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AVL.LinearRegression Method

Computes linear regression of given point set.

Namespace:AvlNet
Assembly:AVL.NET.dll

Syntax

public static void LinearRegression(
	float[] inYValues,
	out AvlNet.LinearFunction outLinearFunction,
	out float[] outEstimatedValues,
	out float[] outResiduals,
	out float outRSquared
)

Parameters

Name Type Range Default Description
inYValuesfloatSequence of ordinates.
outLinearFunctionAvlNet.LinearFunctionLinear function approximating the given point set.
outEstimatedValuesfloatThe result of application of the computed function to the X values.
outResidualsfloatDifference between an input Y value and the corresponding estimated value.
outRSquaredfloatCoefficient 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.

See also