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 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.

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

Windows for defining model and specifying parameters

Check starting parameter estimates:

Check final parameter estimates:

Graphical output:

Unzoomed plot:

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

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