Logistic regression: a separating line and a probability curve
Two clusters of labeled points sit on a plane while a straight line rotates and shifts, searching for the orientation that best separates them, with misclassified points highlighted as it moves. Once settled, the animation shows how each point's signed distance z to that line feeds into sigma(z)=1/(1+e^-z), producing a probability: exactly 0.5 on the boundary, approaching 0 or 1 farther away. Useful for students learning logistic regression and the geometric meaning of decision boundaries.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Two classes of points, a boundary line rotating until few are misclassified, then the sigmoid sigma(z) = 1/(1+e^-z) mapping the signed distance z to a probability: 50/50 on the line, near-certain far from it.
Make the next one in this series
- Show how the loss function (log loss) changes as the boundary rotates toward the optimal fit
- Animate gradient descent updating the line's slope and intercept step by step to minimize error
- Compare a linear decision boundary to a curved one for data that isn't linearly separable
