🧪 Data Science Feature Engineering Simulation

Feature engineering rarely means inventing exotic new data — most of the time it's transforming a raw variable into a set of new columns a model can use, and the simplest possible example is expanding x into powers of x. This simulator builds that expansion live: pick a polynomial degree, and the raw variable becomes φ(x) = [1, x, x², …, x^d], fed into a ridge-regularized linear regression fit in real time to a noisy synthetic dataset. Watch the fitted curve bend to match more of the training scatter as degree rises, while the held-out test points it never saw expose the cost — training error keeps dropping, but test error traces the classic bias-variance U-curve. A regularization slider shows the standard remedy: shrinking the engineered features' coefficients tames the wiggle without removing the features that actually helped.