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Nonlinear regression

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Nonlinear regression is a regression technique in which a nonlinear mathematical model is used to describe the relationship between two variables (Glantz & Slinker, 2001).

For example:

y = 1/(1+exp(a+b*x))


To find the model's parameters, MedCalc uses the Levenberg-Marquardt iterative procedure (Press et al., 2007) that requires the user to supply initial estimates or best guesses of the parameters.

Required input

Non linear regression dialog box


Non linear regression results


This section shows the tolerance and iterations settings.

Next the reason of iteration process termination is given:


Regression equation

The parameter estimates are reported with standard error and 95% Confidence Interval. The Confidence Interval is used to test whether a parameter estimate is significantly different from a particular value k. If a value k is not in the Confidence Interval, then it van be concluded that the parameter estimate is significantly different from k.

For example, when the parameter estimate is 1.28 with 95% CI 1.10 to 1.46 then this parameter estimate is significantly different (P<0.05) from 1.

Analysis of variance

The Analysis of Variance tables gives the Regression model, Residual and Total sum of squares. When MedCalc determines that the model does not include an intercept the "uncorrected" sum of squares is reported and is used for the F-test. When MedCalc determines that the model does include an intercept, the "corrected" sum of squares is reported and is used for the F-test.

Correlation of parameter estimates

This table reports the correlation coefficients between the different parameter estimates. When you find 2 or more parameters to be highly correlated, you may consider reducing the number of parameters or selecting another model.

Scatter diagram & fitted line

This graph displays a scatter diagram and the fitted nonlinear regression line.

Non linear regression graph

Residuals plot

Residuals are the differences between the predicted values and the observed values for the dependent variable.

The residuals plot allows for the visual evaluation of the goodness of fit of the model. Residuals may point to possible outliers (unusual values) in the data or problems with the fitted model. If the residuals display a certain pattern, the selected model may be inaccurate.

Non linear regression residuals graph


See also

External links

Recommended book

Book cover

Primer of Applied Regression & Analysis of Variance.
Glantz, Stanton, Slinker, Bryan

Buy from Amazon

Primer of Applied Regression & Analysis of Variance is a textbook especially created for medical, public health, and social and environmental science students who need applied (not theoretical) training in the use of statistical methods. The book has been acclaimed for its user-friendly style that makes complicated material understandable to readers who do not have an extensive math background. The text is packed with learning aids that include chapter-ending summaries and end-of-chapter problems that quickly assess mastery of the material. Examples from biological and health sciences are included to clarify and illustrate key points. The techniques discussed apply to a wide range of disciplines, including social and behavioral science as well as health and life sciences. Typical courses that would use this text include those that cover multiple linear regression and ANOVA.