Beyond Linearity: Splines, Local Regression, and Generalized Additive Models

Every model in this unit so far has been linear in its parameters — even ridge and lasso only reshape how much each linear coefficient is trusted, not the linear functional form itself. But a relationship like "wage rises with age, then flattens, then declines" is not linear in any single transformation of age. This closing lesson of Topic 3 shows how to relax linearity in a controlled, interpretable way — the natural complement to the previous three lessons' controlled way of relaxing "trust every coefficient equally."