The Towards Data Science post revisits Lasso regression through the lens of vectors and orthogonal projections, a method the author previously used for ordinary linear regression. By swapping calculus for geometric intuition, the piece shows how adding a penalty term translates into shrinking coefficients toward zero. This visual approach demystifies why the solution often lands on a diamond‑shaped constraint region.

Using a tiny house dataset—size, age, and price—the author fits an exact linear model that reproduces the training points but wildly mispredicts a new observation. The resulting high variance illustrates classic overfitting, where the model memorizes rather than generalizes. Introducing Lasso regularization would zero out less informative coefficients, effectively pruning the feature space and improving out‑of‑sample stability.

By framing regression as moving within a multidimensional space, the article reveals that when feature vectors span the target, the optimal point coincides with the data itself—no projection needed. Adding a penalty reshapes the feasible set into a diamond, forcing the solution onto the vector projection boundary and encouraging sparsity. The tutorial equips practitioners with a geometric toolkit for diagnosing and correcting overfit models.