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Parabolic regression

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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.

How to Cite This Entry:
Parabolic regression. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parabolic_regression&oldid=48109
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article