On this Picostat.com statistics page, you will find information about the anscombe data set which pertains to Anscombe's Quartet of ‘Identical’ Simple Linear Regressions. The anscombe data set is found in the datasets R package. You can load the anscombe data set in R by issuing the following command at the console data("anscombe"). This will load the data into a variable called anscombe. If R says the anscombe data set is not found, you can try installing the package by issuing this command install.packages("datasets") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the anscombe R data set. The size of this file is about 364 bytes.

Anscombe's Quartet of ‘Identical’ Simple Linear Regressions

Description

Four x-y datasets which have the same traditional statistical properties (mean, variance, correlation, regression line, etc.), yet are quite different.

Usage

anscombe

Format

A data frame with 11 observations on 8 variables.

Source

Tufte, Edward R. (1989) The Visual Display of Quantitative Information, 13–14. Graphics Press.

References

Anscombe, Francis J. (1973) Graphs in statistical analysis. American Statistician, 27, 17–21.

Examples

require(stats); require(graphics)
summary(anscombe)##-- now some "magic" to do the 4 regressions in a loop:
ff <- y ~ x
mods <- setNames(as.list(1:4), paste0("lm", 1:4))
for(i in 1:4) {
  ff[2:3] <- lapply(paste0(c("y","x"), i), as.name)
  ## or   ff[[2]] <- as.name(paste0("y", i))
  ##      ff[[3]] <- as.name(paste0("x", i))
  mods[[i]] <- lmi <- lm(ff, data = anscombe)
  print(anova(lmi))
}## See how close they are (numerically!)
sapply(mods, coef)
lapply(mods, function(fm) coef(summary(fm)))## Now, do what you should have done in the first place: PLOTS
op <- par(mfrow = c(2, 2), mar = 0.1+c(4,4,1,1), oma =  c(0, 0, 2, 0))
for(i in 1:4) {
  ff[2:3] <- lapply(paste0(c("y","x"), i), as.name)
  plot(ff, data = anscombe, col = "red", pch = 21, bg = "orange", cex = 1.2,
       xlim = c(3, 19), ylim = c(3, 13))
  abline(mods[[i]], col = "blue")
}
mtext("Anscombe's 4 Regression data sets", outer = TRUE, cex = 1.5)
par(op)

--

Dataset imported from https://www.r-project.org.