# anscombe: Anscombe's Quartet of 'Identical' Simple Linear Regressions

Description Usage Format Source References Examples

### Description

Four x-y datasets which have the same traditional statistical properties (mean, variance, correlation, regression line, etc.), yet are quite different.

### Usage

 `1` ```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

 ``` 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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