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LinearRegression

Computes linear regression of given point set.

Syntax

void avl::LinearRegression
(
	const atl::Array<atl::real>& inYValues,
	const atl::Optional<atl::Array<atl::real> >& inXValues,
	avl::LinearFunction& outLinearFunction,
	atl::Array<atl::real>& outEstimatedValues,
	atl::Array<atl::real>& outResiduals,
	atl::real& outRSquared
)

Parameters

Name	Type	Default	Description
inYValues	const Array<real>&		Sequence of ordinates
inXValues	const Optional<Array<real> >&	NIL	Sequence of abscissae, or {0, 1, 2, ...} by default
outLinearFunction	LinearFunction&		Linear function approximating the given point set
outEstimatedValues	Array<real>&		The result of application of the computed function to the X values
outResiduals	Array<real>&		Difference between an input Y value and the corresponding estimated value
outRSquared	real&		Coefficient of determination of output function

Description

The operation fits a straight line through the set of points in such a way, that sum of squared distances (residuals) between points and fitted line is as small as possible.
Fitted line parameters are calculated as follows:
\[B=\frac{ { n\sum\limits_{ i=0 }^n{ x_{i}y_{i} } } - \sum\limits_{i=0}^n{x_{i} }\sum\limits_{i=0}^n{y_{i} } }{n\sum\limits_{i=0}^n{x_{i}^2}-{\sum\limits_{i=0}^n{x} }^2} \]
\[A=\frac{ {}\sum\limits_{i=0}^n{x_{i} } }{n}-B\frac{\sum\limits_{i=0}^n{y_{i} } }{n}\]

Errors

Error type	Description
DomainError	Inconsistent size of arrays in LinearRegression.