LinearModelTest_FullRegression

LinearModelTest_FullRegression(firstSample, secondSample, level=0.05)

Test whether two discrete samples are not linear.

Available usages:

LinearModelTest.FullRegression(firstSample, secondSample)

LinearModelTest.FullRegression(firstSample, secondSample, level)

Parameters
firstSample2-d sequence of float

First tested sample, of dimension n \geq 1.

secondSample2-d sequence of float

Second tested sample, of dimension 1.

levelpositive float < 1

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

Returns
testResultsCollection of TestResult

Results for each component of the linear model including intercept.

See also

LinearModelTest_PartialRegression, LinearModelTest_LinearModelFisher

Notes

The Full Regression Test is used to check the quality of the linear regression model between two samples: firstSample of dimension n and secondSample of dimension 1. If firstSample[i] is the sample extracted from firstSample (i^{th} coordinate of each point of the sample), FullRegression performs the linear regression test on all firstSample[i] and secondSample. The linear regression test tests if the linear regression model between two scalar samples is not significant. It is based on the deviation analysis of the regression.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> dim = 3
>>> distCol = [ot.Normal()] * dim
>>> S = ot.CorrelationMatrix(dim)
>>> S[0, dim - 1] = 0.99
>>> copula = ot.NormalCopula(S)
>>> distribution = ot.ComposedDistribution(distCol, copula)
>>> sample = distribution.getSample(30)
>>> firstSample = sample[:, :2]
>>> secondSample = sample[:, 2]
>>> test_result = ot.LinearModelTest.FullRegression(firstSample, secondSample)
>>> print(test_result)
[class=TestResult name=Unnamed type=Regression binaryQualityMeasure=true p-value threshold=0.05 p-value=0.605 statistic=-0.52335 description=[],class=TestResult name=Unnamed type=Regression binaryQualityMeasure=false p-value threshold=0.05 p-value=9.70282e-27 statistic=44.256 description=[],class=TestResult name=Unnamed type=Regression binaryQualityMeasure=true p-value threshold=0.05 p-value=0.11352 statistic=1.63564 description=[]]