Describing the problem - Linear Example

Simple linear model with two explanatory variables

set.seed(21965)

x1 <- runif(1000)
x2 <- runif(1000)
ex <- rnorm(1000, mean=0, sd=0.1)
yx <- x1+x2+ex

Defining the group for each point.

br <- c(0,.2,.4,.6,.8,1)
x1c <- cut(x1,breaks = br)
x2c <- cut(x2,breaks = br)