Model Fitting

Author

Apurva Nakade

Published

July 17, 2026

Model fitting chooses parameters so a model matches observed data as closely as possible. The apps below explore how model complexity trades off against stability: a model with more free parameters can always fit the data at least as well, but it can also become far more sensitive to the data’s noise.

L1 vs. L2 Regression

Robust Regression

Linear Regression

Drag the outlier severity slider (in either direction) to see the two fits diverge. L2 minimizes \(\sum_i (y_i - \hat y_i)^2\); L1 minimizes \(\sum_i |y_i - \hat y_i|\).…

Polynomial Fits

Bias-Variance Tradeoff

Polynomial Regression

Model Complexity

A low-degree polynomial (e.g. a line) can’t bend to match every point — high bias, low variance, underfitting. A high-degree polynomial can fit the training data almost…