Describing the problem - Linear Example

We could describe the profile by the linear function \(0.5+z\).

linear_profiles |>
  transform(linear_mid_points = c(0.1, 0.3, 0.5, 0.7, 0.9)) |>
  transform(profile_aprox = 0.5 + linear_mid_points)

##           profiles linear_mid_points profile_aprox
## (0,0.2]        0.6               0.1           0.6
## (0.2,0.4]      0.8               0.3           0.8
## (0.4,0.6]      1.0               0.5           1.0
## (0.6,0.8]      1.2               0.7           1.2
## (0.8,1]        1.4               0.9           1.4