Ridge regression fits a degree-8 polynomial to a real, standardized dataset
(simple_data.csv) while adding an \( \ell_2 \) penalty
\( \tfrac{\lambda}{2}\sum_j \beta_j^2 \) to the squared-error loss. Drag the
λ slider: as λ grows, every coefficient is smoothly shrunk toward zero
(but never exactly to zero), the fitted curve flattens, and the solution moves inside
a circular constraint region. The intercept \( \beta_0 \) is never penalized.