Test the nullity of the linear regression model coefficients.

Available usages:

LinearModelTest.LinearModelFisher(firstSample, secondSample)

LinearModelTest.LinearModelFisher(firstSample, secondSample, level)

LinearModelTest.LinearModelFisher(firstSample, secondSample, linearModel)

LinearModelTest.LinearModelFisher(firstSample, secondSample, linearModel, level)

firstSample : 2-d sequence of float

First tested sample, of dimension 1.

secondSample : 2-d sequence of float

Second tested sample, of dimension 1.

linearModel : LinearModel

A linear model. If not provided, it is built using the given samples.

level : positive float < 1

Threshold p-value of the test (= first kind risk), it must be < 1, equal to 0.05 by default.

testResult : TestResult

Structure containing the result of the test.


The LinearModelTest class is used through its static methods in order to evaluate the quality of the linear regression model between two samples (see LinearModel). The linear regression model between the scalar variable Y and the n-dimensional one \vect{X} = (X_i)_{i \leq n} is as follows:

\tilde{Y} = a_0 + \sum_{i=1}^n a_i X_i + \epsilon

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

The LinearModelFisher test checks the nullity of the regression linear model coefficients (Fisher distribution is used).


>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> func = ot.SymbolicFunction('x', '2 * x + 1')
>>> firstSample = sample
>>> secondSample = func(sample) + ot.Normal().getSample(30)
>>> test_result = ot.LinearModelTest.LinearModelFisher(firstSample, secondSample)
>>> print(test_result)
class=TestResult name=Unnamed type=Fisher binaryQualityMeasure=false p-value threshold=0.05 p-value=1 description=[]