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Computes linear regression of given point set.
Namespace: | AvlNet |
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Assembly: | AVL.NET.dll |
Syntax
C++
C#
public static void LinearRegression ( IList<float> inYValues, NullableRef<IList<float>> inXValues, out AvlNet.LinearFunction outLinearFunction, IList<float> outEstimatedValues, IList<float> outResiduals, out float outRSquared )
Parameters
Name | Type | Range | Default | Description | |
---|---|---|---|---|---|
inYValues | System.Collections.Generic.IList<float> | Sequence of ordinates. | |||
inXValues | AvlNet.NullableRef<System.Collections.Generic.IList<float>> | Sequence of abscissae, or {0, 1, 2, ...} by default. Default value: atl::NIL. | |||
outLinearFunction | AvlNet.LinearFunction | Linear function approximating the given point set. | |||
outEstimatedValues | System.Collections.Generic.IList<float> | The result of application of the computed function to the X values. | |||
outResiduals | System.Collections.Generic.IList<float> | Difference between an input Y value and the corresponding estimated value. | |||
outRSquared | float | 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
List of possible exceptions:
Error type | Description |
---|---|
DomainError | Inconsistent size of arrays in LinearRegression. |