Logistic Regression Studio

The same "drag it, watch it converge" treatment as the Linear Regression Studio, applied to classification: a real study-hours-vs-pass/fail dataset, a real sigmoid curve, and — the standout feature — a side-by-side comparison of real cross-entropy loss against the non-convex MSE-on-sigmoid alternative that Logistic Regression, In Full Depth warns about, both computed from scratch.

What to Try

• In Fit It Yourself, drag $w$ and $b$ until every point turns green (correctly classified) — notice the decision boundary (the dashed vertical line) is always a single point on this 1D version, because it's exactly where the sigmoid crosses 0.5.
• In Gradient Descent Lab, run Cross-Entropy from the default bad starting point and watch accuracy climb from near-zero to a respectable fit within a few hundred steps.
• Now switch to MSE (naive) and Reset — same starting point, same learning rate, same data. Watch it get stuck: loss barely moves, dw/db in the step log shrink toward zero, and the loss landscape panel visibly looks bumpier and flatter near the (wrong) starting region than cross-entropy's landscape did. That's a vanishing gradient, live — the sigmoid's own derivative ($\hat{p}(1-\hat{p})$, at most 0.25) multiplies directly into the naive loss's gradient and crushes it near saturation, exactly the mechanism Logistic Regression's "Why Not Just Use MSE Loss?" describes in prose.
• Push the learning rate slider up in either loss mode and watch the loss stop decreasing monotonically and start bouncing around instead — real oscillation, not a scripted effect.

Back to Visual Lab Overview.