Create new versions of Anscombe's quartet

Source: R/anscombise.R

Modifies a dataset x so that it shares sample summary statistics with Anscombe's quartet.

anscombise(x, which = 1, idempotent = TRUE)

Arguments

x

A numeric matrix or data frame. Each column contains observations on a different variable. Missing observations are not allowed.

which

An integer in {1, 2, 3, 4}. Which of Anscombe's datasets to use as the target dataset. Obviously, this makes very little difference.

idempotent

A logical scalar. If idempotent = TRUE then applying anscombise to one of the datasets in Anscombe's Quartet will return the dataset unchanged, apart from a change of class. If idempotent = FALSE then the returned dataset will be a rotated version of the original dataset, with the same summary statistics. See Details.

Value

An object of class c("anscombe", "matrix", "array") with plot and print methods. This returned dataset has the following summary statistics in common with Anscombe's quartet.

  • The sample means of each variable.

  • The sample variances of each variable.

  • The sample correlation matrix.

  • The estimated regression coefficients from least squares linear regressions of each variable on each other variable.

The target and new summary statistics are returned as attributes old_stats and new_stats and the chosen Anscombe's quartet dataset as an attribute old_data.

Details

The input dataset x is modified by shifting, scaling and rotating it so that its sample mean and covariance matrix match those of the Anscombe quartet.

The rotation is based on the square root of the sample correlation matrix. If idempotent = FALSE then this square root is based on the Cholesky decomposition this matrix, using chol. If idempotent = TRUE the square root is based on the spectral decomposition of this matrix, using the output from eigen. This is a minimal rotation square root, which means that if the input data x already have the exactly/approximately the required summary statistics then the returned dataset is exactly/approximately the same as the target dataset.

See also

mimic to modify a dataset to share sample summary statistics with another dataset.

datasets::anscombe for Anscombe's Quartet and anscombe for Anscombe's Quartet as 4 separate datasets.

input_datasets: input1 to input8 for some input datasest of the same size as those in Anscombe's quartet.

Examples

# Produce Anscombe-like datasets using input1 to input8

a1 <- anscombise(input1, idempotent = FALSE)
plot(a1)

a2 <- anscombise(input2)
plot(a2)

a3 <- anscombise(input3, idempotent = FALSE)
plot(a3)

a4 <- anscombise(input4, idempotent = FALSE)
plot(a4)

a5 <- anscombise(input5, idempotent = FALSE)
plot(a5)

a6 <- anscombise(input6)
plot(a6)

a7 <- anscombise(input7, idempotent = FALSE)
plot(a7)

a8 <- anscombise(input8, idempotent = FALSE)
plot(a8)


# Old faithful to new faithful
new_faithful <- anscombise(datasets::faithful, which = 4)
plot(new_faithful)

# Then check that the sample summary statistics are the same
plot(new_faithful, input = TRUE)


# Map of Italy
got_maps <- requireNamespace("maps", quietly = TRUE)
if (got_maps) {
  italy <- mapdata("Italy")
  new_italy <- anscombise(italy, which = 4)
  plot(new_italy)
}