Since Y is bounded by 0 and 1, ordinary least squares regression is not well-suited. You could try beta regression. In R there is the betareg package.

Try something like this

install.packages("betareg")
library(betareg)
betamod1 <- betareg(y~x, data = DATASETNAME)

more info

Since Y is bounded by 0 and 1, ordinary least squares regression is not well-suited. You could try beta regression. In R there is the betareg package.

Try something like this

install.packages("betareg")
library(betareg)
betamod1 <- betareg(y~x, data = DATASETNAME)

more info

EDIT: If you'd like a full account of beta regression, its advantages and disadvantages, see A better lemon squeezer: Maximum likelihood regression with beta distributed dependent variables by Smithson and Verkuilen