Statistics Definitions > Curvilinear RegressionCurvilinear regression analysis fits curves to data instead of the straight lines you see in linear regression. Technically, it’s a catch all term for any regression that involves a curve. For example, quadratic regression and cubic regression. About the only type that isn’t includes in this catch-all definition is simple linear regression.
Although Cartesian coordinate planes are drilled into us in school, the reality is very few real life events or data sets fit that neatly right-angled system. Coordinate systems are curvilinear if they are made from intersecting, curved surfaces.
The mathematics behind these beautiful coordinate systems are beyond the scope of this statistics site. However, you can find what I consider to be a clear description (mathematically speaking) of the system on James Foadi’s site.
Foadi, J. 2005. Gradient, Divergence and Curl. Available online here.
Stephanie Glen. "Curvilinear Regression" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/curvilinear/
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