Parabolic regression

polynomial regression

A regression model in which the regression functions are polynomials. More precisely, let and be random vectors taking values and , and suppose that

exists (i.e. suppose that exist). The regression is called parabolic (polynomial) if the components of the vector are polynomial functions in the components of the vector . For example, in the elementary case where and are ordinary random variables, a polynomial regression equation is of the form

where are the regression coefficients. A special case of parabolic regression is linear regression. By adding new components to the vector , it is always possible to reduce parabolic regression to linear regression. See Regression; Regression analysis.

References

[1]	H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946)
[2]	G.A.F. Seber, "Linear regression analysis" , Wiley (1977)

Comments

The phrase "parabolic regression" is seldom used in the Western literature; one uses "polynomial regression" almost exclusively.