None, really. A hand-held calculator may not perform the necessary calculations but that seems to me the only drawback.
But that is less of a problem that trying to force a quadratic relationship between two variables into a linear model!
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of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
158 I believe
the prefix of regression is regress
setback or regression
The sample regression function is a statistical approximation to the population regression function.