File:Anscombe.svg

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Anscombe.svg‎ (SVG file, nominally 990 × 677 pixels, file size: 88 KB)

[edit] Description

This graphic represents the four datasets defined by Francis Anscombe for which some of the usual statistical properties (mean, variance, correlation and regression line) are the same, even though the datasets are different.

Property	Value
Mean of each $x$ variables	9.0
Variance of each $x$ variables	11.0
Mean of each $y$ variables	7.5
Variance of each $y$ variables	4.12
Correlation between each $x$ and $y$ variable	0.816
Regression line	$y = 3 + 0.5 x$

The graphic was created by User:Schutz for Wikipedia on 13 June 2006, using the R statistical project. The program that generated the graphic is given below; it is based on the example provided with the help page of the R dataset anscombe (accessible using the command help(anscombe)), and was slightly modified to improve the result. The graph was exported in postscript format, converted to SVG using the pstoedit command, and the layout was slightly modified using Inkscape before upload.

References:

Anscombe, Francis J. (1973) Graphs in statistical analysis. American Statistician, 27, 17–21.
R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. 2006. ISBN 3-900051-07-0. http://www.R-project.org

 postscript("anscombe.ps")
 par(las=1)
 
 
  ##-- 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))
  }
  
  ## Now, do what you should have done in the first place: PLOTS
  op <- par(mfrow=c(2,2), mar=1.5+c(4,4,1,1), oma=c(0,0,0,0),
            lab=c(6,6,7), cex.lab=1.5, cex.axis=1.3, mgp=c(3,1,0))
  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 = 2.5,
         xlim=c(3,19), ylim=c(3,13))
    abline(get(paste("lm.",i,sep="")), col="blue")
  }
   
  dev.off()

This chart was created with R.

Note: See library(alr3), data(anscombe) for the original dataset. Check ?anscombe for information on the order in which the variables should be regressed (plotted). One simpler way to perform the above mentioned regressions would be to run code similar to:

require(car)
require(alr3)
scatterplot(y1~x1, reg.line=lm, smooth=TRUE, labels=FALSE, boxplots='xy', span=0.5, data=anscombe)

[edit] Licensing

The R project is licensed under the GPL [1]; since this image is a derived work, it is also licenced under the GPL.

This work is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version. This work is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See version 2 and version 3 of the GNU General Public License for more details.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	00:07, 15 January 2007		990×677 (88 KB)	Schutz (talk \| contribs)
	00:05, 15 January 2007		990×677 (88 KB)	Schutz (talk \| contribs)
	21:37, 13 June 2006		1,044×750 (94 KB)	Schutz (talk \| contribs)
	18:27, 13 June 2006		1,125×875 (94 KB)	Schutz (talk \| contribs)