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Published in:
2009 | OriginalPaper | Chapter
Polynomial Regression
Authors : Richard M. Heiberger, Erich Neuwirth
Published in: R Through Excel
Publisher: Springer New York
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If the relationship between a response variable
Y
and an explanatory variable
X
is believed to be nonlinear, it is sometimes possible to model the relationship by adding an
X
2
-term to the model in addition to an
X
-term. For example, if
Y
is product demand and
X
is advertising expenditure on the product, an analyst might feel that beyond some value of
X
, there is “diminishing marginal returns” on this expenditure. Then the analyst would model
Y
as a function of
X
and
X
2
, and possibly other predictor variables, and anticipate a significant negative coefficient for
X
2
. Occasionally a need is encountered for higher-order polynomial terms.