anscombe

Documentation

Anscombe's Quartet of ‘Identical’ Simple Linear Regressions

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.

R project statistics dataset table
x1 == x2 == x3 the integers 4:14, specially arranged
x4 values 8 and 19
y1, y2, y3, y4 numbers in (3, 12.5) with mean 7.5 and sdev 2.03

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)
Title Authored on Content type
OpenIntro Statistics Dataset - dream August 9, 2020 - 12:25 PM Dataset
OpenIntro Statistics Dataset - winery_cars August 9, 2020 - 2:38 PM Dataset
R Dataset / Package HSAUR / toothpaste March 9, 2018 - 1:06 PM Dataset
R Dataset / Package HSAUR / pottery March 9, 2018 - 1:06 PM Dataset
R Dataset / Package HistData / Guerry March 9, 2018 - 1:06 PM Dataset
Attachment Size
dataset-68467.csv 364 bytes

This documentation is licensed under GPLv3 or later.