Describing the problem - Linear Example
Counting the number of observations of each group of \(X^1\).
## (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