Key Nonlinear Regression Features
105+ Built-In Equations
Prism includes over 105 built-in curve-fitting equations organized into categories: dose-response, enzyme kinetics, exponential, growth, pharmacokinetics, binding, pharmacodynamics, and more. You can use any of these equations with a single click or write your own custom equation using Prism's equation editor.
Growth Equations
Prism provides a comprehensive library of growth models including exponential growth, exponential decay, biphasic exponential, Gompertz, logistic growth, and polynomial growth. These models are commonly used in microbiology, cell biology, and ecology to characterize population growth dynamics.
Sigmoidal Dose-Response Curves
The sigmoidal and log-sigmoidal families include four-parameter logistic (4PL), three-parameter logistic, variable slope (Hill equation), and normalized sigmoidal models. Prism fits these curves with one click and reports EC50 (or IC50), Hill slope, top, and bottom with confidence intervals.
Global (Shared Parameter) Regression
Global nonlinear regression fits multiple data sets simultaneously, sharing some parameters across datasets while allowing others to vary. This is useful for fitting dose-response curves from multiple experiments where you expect a common EC50 but different maximum responses, or for fitting binding assays where the Bmax should be the same across conditions.
Robust Nonlinear Regression
Standard least-squares fitting is sensitive to outliers. Prism's robust nonlinear regression uses the bisquare (Tukey biweight) method, which automatically downweights points that are far from the curve, reducing the influence of outliers without requiring you to identify and remove them manually.
Outlier Identification
For standard (non-robust) fitting, Prism can identify outliers using the ROUT method (Robust nonlinear regression followed by OUTlier identification). ROUT uses a maximum false discovery rate (Q) to flag outliers and optionally removes them from the fit, giving you a principled, reproducible way to handle outliers.
Model Comparison
When you are unsure which equation fits your data best, Prism's model comparison feature tests whether a more complex model fits significantly better than a simpler one. Prism uses an extra sum-of-squares F test or the Akaike Information Criterion (AIC) to compare models objectively.
Confidence Intervals and Bands
Prism reports asymmetric (likelihood-based) or symmetric (delta method) confidence intervals for every fitted parameter. Confidence bands and prediction bands can be plotted alongside the fitted curve, visually communicating the uncertainty in the fit.
How It Works in Prism
Enter your XY data in a Prism XY table.
Click Analyze, then choose Nonlinear regression (curve fit) from the XY analyses list.
Select an equation from the built-in library or enter a custom equation.
Set initial parameter values (Prism usually provides good defaults).
Configure options: robust fitting, outlier detection, confidence intervals, and whether to compare models.
Click OK. Prism fits the curve, overlays it on your graph, and reports all parameters with confidence intervals in a results sheet.
Why Prism for Nonlinear Regression?
Prism's nonlinear regression combines the power of a professional curve-fitting engine (Levenberg-Marquardt algorithm) with a results-oriented interface that automatically generates publication-quality graphs, reports goodness of fit statistics (R², SS), and flags convergence problems. No scripting is required.