Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Curvilinear Regression

Simple linear regression has been developed to fit straight lines to data points. However, sometimes the relationship between two variables may be represented by a curve instead of a straight line. Such "non-linear" relationships need not be non-linear in a mathematical sense. For example, a parabolic relationship may be well-modeled by a (modified) linear regression, since a parabola is a linear equation, as far as its parameters are concerned. Sometimes, such relationships are called "curvilinear".

Hint: Please note that the term "non-linear" has a double meaning: first, people use the term when they think of curves which are not straight lines, and secondly, a non-linear relationship in its mathematical sense is a function which relates the x and y variable(s) by one or more non-linear functions (such as a cosine). More details can be found here.

There are several ways to fit a curve other than a line (or, generally speaking, an n-dimensional hyperplane) to the data:

The first two approaches require the type of functional relationship to be known. In many standard cases, the second approach may be appropriate.

Last Update: 2012-10-08