| anscombe {base} | R Documentation |
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)