# HypothesisTest_PartialRegression¶

`HypothesisTest_PartialRegression`(firstSample, secondSample, selection, level=0.05)

Test whether two discrete samples are independent.

Available usages:

HypothesisTest.PartialRegression(firstSample, secondSample, selection)

HypothesisTest.PartialRegression(firstSample, secondSample, selection, level)

Parameters: firstSample2-d sequence of floatFirst tested sample, of dimension . secondSample2-d sequence of floatSecond tested sample, of dimension 1. selectionsequence of int, maximum integer value List of indices selecting which subsets of the first sample will successively be tested with the second sample through the regression test. levelpositive 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 Partial Regression Test is used to check the quality of the linear regression AnalyticalFmodel between two samples: firstSample of dimension n and secondSample of dimension 1. The parameter selection enables to select specific subsets of the firstSample to be tested.

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]
>>> selection = [1]
>>> test_result = ot.HypothesisTest.PartialRegression(firstSample, secondSample, selection)
>>> print(test_result)
[class=TestResult name=Unnamed type=Regression binaryQualityMeasure=true p-value threshold=0.05 p-value=0.579638 description=[]]
```