Why do starting values matter?

The iterative algorithm searches for a minimum from the given point; a poor start may end in a local minimum or fail to converge. Start from a plot of the data or a linearized estimate.

When is a polynomial enough?

When you only need to describe curvature without physical meaning of the parameters. A high-order polynomial, however, behaves unpredictably outside the data range.

Nonlinear regression

Definition

Nonlinear regression fits data with a model that is nonlinear in its parameters — exponential growth, a logistic curve, Michaelis–Menten kinetics, dose–response. Parameters are found iteratively (Levenberg–Marquardt, Gauss–Newton) by minimizing the sum of squares, so starting values matter.

Regression & models

Whenever possible, prefer a model that can be linearized or expressed as a polynomial — it is more stable and easier to interpret. Choose a genuinely nonlinear model where it has physical or biological meaning (saturation, half-life), and check the results with a fit plot and residuals.

Quality is described by the proportion of explained variance and the standard errors of the parameters; watch convergence in the iteration history. For convergence trouble try other starting values or parameter constraints.

In Statistica

Statistics → Advanced Linear/Nonlinear Models → Nonlinear Estimation lets you type any custom equation, offers predefined models (exponential, logistic, probit, logit) and the Levenberg–Marquardt, quasi-Newton and simplex algorithms, with a fit plot, residuals and parameter estimates with intervals. The guide How to do nonlinear regression walks through it step by step.

Available from edition: Statistica Desktop

Related terms

Knowledgebase guides

How to do nonlinear regression

FAQ

Why do starting values matter?: The iterative algorithm searches for a minimum from the given point; a poor start may end in a local minimum or fail to converge. Start from a plot of the data or a linearized estimate.
When is a polynomial enough?: When you only need to describe curvature without physical meaning of the parameters. A high-order polynomial, however, behaves unpredictably outside the data range.

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Regression & models

Linear regression Logistic regression Generalized linear models (GLM)Time series and forecasting Survival analysis All terms →

Updated: September 2026.