Logistic
An S-shaped rise from 0 to a plateau A. Use it for population growth, autocatalytic reactions and other growth that starts slowly, speeds up and then saturates.
Fit the example dataStart with your own data
Example: NIST’s Rat42 pasture yield data, 9 points with y uncertainties, opened as a new copy you can edit.
Parameters
- Upper plateau. The lower plateau is 0.
- Growth rate, in inverse units of x. Larger values give a steeper step; negative values give a falling curve.
- Midpoint: the x at which y = A/2.
Tips
- Automatic starting values try a range of steepness and midpoints and solve A exactly. To start by hand: A near the plateau, C near the midpoint, and B ≈ 4.4 divided by the distance in x over which y rises from 10% to 90% of A.
- The lower plateau is fixed at 0. For data that level off at another value, use Logistic with Baseline.
- For a step that is symmetric in log x, such as a dose–response curve, use Logistic 4PL (Hill).