This is an animation using the manipulate package in R-studio. It uses the Anscombe data - you get to choose which pair. Then you slide through the datasets and the line is computed omitting that data point, and the leave one out residual is illustrated. I would like to tidy up a few details on this, but it works as a first step.

LOO.R

require(MASS)
require(manipulate)
data(anscombe)

plotit <- function(whichpair, i){
  eval(parse(text = paste("sortit <- order(anscombe$x", whichpair, ")", sep = "")))
  eval(parse(text = paste("data.df <- data.frame(x=anscombe$x", whichpair, "[sortit], y=anscombe$y", whichpair, "[sortit])", sep = "")))
  
  ylims <- c(min(data.df$y)*0.8, max(data.df$y)*1.2)
  xlims <- c(min(data.df$x)*0.8, max(data.df$x)*1.2)
  ytext1 <- ylims[1] + 0.8 * (ylims[2]-ylims[1])
  ytext2 <- ylims[1] + 0.7 * (ylims[2]-ylims[1])
  xtext <- ylims[1] + 0.2 * (xlims[2]-xlims[1])
   
  
  #i <-  4
  cols = rep("green", 11)
  cols[i] <- "red"
  pchs <- rep(16, 11)
  pchs[i] <- 4
  par(bty = "n", xpd = NA, las = 1)
  plot(data.df$y~data.df$x, pch = pchs, col = cols, ylim = ylims, xlab = "x", ylab = "y", main = "Illustration of \n leave one out residuals", xlim = xlims)

  text(data.df$x, rep(4,11), round(studres(lm(data.df$y~data.df$x)),2), cex = 0.4)
  m1 <- lm(data.df$y[-i] ~ data.df$x[-i])
  sigma2 <- summary(m1)$sigma^2
  t1 <- bquote(hat(sigma)^2 == .(round(sigma2,6)))
  text(xtext, ytext2, t1)
  t3 <- bquote(paste(hat(beta)[1]==.(round(coef(m1)[1],2))," ", hat(beta)[2]==.(round(coef(m1)[2],2))))
  text(xtext, ytext1, t3)
  abline(m1, col = "blue")
  ##??pred.df <- data.frame(x=data.df$x[i])
  ##??yhat <- predict(m1, newdata=pred.df)
  yhat <- coef(m1)[1] + coef(m1)[2] * data.df$x[i]
  posit <- sign(yhat) + 2
  t2 <- bquote(e[-i] == .(round(data.df$y[i]-yhat, 2)))
  text(data.df$x[i], data.df$y[i], t2, col = "red", pos = posit, offset = 2)
  arrows(data.df$x[i], yhat, data.df$x[i], data.df$y[i], length = 0.01, col = "red")
  ##Sys.sleep(2)
 } 
  

manipulate(
  plotit(whichpair, thepoint), 
  whichpair = picker("One"="1", "Two"="2", "Three"="3", "Four"= "4", label = "Which Anscombe Data Set"), 
  thepoint = slider(1, 11, step = 1,  label = "Which point")  )