The LASSO fits a degree-8 polynomial to a real, standardized dataset
(simple_data.csv) while adding an \( \ell_1 \) penalty
\( \lambda\sum_j |\beta_j| \) to the squared-error loss. Drag the λ slider:
as λ grows, the soft-threshold update drives coefficients to exactly zero
(sparsity), the fitted curve simplifies, and the solution moves toward the
corners of a diamond-shaped constraint region — which is precisely why the
LASSO selects variables. The intercept \( \beta_0 \) is never penalized.