Huber regression bends but doesn't break — a quadratic core, linear tails, and one line of IRLS reweighting

Ordinary least squares has no defence against a far-off point. Because it minimises the sum of squared residuals, a point twice as far off pays four times the penalty, and one ten times as far pays a hundred — so the fitted line is dragged toward whichever point is worst. Its breakdown point is zero: a single wild observation can ruin the fit. Huber regression keeps least-squares' smooth, convex world but caps that runaway growth. Here's how I built it from scratch — it's barely more code than…