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".
||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.