Input: 2D Manifold Coordinates
Z ∈ ℝ42×2
42 county-years × 2 dimensions
Manifold Coordinates:
z₁: Metabolic Vigor
z₂: Phenological Timing
Each point's position encodes phenological signature
Regression Model Selection
Corn% = β₀ + β₁·z₁ + β₂·z₂ + ε
Linear relationship on manifold
Models Evaluated (Leave-One-Out CV):
KNN (k=5)
RMSE: 6.33% | MAE: 4.90%
✓ Linear Regression (Ridge, α=1.0)
RMSE: 5.96% | MAE: 4.60% ⭐ BEST
Polynomial (deg=2)
RMSE: 6.66% | MAE: 5.26%
Gaussian Process
RMSE: 9.42% | MAE: 7.32%
Selected: Ridge Regression
Best RMSE + uniform residuals
Linear model indicates composition varies linearly on 2D manifold
Output: Crop Composition Predictions
Generalization Gap: 1.36%
Exceptional temporal stability!
Model generalizes across years without retraining