# LinearModelTest_LinearModelResidualMean¶

LinearModelTest_LinearModelResidualMean(*args)

Test zero mean value of the residual of the linear regression model.

Available usages:

LinearModelTest.LinearModelResidualMean(firstSample, secondSample)

LinearModelTest.LinearModelResidualMean(firstSample, secondSample, level)

LinearModelTest.LinearModelResidualMean(firstSample, secondSample, linearModel)

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

Parameters: 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 Threshold p-value of the test (= first kind risk), it must be , equal to 0.05 by default. testResult : TestResult Structure containing the result of the test.

Notes

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 and the -dimensional one is as follows: where is the residual, supposed to follow the standard Normal distribution.

The LinearModelResidualMean Test checks, under the hypothesis of a gaussian sample, if the mean of the residual is equal to zero. It is based on the Student test (equality of mean for two gaussian samples).

Examples

>>> 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.LinearModelResidualMean(firstSample, secondSample)
>>> print(test_result)
class=TestResult name=Unnamed type=ResidualMean binaryQualityMeasure=true p-value threshold=0.05 p-value=1 description=[]