# Curvilinear Definition

Statistics Definitions > Curvilinear

## Overview / A General Sense of the Word

A curvilinear line is a smooth curve like a parabola or logarithmic curve. When we call something curvilinear though, we aren’t saying it’s just a curve. It’s a group of curves that have some type of purpose. For example, a curve drawn on a paper is just a curve. But if a regression analysis spits out a curve, then that’s considered curvilinear regression. Why? During the regression, the procedure considers an infinite number of curves — or at the least, a very large family of curves. That leads us to a slightly more formal (and general) definition: something that is formed or characterized by a set of curved lines. Note though, that (like many terms in probability and statistics), the exact use of the word will depend on in what context you are using it in.

## Curvilinear Regression

Curvilinear 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.

## Coordinates

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.

Comparison to Affine (bottom right) and Cartesian (bottom left) coordinates in two dimensional space. Image: Bbanerje|Wikimedia Commons.

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.

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