Mathematics-Online lexicon: Regression Line

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	Mathematics-Online lexicon:
	Regression Line

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A best fitting line,

$\displaystyle p(t) = u + vt\, ,$

to a set of points

, $i=1,\ldots,n$ , can be determined by minimizing the sum of the squares of the errors

$\displaystyle \sum_{i=1}^n (f_i - p(t_i))^2\, .$

$\includegraphics[width=.7\moimagesize]{a_ausgleichsgerade}$

If we have at least two different -coordinates, we obtain the following formulas for the axis intercept and the slope :

$\displaystyle u$	$\displaystyle = \frac{(\sum t_i^2)(\sum f_i)-(\sum t_i)(\sum t_if_i)} {n(\sum t_i^2)-(\sum t_i)^2}$
$\displaystyle v$	$\displaystyle =\frac{n(\sum t_i f_i)-(\sum t_i)(\sum f_i)} {n(\sum t_i^2)-(\sum t_i)^2}\, .$

Annotation:

automatically generated 3/20/2007