When the equation comes from the mechanism — a saturating enzyme, an exponential decay, a logistic growth — the right model is nonlinear and its parameters mean something. Magic Stat fits these by nonlinear least squares with the same optimum and standard errors as R's nls, and lets you write your own equation when none of the built-in ones fits.
Nonlinear regression fits a model whose parameters enter the equation in a nonlinear way — Vmax and Km in Michaelis–Menten, or a rate and a scale in an exponential. The estimates are found by iterative search rather than in one algebraic step, and they come with standard errors, t statistics and confidence intervals, under the same asymptotic theory used by R's nls.
The catch is identifiability and starting values. A model whose parameters trade off against each other has no single well-defined optimum, and a poor starting point can send the search off. Magic Stat uses the same starting values as R's selfStart for each built-in model, and if the requested start fails it will try sensible alternatives rather than return nothing — but a model that is not supported by the data can still fail, and that is a real result.
The model comparison numbers — AIC and BIC — are computed in R's convention, so two models fitted to the same data can be compared on equal footing.
nls from the standard starting values.Models: Michaelis–Menten (Vm·x/(K+x)) · Exponential (a·e^(b·x)) · Asymptotic (Asym+(R0−Asym)·e^(−e^lrc·x)) · Logistic (Asym/(1+e^((xmid−x)/scal))) · Power (a·x^b).
Custom formula: write the equation yourself — e.g. y = c + A*sin(2*pi*t/12 + phi) — using the selected columns as variables; free symbols become fitted parameters.
From the mechanism. Michaelis–Menten for saturation, exponential for growth or decay, logistic for S-shaped growth, power for scaling. If no mechanistic form applies, a polynomial or a custom equation is the more honest route.
It usually means poor starting values or a model the data cannot support. Magic Stat tries the standard start and, if that fails, alternative starts. If it still fails, the parameters are not identifiable from your data — a genuine answer, not a software bug.
A polynomial is flexible but its coefficients have no mechanistic meaning. A nonlinear model encodes the process, so parameters such as a rate or a half-saturation constant can be reported and interpreted. Use the nonlinear model when you have the equation.
No. R's nls is the reference these results are built to match. If you need specialised variance structures or weights beyond what is here, R's modelling framework remains the broader tool.
No. Everything runs on your machine. The only automatic signal is an anonymous installation counter.