(This is a draft and truncated version - for final and full version, see. Concise Encyclopedia of Biostatistics for Medical Professionals) ​curvilinear regression, see. Polynomial analysis is an extension of simple linear regression, where a model is used to allow for the existence of a systematic dependence of the independent. Curvilinear Regression. When we have nonlinear relations, we often assume an intrinsically linear model (one with transformations of the IVs) and then we fit data to the model using polynomial regression. That is, we employ some models that use regression to fit curves instead of straight lines.


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Contrary to how it sounds, curvilinear regression uses a linear model to fit a curved line to data points.

Curvilinear regression makes use of various transformations of variables to achieve its fit. Curvilinear regression regression should not be confused with nonlinear regression NL.

Examples Fernandez-Juricic et al.


They counted breeding sparrows per hectare curvilinear regression 18 parks in Madrid, Spain, and also counted the number of people per minute walking through each park both measurement variables. Graph of sparrow abundance vs.

  • Curvilinear regression - definition of curvilinear regression by The Free Dictionary
  • Handbook of Biological Statistics
  • An R Companion for the Handbook of Biological Statistics

This seems biologically plausible; the data suggest that there is some intermediate level of human traffic that is best for house sparrows. Perhaps areas with too many humans scare the sparrows away, while areas with too few humans favor other birds that outcompete the sparrows for nest sites or something.

Even though the cubic equation fits significantly better than the quadratic, it's more difficult to imagine a plausible curvilinear regression explanation for this.

I'd want to see more samples from areas with more than 35 people per hectare per minute before I accepted that the sparrow abundance really starts to increase again above that level of pedestrian traffic.

The data are shown below in the SAS example. Adding the cubic and quartic terms does not significantly increase the R2. The first part of the graph is curvilinear regression surprising; it's easy to imagine why bigger tortoises would have more eggs.

R Companion: Curvilinear Regression

The decline in egg number above mm carapace length is the interesting result; it suggests that egg production declines in these tortoises as curvilinear regression get old and big. X-ray of a tortoise, showing eggs.


Graph of clutch size curvilinear regression of eggs vs. Graphing the results As shown above, you graph a curvilinear regression the same way you would a linear regression, a scattergraph with the independent variable on the X axis and the dependent variable on the Y axis.

In general, you shouldn't show the regression line for values outside the range of observed X values, as extrapolation with polynomial regression is even more likely than linear regression to yield ridiculous results.

Curvilinear regression - Handbook of Biological Statistics

For example, extrapolating the quadratic equation relating tortoise carapace length and number of eggs predicts that tortoises with carapace length less than mm or greater than mm would have negative numbers of eggs.

Similar tests Before performing a curvilinear regression, you should try different transformations when faced with an obviously curved relationship between an X and a Y variable. A linear equation relating transformed variables is simpler and more elegant than a curvilinear equation relating untransformed variables.

You should also remind yourself of your reason for doing a regression. If curvilinear regression purpose is prediction of unknown values of Y corresponding to known values of X, then you need an equation that fits the data points well, and a polynomial regression may be appropriate if transformations do not work.

However, if your purpose is testing the null hypothesis that there is no relationship between X and Y, and a linear regression gives a significant result, you may want to stick with the linear regression even if curvilinear gives a significantly better fit.

Curvilinear regression

Using a less-familiar technique that yields a more-complicated equation may cause your readers to be a bit suspicious of your results; they may feel you went fishing around curvilinear regression a statistical test that supported your hypothesis, especially if there's no obvious biological reason for an equation with terms containing exponents.

Spearman rank correlation is a nonparametric test of the association between two variables. The package nlmrt uses a different process for determining the iterations, and may be better to fit difficult models.


If you wish to have an overall p-value for the model and a pseudo-R-squared for the model, the model curvilinear regression need to be compared with a null model. Technically for this to be valid, the null model must be nested within the fitted model.

That means that the null model is a special case of the fitted model. They are therefore considered nonlinear models.