Train points
Test points
Fitted model ŷ(x)
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This simulation builds predictive models the way a data scientist actually validates them: fit a polynomial regression of any complexity to noisy synthetic data, then check whether it generalizes. Points are split into a training set the model learns from and a held-out test set it never sees during fitting, rendered in 3D on separate planes so the split is visible at a glance. Pick the true underlying relationship — linear, quadratic, or sinusoidal — dial in noise, and slide model complexity from a straight line to a degree-9 polynomial while live train/test mean-squared-error and test R² reveal the exact moment a model stops explaining the pattern and starts memorizing the noise: the bias-variance tradeoff that governs every real forecasting and regression system.