F1(x) = F0 + η · h1(x) = 50 + 0.1 × 18 = 51.8.
After one round, the prediction moved from 50 toward 80 — but only to 51.8, a small fraction of the way. That’s not a mistake in the arithmetic; it’s the shrinkage (learning rate η) doing its job on purpose. A residual of 30 was found; the model chose to act on only 10% of it (η = 0.1) this round, leaving a residual of 80 − 51.8 = 28.2 for the next round’s weak learner to chase.
Why deliberately underreact. If each round fully corrected its residual (η = 1, no shrinkage), the very first weak learner to perfectly fit the training residuals would drive training error to near zero immediately — which is exactly the overfitting failure mode lesson 3 named: a model that has memorized the specific noise in this training batch rather than the general pattern. Small η forces the correction to be spread across many rounds, each contributing only a sliver, so the final model reflects a slow consensus of many weak, residual-chasing trees rather than one learner’s confident (and likely noise-fitting) full correction. The practical cost: more rounds are needed to reach a good fit — shrinkage trades training speed for generalization, a direct, intentional bias/variance-style knob (higher η fits faster and risks overfitting; lower η is safer but slower and needs more rounds).
Bagging (lesson 10) vs boosting (this lesson) is the sharpest contrast in this whole stage. Bagging’s trees are grown independently and in parallel, each blind to what the others predict — averaging works because their errors are (imperfectly) independent, which is a variance play. Boosting’s trees are grown sequentially and dependently — each one’s entire existence is a reaction to what came before, deliberately targeting the specific gap the ensemble-so-far left open, which is a bias play. A forest of independent guessers vs. a relay team where each runner picks up exactly where the last one stopped — same “combine many trees” surface, opposite mechanism, opposite failure mode each guards against.
Where this goes: boosting builds a strong model by stacking many weak, correction-focused trees — but which features each of those trees actually leaned on to make its corrections is a question worth its own skepticism, next lesson.