ols-tls

regression-confusion.R

library(ggplot2)

# the data
dd <- data.frame(x = c(0,3,6,9,10,14), 
                 y = c(7,2,8,6,12,7))

# OLS model

mod <- lm(y ~ x, dd)

# TLS 'coefficients'
# from https://stats.stackexchange.com/questions/13152/how-to-perform-orthogonal-regression-total-least-squares-via-pca

v <- prcomp(cbind(dd$x,dd$y))$rotation
betax_tls <- v[2,1]/v[1,1] 
beta0_tls <- mean(dd$y) - beta*mean(dd$x)

# add fitted values and some other stuff to a tidy version of dd
both <- rbind(dd, dd) |> 
  transform(model = rep(c("ols", "tls"), each = nrow(dd)),
            fit = c(fitted(mod),  
                    beta0_tls + dd$x * betax_tls),
            res = c(dd$y - fitted(mod),  
                    dd$y - (beta0_tls + dd$x * betax_tls))
  )

ggplot(both, aes(x, y)) + 
  geom_point(size = 3, color = "darkgrey") + 
  geom_line(aes(x, fit, color = model)) + 
  annotate("text", x = both$x, y = both$y-0.5, 
           label = paste0("(", both$x, ",", both$y, ")"),
           hjust = "inward", alpha = 0.5) +
  lims(x = c(0, 15), y = c(0, 14)) +
  scale_x_continuous(breaks = 0:16, minor_breaks = NULL) +
  scale_y_continuous(breaks = 0:16, minor_breaks = NULL) +
  theme_minimal()