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% File src/library/datasets/man/anscombe.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2018 R Core Team
% Distributed under GPL 2 or later

\name{anscombe}
\docType{data}
\alias{anscombe}
\title{\I{Anscombe}'s Quartet of \sQuote{Identical} Simple Linear Regressions}
\description{
  Four \eqn{x}-\eqn{y} datasets which have the same traditional
  statistical properties (mean, variance, correlation, regression line,
  etc.), yet are quite different.
}
\usage{anscombe}
\format{
  A data frame with 11 observations on 8 variables.
  \tabular{rl}{
    \code{x1} == \code{x2} == \code{x3} \tab the integers 4:14, specially arranged \cr
    \code{x4}             \tab values 8 and 19 \cr
    \code{y1}, \code{y2}, \code{y3}, \code{y4} \tab numbers in (3, 12.5)
    with mean 7.5 and standard deviation 2.03}
}
\source{
  Tufte, Edward R. (1989).
  \emph{The Visual Display of Quantitative Information}, 13--14.
  Graphics Press.
}
\references{
  Anscombe, Francis J. (1973).
  Graphs in statistical analysis.
  \emph{The American Statistician}, \bold{27}, 17--21.
  \doi{10.2307/2682899}.
  
}
\examples{
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)
}
\keyword{datasets}