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LinearRegression

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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.