ~ aas, data = arsenate, stdpat = c(1, 0,     1, 0))
#
#n= 30
#               Coef  se(coef) lower 0.95 upper 0.95
#Intercept 0.4293665 0.3079456 -0.1741959   1.032929
#Slope     0.8759571 0.1180054  0.6446708   1.107244
#
#   Scale= 0.7899665

fit.errors <- deming(aes ~ aas, data=arsenate, xstd=se.aas, ystd=se.aes)
print(fit.errors)
#Call:
#deming(formula = aes ~ aas, data = arsenate, xstd = se.aas, ystd = se.aes)
#
#n= 30
#               Coef  se(coef) lower 0.95 upper 0.95
#Intercept 0.1064481 0.2477071 -0.3790489  0.5919451
#Slope     0.9729928 0.1429651  0.6927863  1.2531993
#
#   Scale= 1.165495

plot(aes ~ aas, data=arsenate)
abline(fit.lm, lty = 2)
abline(fit.deming, col = "red")
abline(fit.errors, col = "blue")

legend("topleft", legend = c("Deming", "with measured errors","OLS"),
lty = c(1, 1:2), col = c("red", "blue","black")) Apparently the Jackknife technique is used to get the standard errors. You probably should read the package vignette and have a look at the references therein.

• Thank you! In case someone asks in future, I then used the following to extract intercept and se of intercept. Intercept = fit.deming$coefficients . se = sqrt(diag(fit.deming$variance)) Sep 29, 2015 at 7:51