Difference between revisions of "Regression surface"
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''regression hypersurface'' | ''regression hypersurface'' | ||
| − | The general geometric representation of a [[Regression|regression]] equation. If one is given random variables | + | The general geometric representation of a [[Regression|regression]] equation. If one is given random variables $ X _ {1} \dots X _ {n} $ |
| + | and | ||
| − | + | $$ | |
| + | f ( x _ {2} \dots x _ {n} ) = \ | ||
| + | {\mathsf E} ( X _ {1} \mid X _ {2} = x _ {2} \dots X _ {n} = x _ {n} ) | ||
| + | $$ | ||
| − | is the regression of | + | is the regression of $ X _ {1} $ |
| + | with respect to $ X _ {2} \dots X _ {n} $, | ||
| + | then the equation $ y = f ( x _ {2} \dots x _ {n} ) $ | ||
| + | describes the corresponding regression hypersurface in an $ n $- | ||
| + | dimensional space. When $ n = 2 $, | ||
| + | a regression hypersurface is usually called a regression curve. These terms are sometimes used to emphasize that the corresponding regression equations are not linear. In the linear case, a regression hypersurface or curve is called a regression plane or line, respectively. See [[Regression|Regression]]. | ||
Latest revision as of 08:10, 6 June 2020
regression hypersurface
The general geometric representation of a regression equation. If one is given random variables $ X _ {1} \dots X _ {n} $ and
$$ f ( x _ {2} \dots x _ {n} ) = \ {\mathsf E} ( X _ {1} \mid X _ {2} = x _ {2} \dots X _ {n} = x _ {n} ) $$
is the regression of $ X _ {1} $ with respect to $ X _ {2} \dots X _ {n} $, then the equation $ y = f ( x _ {2} \dots x _ {n} ) $ describes the corresponding regression hypersurface in an $ n $- dimensional space. When $ n = 2 $, a regression hypersurface is usually called a regression curve. These terms are sometimes used to emphasize that the corresponding regression equations are not linear. In the linear case, a regression hypersurface or curve is called a regression plane or line, respectively. See Regression.
Regression surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Regression_surface&oldid=17160