/usr/include/openturns/swig/LinearModelTest_doc.i is in libopenturns-dev 1.7-3.
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"Test the quality of the linear regression model.
Based on the adjusted :math:`R^2` indicator.
**Available usages**:
LinearModelTest.LinearModelAdjustedRSquared(*firstSample, secondSample*)
LinearModelTest.LinearModelAdjustedRSquared(*firstSample, secondSample, level*)
Parameters
----------
fisrtSample : 2-d sequence of float
First tested sample, of dimension 1.
secondSample : 2-d sequence of float
Second tested sample, of dimension 1.
level : positive float :math:`< 1`
Threshold p-value of the test (= 1 - first type risk), it must be
:math:`< 1`, equal to 0.95 by default.
Returns
-------
testResult : :class:`~openturns.TestResult`
Structure containing the result of the test.
See Also
--------
LinearModelTest_LinearModelRSquared, LinearModelTest_LinearModelFisher,
LinearModelTest_LinearModelResidualMean
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 :class:`~openturns.LinearModel`). The linear regression model between the
scalar variable :math:`Y` and the :math:`n`-dimensional one
:math:`\\\\vect{X} = (X_i)_{i \\\\leq n}` is as follows:
.. math::
\\\\tilde{Y} = a_0 + \\\\sum_{i=1}^n a_i X_i + \\\\epsilon
where :math:`\\\\epsilon` is the residual, supposed to follow the standard Normal
distribution.
The LinearModelAdjustedRSquared test checks the quality of the linear
regression model. It evaluates the indicator :math:`R^2` adjusted (regression
variance analysis) and compares it to a level.
Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> func = ot.NumericalMathFunction('x', '2 * x + 1')
>>> firstSample = sample
>>> secondSample = func(sample) + ot.Normal().getSample(30)
>>> test_result = ot.LinearModelTest.LinearModelAdjustedRSquared(firstSample, secondSample)
>>> print(test_result)
class=TestResult name=Unnamed type=AdjustedRSquared binaryQualityMeasure=false p-value threshold=0.95 p-value=0.815998 description=[]
"
// ---------------------------------------------------------------------
%feature("docstring") OT::LinearModelTest::LinearModelFisher
"Test the nullity of the linear regression model coefficients.
**Available usages**:
LinearModelTest.LinearModelFisher(*firstSample, secondSample*)
LinearModelTest.LinearModelFisher(*firstSample, secondSample, level*)
Parameters
----------
fisrtSample : 2-d sequence of float
First tested sample, of dimension 1.
secondSample : 2-d sequence of float
Second tested sample, of dimension 1.
level : positive float :math:`< 1`
Threshold p-value of the test (= 1 - first type risk), it must be
:math:`< 1`, equal to 0.95 by default.
Returns
-------
testResult : :class:`~openturns.TestResult`
Structure containing the result of the test.
See Also
--------
LinearModelTest_LinearModelRSquared, LinearModelTest_LinearModelAdjustedRSquared,
LinearModelTest_LinearModelResidualMean
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 :class:`~openturns.LinearModel`). The linear regression model between the
scalar variable :math:`Y` and the :math:`n`-dimensional one
:math:`\\\\vect{X} = (X_i)_{i \\\\leq n}` is as follows:
.. math::
\\\\tilde{Y} = a_0 + \\\\sum_{i=1}^n a_i X_i + \\\\epsilon
where :math:`\\\\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).
Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> func = ot.NumericalMathFunction('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=[]
"
// ---------------------------------------------------------------------
%feature("docstring") OT::LinearModelTest::LinearModelRSquared
"Test the quality of the linear regression model based on the :math:`R^2` indicator.
**Available usages**:
LinearModelTest.LinearModelRSquared(*firstSample, secondSample*)
LinearModelTest.LinearModelRSquared(*firstSample, secondSample, level*)
Parameters
----------
fisrtSample : 2-d sequence of float
First tested sample, of dimension 1.
secondSample : 2-d sequence of float
Second tested sample, of dimension 1.
level : positive float :math:`< 1`
Threshold p-value of the test (= 1 - first type risk), it must be
:math:`< 1`, equal to 0.95 by default.
Returns
-------
testResult : :class:`~openturns.TestResult`
Structure containing the result of the test.
See Also
--------
LinearModelTest_LinearModelAdjustedRSquared, LinearModelTest_LinearModelFisher, LinearModelTest_LinearModelResidualMean
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 :class:`~openturns.LinearModel`). The linear regression model between the
scalar variable :math:`Y` and the :math:`n`-dimensional one
:math:`\\\\vect{X} = (X_i)_{i \\\\leq n}` is as follows:
.. math::
\\\\tilde{Y} = a_0 + \\\\sum_{i=1}^n a_i X_i + \\\\epsilon
where :math:`\\\\epsilon` is the residual, supposed to follow the standard Normal
distribution.
The LinearModelRSquared test checks the quality of the linear
regression model. It evaluates the indicator :math:`R^2` (regression
variance analysis) and compares it to a level.
Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> func = ot.NumericalMathFunction('x', '2 * x + 1')
>>> firstSample = sample
>>> secondSample = func(sample) + ot.Normal().getSample(30)
>>> test_result = ot.LinearModelTest.LinearModelRSquared(firstSample, secondSample)
>>> print(test_result)
class=TestResult name=Unnamed type=RSquared binaryQualityMeasure=false p-value threshold=0.95 p-value=0.822343 description=[]
"
// ---------------------------------------------------------------------
%feature("docstring") OT::LinearModelTest::LinearModelResidualMean
"Test zero mean value of the residual of the linear regression model.
**Available usages**:
LinearModelTest.LinearModelResidualMean(*firstSample, secondSample*)
LinearModelTest.LinearModelResidualMean(*firstSample, secondSample, level*)
Parameters
----------
fisrtSample : 2-d sequence of float
First tested sample, of dimension 1.
secondSample : 2-d sequence of float
Second tested sample, of dimension 1.
level : positive float :math:`< 1`
Threshold p-value of the test (= 1 - first type risk), it must be
:math:`< 1`, equal to 0.95 by default.
Returns
-------
testResult : :class:`~openturns.TestResult`
Structure containing the result of the test.
See Also
--------
LinearModelTest_LinearModelAdjustedRSquared, LinearModelTest_LinearModelFisher, LinearModelTest_LinearModelRSquared
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 :class:`~openturns.LinearModel`). The linear regression model between the
scalar variable :math:`Y` and the :math:`n`-dimensional one
:math:`\\\\vect{X} = (X_i)_{i \\\\leq n}` is as follows:
.. math::
\\\\tilde{Y} = a_0 + \\\\sum_{i=1}^n a_i X_i + \\\\epsilon
where :math:`\\\\epsilon` 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.NumericalMathFunction('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=[]
"
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