Where should a tree cut BMI?

Left: the rule predicts the average progression of the training patients on each side of the cut; each red segment is one patient's miss. Right: the training RMSE of that rule for every cut, one candidate between each pair of neighboring BMI values. Click on it to move the cut. A tree tries every candidate and keeps the lowest point.

Data: Efron, Hastie, Johnstone, and Tibshirani (2004), "Least Angle Regression," Annals of Statistics 32(2); the unscaled copy in scikit-learn, load_diabetes(scaled=False). The 331 training patients of the Lecture 9 split (train_test_split(test_size=0.25, random_state=507)). The data block below is written by lecture-10-notebook-2026-10-08-v1.ipynb.