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''regression hypersurface''

The general geometric representation of a [[Regression|regression]] equation. If one is given random variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806601.png" /> and

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806602.png" /></td> </tr></table>

is the regression of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806603.png" /> with respect to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806604.png" />, then the equation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806605.png" /> describes the corresponding regression hypersurface in an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806606.png" />-dimensional space. When <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080660/r0806607.png" />, 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]].