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LinearRegression (LinearRegression LSE)

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Module: FoundationBasic

Computes linear regression of given point set.

Name Type Description
Input value inYValues RealArray Sequence of ordinates
Input value inXValues RealArray* Sequence of abscissae, or {0, 1, 2, ...} by default
Output value outLinearFunction LinearFunction Linear function approximating the given point set
Output value outEstimatedValues RealArray The result of application of the computed function to the X values
Output value outResiduals RealArray Difference between an input Y value and the corresponding estimated value
Output 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 in Error Handling.

List of possible exceptions:

Error type Description
DomainError Inconsistent size of arrays in LinearRegression.

Complexity Level

This filter is available on Advanced Complexity Level.

Filter Group

This filter is member of LinearRegression filter group visible as LSE.