Remove outliers from correlation coefficient calculation

Question

Assume we have two numeric vectors x and y. The Pearson correlation coefficient between x and y is given by

Answer 1

You might try bootstrapping your data to find the highest correlation coefficient, e.g.:

x <- cars$dist
y <- cars$speed
percent <- 0.9         # given in the question above
n <- 1000              # number of resampling
boot.cor <- replicate(n, {tmp <- sample(round(length(x)*percent), replace=FALSE); cor(x[tmp], y[tmp])})

And after run max(boot.cor). Do not be dissapointed if all the correlation coefficients will be all the same :)