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LinearRegression

Computes linear regression of given point set.

Name	Type	Description
inYValues	Real Array	Sequence of ordinates
inXValues	Real Array *	Sequence of abscissae, or {0, 1, 2, ...} by default
outLinearFunction	LinearFunction	Linear function approximating the given point set
outEstimatedValues	Real Array	The result of application of the computed function to the X values
outResiduals	Real Array	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

This filter can throw an exception to report error. Read how to deal with errors here: Error Handling

Error type	Description
DomainError	Inconsistent size of arrays in LinearRegression.

Complexity Level

This filter is available on Basic Complexity Level.

Filter Group

This filters is member of LinearRegression filter group.