Image:Anscombe.svg
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Anscombe.svg (990 × 677 pixel, file size: 88 KB, MIME type: image/svg+xml)
| This is a file from the Wikimedia Commons. The description on its description page there is shown below. |
[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 + 0.5x |
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. |
[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 the GNU General Public License for more details.
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