R: Anscombe's Quartet of ``Identical'' Simple Linear Regressions

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

    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)

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