Lab · c14.s05.L1

Logistic boundary

A straight-line score becomes a probability through one fixed squash, and the line's zero crossing is the boundary where the chance is one half.

Question: How does a straight line become a probability, and where is the boundary?

Synthetic Synthetic: the 40 labelled points are draws from a logistic model with the fixed seed recorded here; the curves are exact evaluations of the same formula, not measured data. The frames step from the bare score line to the squashed probability curve, then through steeper, gentler, flat and shifted lines, and back to the opening boundary.

Lab controls

Slope of the line1.6

Left/Down: -0.2; Right/Up: +0.2; Page Down: -1.0; Page Up: +1.0; Home: 0.0; End: 2.4

Intercept of the line-1

Left/Down: -0.5; Right/Up: +0.5; Page Down: -1.5; Page Up: +1.5; Home: -3.0; End: 3.0

Frame 1 of 8: A line, not a probabilityThe score is a straight line: at x = -2 its value is -4.2, at x = 0 it is -1.0 and at x = 2 it is 2.2. A score of 2.2 is not a chance, and neither is -4.2.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

Two stacked panels share one input axis. The top panel draws a straight line, the score; the bottom draws that same score squashed into a chance between 0 and 1, with 40 labelled points scattered around it. A dashed gold line marks the input where the score is zero, and there the chance is one half. Raising the slope steepens the S-curve; moving the intercept slides the boundary sideways; a flat line has no boundary.

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Caption status: synthetic. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.