Anscombe's Quartet of ``Identical'' Simple Linear Regressions
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) |
| | mean(y<j>) = 7.5 and st.dev = 2.03 |
Description
Four x-y datasets which have the same traditional
statistical properties (mean, variance, correlation, regression line,
etc.), yet are quite different.Source
Edward R. Tufte (1989). The Visual Display of Quantitative Information;
Graphics Press, p.13-14.References
Francis J. Anscombe (1973). Graphs in Statistical Analysis;
American Statistician, 27, 17-21.Examples
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)