Polynomial regression

Polynomial regression is a form of regression analysis in statistics in which the relationship between an independent variable x and a dependent variable y is modeled as a polynomial in x. It fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, written E(y given x). Although the fitted curve is nonlinear in x, the problem is linear as a statistical estimation task, because the regression function is linear in the unknown parameters that are estimated from the data. For that reason polynomial regression counts as a special case of multiple linear regression. The explanatory variables produced by expanding the baseline variable into powers, such as x squared and x cubed, are called higher-degree terms, and the same expanded variables are also used in classification settings. The technique is a standard way to let a linear fitting method follow a curved trend without leaving the ordinary least squares framework.