# 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. However, in order for a curve to be called “curviliaer”, it must have some kind of purpose. In statistics, that purpose is usually some kind of regression analysis. 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

Quadratic regression. BradBeattie|Wikimedia Commons

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.

Reference:
Foadi, J. 2005. Gradient, Divergence and Curl. Available online here.

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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