Polynomial models can be used in situations where the relationship between response and explanatory variables is curvilinear. Sometimes, a nonlinear relationship in a small range of explanatory variables can also be modeled by polynomials.
A polynomial quadratic (squared) or cubic (cubed) term turns a linear regression model into a polynomial curve. However, since it is the explanatory variable that is squared or cubed and not the Beta coefficient, it still qualifies as a linear model. This makes it a nice, straightforward way to model curves, without having to model complicated nonlinear models.
In polynomial regression, some predictors appear in degrees equal to or greater than two. The model continues to be linear in its parameters. For example, a second-degree parabolic regression model looks like this:
This model can easily be estimated by...
