Curve Fitting: Fit and Compare Nonlinear Models Online
What is Curve Fitting?
Curve fitting is used when a scatter plot shows a clearly curved relationship, such as diminishing growth, saturation or acceleration, that linear regression cannot capture. Common candidate models include quadratic and cubic polynomials, exponential Y = a * e^(b*X), logarithmic Y = a + b * ln(X), power Y = a * X^b, and growth or saturation models such as Michaelis-Menten and Gompertz. The tool fits several candidate models automatically and compares them side by side.
When to Use It
Use curve fitting whenever theory or the scatter plot suggests a nonlinear relationship between X and Y, such as wear over time, learning curves, chemical kinetics or response saturation. It is also useful when you need a predictive equation for interpolation within the observed data range. If several models fit similarly well, prefer the simpler one that also makes business or physical sense.
How to Use It (Step by Step)
Paste two columns of X-Y data; the tool first draws a scatter plot so you can see the trend, then automatically tries multiple curve models and lists them with fit statistics. Lock a model to view its parameters, equation and predicted values, or enter a new X to get a predicted Y with a prediction interval. Check the residual plot to confirm the model is adequate, and transform the data if needed before refitting.
Key Formulas / Example
Polynomial models are solved by least squares directly; nonlinear models such as exponential, power and growth curves use iterative estimation such as the Levenberg-Marquardt algorithm. Model quality is compared with R-squared, adjusted R-squared and residual standard deviation, where high R-squared with random, trend-free residuals is best. Avoid overfitting: more parameters fit noise, so prefer the model with few parameters and a reasonable explanation when R-squared values are close.