Partial coefficient of correlation
Let have 3 variables, x, y and a: x <- rnorm(100, mean=10, sd=2) y <- x+rnorm(100, mean=20, sd=5) a <- rnorm(100, mean=10, sd=2) df <- data.frame(x=x, y=y, a=a) The partial coefficient correlation between x and y relative to a is the correlation coefficient of the residuals of the linear regression of x and y over a: pcor <- function(df) { ax <- lm(x ~ a, data=df) ay <- lm(y ~ a, data=df) rx <- residuals(ax) ry <- residuals(ay) return(cor(rx, ry)) } pcor(df) Let confirm with the package ppcor: library("ppcor") ppcor::: pcor(df)$estimate[2, 1] Note that I use ppcor:::pcor() to be sure that the version of pcor in the package is used. It works: we obtained the same result. It should be noted that ppcor:::pcor() is more rapid than my version of pcor() even if it estimate 3 partial correlations and me only one ! > system.time( + for (i in 1:10000) ppcor:::pcor(df)$estima