Non-linear Models

This webpage performs non-linear regression.
It extends John Pezzullo's to handle more than 8 parameters. For more information take a thorough look at John's excelent page.
As is, this page is a simple implementation with only minor error reporting.
It is possible to plot 1-Dimensional models with prediction confidence bands. June 2020.


  1. Dependent variable ~ model
  2. List parameter(s): param=value, ...
The regression equation must contain the '~' (tilde symbol) separating the dependent variable from the model, eg.
        y ~ (a - c) * exp(-b * x) + c
All parameters must have initial values.
To transform a variable or a parameter just wrap it in a function call, eg. log(x).
Iterations min: 50, max: 250
Confidence level %
In some cases the iteration process may fail to converge. Then try:
  • change the initial value(s) of the parameter(s)
  • increase the number of iterations
  • plot your data and reconsider the model
Include plot Depicts the original data and predicted values with conf. bands
Plotting requires a 1-Dimensional model, ie. one independent variable only. Change 'None' below to the name of the independent variable
Independent variable name
The confidence interval is calculated using either the Delta method (default) or the Bootstrapped method. Be sure to state the independent variable name above.
Number of boot samples
  • Increasing the number of bootstrap samples results in more precise CI estimation but increase the risk of non-converging samples and the calculation may take considerable more time.