In paulnorthrop/stat0002: Introduction to Probability and Statistics

knitr::opts_chunk$set(comment = "", prompt = TRUE, collapse = TRUE,
                      fig.width = 7, fig.height = 5, fig.align = 'center')
knitr::opts_knit$set(global.par = TRUE)

required <- c("anscombiser")
if (!all(unlist(lapply(required, function(pkg) requireNamespace(pkg, quietly = TRUE)))))
  knitr::opts_chunk$set(eval = FALSE)

This vignette provides some R code that is related to some of the content of Chapter 10 of the STAT0002 notes correlation.

library(stat0002)

par(mar = c(4, 4, 1, 1))

Example data

We use the exchange rate data described at the start of Section 10.1 of the notes. These data are available in the data frame exchange. We look at the first 6 rows of the data and the last 6 rows and produce plots like Figures 10.1 and 10.2 of the notes.

head(exchange)
tail(exchange)
# Figure 10.1
plot(exchange, pch = 16, xlab = "Pounds sterling vs. US dollars",
     ylab = "Pounds sterling vs. Canadian dollars", bty = "l", 
     main = "Raw data")
# Calculate the log-returns
USDlogr <- diff(log(exchange$USD.GBP))
CADlogr <- diff(log(exchange$CAD.GBP))
# Figure 10.2
plot(USDlogr, CADlogr, pch = 16, xlab = "Pounds sterling vs. US dollars",
     ylab = "Pounds sterling vs. Canadian dollars", bty = "l", 
     main = "Log-returns" )

The R function cor

R provides a function cor to calculate sample correlation coefficients. By default, it calculates the sample (product moment) correlation coefficient given in Section 10.2.1.

We can supply either two vectors x and y of equal length or a matrix with columns containing the vectors of data for which we want to calculate the sample correlation coefficient. In this case, we create a 2-column matrix using cbind function to combine the 2 vectors USDlogr and CADlogr columnwise into a matrix.

If we supply a matrix then R will return a matrix containing the sample correlation coefficients between all possible pairs of columns in the input matrix, including between each column and itself, which produces values of 1 on the diagonal of the output matrix. If we supply vectors x and y then it does not matter which vector is entered as x and which as y.

cor(x = USDlogr, y = CADlogr)
cor(x = CADlogr, y = USDlogr)
cor(x = cbind(USDlogr, CADlogr))

Anscombe's Quartet of datasets

In Section 10.3.6 Anscombe's Quartet of dataset are provided in Figure 10.9. These 4 datasets are available as separate data frames in the anscombiser package @anscombiser. Use install.packages("anscombiser") to install this package.

library(anscombiser)

cor(anscombe1)
cor(anscombe2)
cor(anscombe3)
cor(anscombe4)

We see that the paired data in these datasets have almost exactly the same sample correlation coefficient. They have many other summary statistics in common. See Section 10.3.6 for details.

The method argument to cor enables us to ask R to calculate Spearman's rank correlation coefficient (See Section 2.3.5). The values of this sample correlation coefficient differ between these datasets.

cor(anscombe1, method = "spearman")
cor(anscombe2, method = "spearman")
cor(anscombe3, method = "spearman")
cor(anscombe4, method = "spearman")

References

paulnorthrop/stat0002 documentation built on Oct. 10, 2024, 1:27 p.m.