# LinearModelFactory¶

class LinearModelFactory(*args)

Class used to create a linear model from numerical samples.

Refer to Linear regression.

Notes

This class is used in order to create a linear model from numerical samples. The linear regression model between the scalar variable and the -dimensional one writes as follows:

where is the residual, supposed to follow the standard Normal distribution.

Each coefficient is evaluated from both samples and and is accompagnied by a confidence interval and a p-value (which tests if they are significantly different from 0.0).

This class enables to test the quality of the model. It provides only numerical tests. If is scalar, a graphical validation test exists, that draws the residual couples , where the residual is evaluated on the samples : with . The method is VisualTest_DrawLinearModelResidual.

Attributes: thisown The membership flag

Methods

 build(*args) Build the linear model from numerical samples.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

build(*args)

Build the linear model from numerical samples.

Available usages:

build(Xsample, Ysample)

build(Xsample, Ysample, level)

Parameters: Xsample : 2-d sequence of float Input sample, of dimension . Ysample : 2-d sequence of float Output sample, of dimension 1. level : positive float The level value of the confidence intervals of each coefficient of the linear model, equal to 0.95 by default. linearModel : LinearModel The linear model built from the samples : , where is the random residual with zero mean.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> Xsample = distribution.getSample(30)
>>> func = ot.SymbolicFunction(['x'], ['2 * x + 1'])
>>> Ysample = func(Xsample) + ot.Normal().getSample(30)
>>> LMF = ot.LinearModelFactory()
>>> linearModel = LMF.build(Xsample, Ysample)
>>> print(linearModel)
LinearModel name=Unnamed regression=[1.1802,2.0034] confidence intervals=[0.887852, 1.47256]
[1.70439, 2.3024] p-Values=[1.87486e-07,5.10531e-12]

thisown

The membership flag