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

data(anscombe)

Format

A data frame with 11 observations on 8 variables.

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)
data(anscombe)
summary(anscombe)

##-- now some "magic" to do the 4 regressions in a loop:
ff <- y ~ x
for(i in 1:4) {
  ff[2:3] <- lapply(paste(c("y","x"), i, sep=""), as.name)
  ## or   ff[[2]] <- as.name(paste("y", i, sep=""))
  ##      ff[[3]] <- as.name(paste("x", i, sep=""))
  assign(paste("lm.",i,sep=""), lmi <- lm(ff, data= anscombe))
  print(anova(lmi))
}

## See how close they are (numerically!)
sapply(objects(pat="lm\.[1-4]$"), function(n) coef(get(n)))
lapply(objects(pat="lm\.[1-4]$"), function(n) summary(get(n))$coef)

## Now, do what you should have done in the first place: PLOTS
op <- par(mfrow=c(2,2), mar=.1+c(4,4,1,1), oma= c(0,0,2,0))
for(i in 1:4) {
  ff[2:3] <- lapply(paste(c("y","x"), i, sep=""), as.name)
  plot(ff, data =anscombe, col="red", pch=21, bg = "orange", cex = 1.2,
       xlim=c(3,19), ylim=c(3,13))
  abline(get(paste("lm.",i,sep="")), col="blue")
}
mtext("Anscombe's 4 Regression data sets", outer = TRUE, cex=1.5)
par(op)