# 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

1 |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
require(stats); require(graphics)
summary(anscombe)
##-- now some "magic" to do the 4 regressions in a loop:
ff <- y ~ x
mods <- setNames(as.list(1:4), paste0("lm", 1:4))
for(i in 1:4) {
ff[2:3] <- lapply(paste0(c("y","x"), i), as.name)
## or ff[[2]] <- as.name(paste0("y", i))
## ff[[3]] <- as.name(paste0("x", i))
mods[[i]] <- lmi <- lm(ff, data = anscombe)
print(anova(lmi))
}
## See how close they are (numerically!)
sapply(mods, coef)
lapply(mods, function(fm) coef(summary(fm)))
## Now, do what you should have done in the first place: PLOTS
op <- par(mfrow = c(2, 2), mar = 0.1+c(4,4,1,1), oma = c(0, 0, 2, 0))
for(i in 1:4) {
ff[2:3] <- lapply(paste0(c("y","x"), i), as.name)
plot(ff, data = anscombe, col = "red", pch = 21, bg = "orange", cex = 1.2,
xlim = c(3, 19), ylim = c(3, 13))
abline(mods[[i]], col = "blue")
}
mtext("Anscombe's 4 Regression data sets", outer = TRUE, cex = 1.5)
par(op)
``` |

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