Linear Regression Studio

A real, noisy "study hours vs. exam score" dataset with two modes: drag the line yourself and watch MSE respond, or hand control to real batch gradient descent and watch it converge (or diverge) live — the exact formulas from Linear Regression, In Full Depth, not a mockup.

What to Try

• In Fit It Yourself, get the MSE as low as you can by hand, then flip on the Outlier toggle and watch it jump — a direct, visceral answer to why squared error punishes big misses so much harder than small ones.
• Turn the Noise slider up and notice how much harder it gets to find a clearly "best" line by eye — real data rarely fits perfectly, and that's exactly why a systematic optimization procedure (gradient descent) beats guess-and-check.
• In Gradient Descent Lab, start at the default learning rate and hit Play — watch the two panels move in sync: the line settling into the data on the left, the point sliding down the real MSE surface on the right.
• Push the learning rate slider toward its max and watch it diverge instead of converge — the step log will show w and b exploding. That's not a bug; it's the exact failure mode Optimizers, In Full Depth warns about, reproduced on real data.
• Compare the shape of the loss landscape here to the synthetic bowl in the Gradient Descent Explorer — both are genuinely quadratic in their parameters, which is exactly why linear regression's cost surface has no false local minima to get stuck in.

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