Describing the problem - Linear Example

Counting the number of observations of each group of \(X^1\).

( x1_dist_matrix <- colSums(count_matrix) / sum(count_matrix) )

##   (0,0.2] (0.2,0.4] (0.4,0.6] (0.6,0.8]   (0.8,1] 
##     0.198     0.197     0.173     0.228     0.204

PD profile for \(X^1\) (expected value).

linear_profiles <- (y_mean_matrix %*% x1_dist_matrix) |> round(digits = 1)

colnames(linear_profiles) <- "profiles"

linear_profiles

##           profiles
## (0,0.2]        0.6
## (0.2,0.4]      0.8
## (0.4,0.6]      1.0
## (0.6,0.8]      1.2
## (0.8,1]        1.4