Nonlinear Regression
Nonlinear regression module allows you to fit and analyze regression models of the general form

y = F(x,p)

Where y is a response variable, x = (x1, x2, . . . xq) are values of the explanatory variables (written as a vector). q is the number of explanatory variables in the regression model. There are m parameters, p = (p1, p2, . . ., pm) in the model. F(x,p) is a function of explanatory variables and parameters. Maximum theoretical number of parameters is 32, maximum number of variables is 254. Ideally, x is assumed to be a deterministic, i.e. non-random vector, which is either purportedly set to prespecified values or its values are found out via an essentially error-free procedure. y depends on x, but the dependence is blurred by the presence of a random error e. Vector of model parameters p are estimated from data by the nonlinear least squares method. The user can specify a desired nonlinear model.

PDF Nonlinear Regression - Pdf manual

  • Calculate parameters of any nonlinear model.
  • Fit a curve given any nonlinear function.
  • Prediction based on the model.
  • Calibration models.
  • Powerful and extensive choice of diagnostic plots and statistics.
  • Quick and intuitive model building.
  • Segmented models

Optimization methods:
  • Gauss-Newton
  • Marquardt
  • Gradient-Cauchy
  • Dog Leg
  • Adaptive gradient
  • Simplex
Output information:
  • Significance level
  • Degrees of freedom
  • Explanatory variables
  • Response
  • Model
  • Initial parameter values
  • Iterations
  • Termination Type
  • Computation time
  • Max. iteration number
  • Termination criterion
  • Parameter estimates
  • Parameter correlation matrix
  • Residual analysis
  • Y observed
  • Y predicted
  • Std. error of Y
  • Raw residual
  • Residual [%Y]
  • Weights
  • Residual sum of squares
  • Mean of absolute residuals
  • Residual standard deviation
  • Residual variance
  • Residual skewness
  • Residual curtosis

Examples of computations and output
Nonlinear Regression

Windows for defining model and specifying parameters
Nonlinear Regression

Check starting parameter estimates:
Nonlinear Regression

Check final parameter estimates:
Nonlinear Regression

Graphical output:
Nonlinear Regression

Unzoomed plot:
Nonlinear Regression

Parameter estimates:
  Parameter Std. Deviation Lower CI Upper CI
P1 9.629958625 1.437580742 6.730800758 12.52911649
P2 307.3445052 14.46291436 278.1772587 336.5117518
P3 -1.270317008 0.05458188634 -1.380391873 -1.160242144

Correlation matrix of parameters:
  P1 P2 P3
P1 1 0.8340193618 -0.9338794208
P2 0.8340193618 1 -0.9708823844
P3 -0.9338794208 -0.9708823844 1