Implement the standard deviation.

lib/src/Uncertainty/Algorithm/MetaModel/LinearModel/LinearModelAnalysis.cxx

@@ -316,7 +316,17 @@ Scalar LinearModelAnalysis::getFisherPValue() const
   return FisherSnedecor(dofModel, dof).computeComplementaryCDF(FStatistic);
 }
 
-/* Kolmogorov-Smirnov normality test */
+/* Estimator of the standard deviation */
+Scalar LinearModelAnalysis::getResidualsStandardError() const
+{
+  const Scalar sigma2 = linearModelResult_.getSampleResiduals().computeRawMoment(2)[0];
+  const UnsignedInteger dof = linearModelResult_.getDegreesOfFreedom();
+  const UnsignedInteger n = linearModelResult_.getSampleResiduals().getSize();
+  const Scalar stdError = std::sqrt(sigma2 * n / dof);
+  return stdError;
+}
+
+/* Kolmogorov-Smirnov normality test of the residuals */
 TestResult LinearModelAnalysis::getNormalityTestResultKolmogorovSmirnov() const
 {
   // We check that residuals are centered with variance = sigma2
@@ -327,13 +337,13 @@ TestResult LinearModelAnalysis::getNormalityTestResultKolmogorovSmirnov() const
   return FittingTest::Kolmogorov(residuals, dist);
 }
 
-/* Anderson-Darling normality test */
+/* Anderson-Darling normality test of the residuals */
 TestResult LinearModelAnalysis::getNormalityTestResultAndersonDarling() const
 {
   return NormalityTest::AndersonDarlingNormal(linearModelResult_.getSampleResiduals());
 }
 
-/* Chi-Squared normality test */
+/* Chi-Squared normality test of the residuals */
 TestResult LinearModelAnalysis::getNormalityTestResultChiSquared() const
 {
   // Using OT::FittingTest::ChiSquared
@@ -342,7 +352,7 @@ TestResult LinearModelAnalysis::getNormalityTestResultChiSquared() const
   return FittingTest::ChiSquared(residuals, normalDistribution);
 }
 
-/* Cramer Von Mises normality test */
+/* Cramer Von Mises normality test of the residuals */
 TestResult LinearModelAnalysis::getNormalityTestCramerVonMises() const
 {
   return NormalityTest::CramerVonMisesNormal(linearModelResult_.getSampleResiduals());

lib/src/Uncertainty/Algorithm/MetaModel/LinearModel/openturns/LinearModelAnalysis.hxx

@@ -71,16 +71,19 @@ public:
   Scalar getFisherScore() const;
   Scalar getFisherPValue() const;
 
-  /** Kolmogorov-Smirnov normality test */
+  /** Estimator of the standard deviation */
+  Scalar getResidualsStandardError() const;
+
+  /** Kolmogorov-Smirnov normality test of the residuals */
   TestResult getNormalityTestResultKolmogorovSmirnov() const;
 
-  /** Anderson-Darling normality test */
+  /** Anderson-Darling normality test of the residuals */
   TestResult getNormalityTestResultAndersonDarling() const;
 
-  /** Chi-Squared normality test */
+  /** Chi-Squared normality test of the residuals */
   TestResult getNormalityTestResultChiSquared() const;
 
-  /** Cramer Von mises normality test */
+  /** Cramer Von mises normality test of the residuals */
   TestResult getNormalityTestCramerVonMises() const;
 
   /* [0] Draw model versus fitted values */

python/doc/examples/meta_modeling/general_purpose_metamodels/plot_linear_model.py

@@ -45,8 +45,8 @@
 import openturns.viewer as viewer
 
 # %%
-# Generation of the data set
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Simulate the data set
+# ~~~~~~~~~~~~~~~~~~~~~
 #
 # We first generate the data and we add noise to the output observations:
 
@@ -125,12 +125,12 @@
 #   Most of the variance is explained by the linear model.
 # - The F-test tests if all the coefficients are simultaneously zero.
 #   The `Fisher-Snedecor` p-value is lower than 1%. 
-#   The linear model assumption is accepted.
+#   Hence, there is at least one nonzero coefficient.
 # - The normality test checks that the residuals have a normal distribution.
-#   The normality assumption can be rejected if the p-value is close to zero
-#   (say, lower than 0.05).
+#   The normality assumption can be rejected if the p-value is close to one 
+#   (say, larger than 0.05).
 #   Based on the different statistical tests, we see that all p-values 
-#   are larger than 0.05: the normality assumption is accepted.
+#   are close to zero: the normality assumption of the residuals is accepted.
 #
 
 # %%
@@ -187,7 +187,7 @@
 
 # %%
 # In this case, there seem to be no obvious influential outlier characterized 
-# by large leverage and residual values, as is also shown in the figure below:
+# by large leverage and residual values.
 #
 # Similarly, we can also plot Cook's distances as a function of the sample 
 # leverages:

python/src/LinearModelAnalysis.i

@@ -33,7 +33,6 @@ def __LinearModelAnalysis_repr_html(self):
     tscores = self.getCoefficientsTScores()
     pValues = self.getCoefficientsPValues()
     names = lmResult.getCoefficientsNames()
-    sigma2 = lmResult.getSampleResiduals().computeRawMoment(2)[0]
     dof = lmResult.getDegreesOfFreedom()
     n = lmResult.getSampleResiduals().getSize()
     maximumNameLength = 20
@@ -78,7 +77,7 @@ def __LinearModelAnalysis_repr_html(self):
 
     # Print statistics
     html += "<ul>\n"
-    stdError = math.sqrt(sigma2 * n / dof)
+    stdError = self.getResidualsStandardError()
     html += f"  <li>Residual standard error: {stdError:.4e} " \
             f"on {dof} degrees of freedom </li>\n"
 

python/src/LinearModelAnalysis_doc.i.in

@@ -82,7 +82,7 @@ confidenceInterval : :class:`~openturns.Interval`
 // ---------------------------------------------------------------------
 
 %feature("docstring") OT::LinearModelAnalysis::getFisherScore
-"Accessor to the Fisher test.
+"Accessor to the Fisher statistics.
 
 Returns
 -------
@@ -101,9 +101,21 @@ fisherPValue : float
 
 // ---------------------------------------------------------------------
 
+%feature("docstring") OT::LinearModelAnalysis::getResidualsStandardError
+"Accessor to the standard error of the residuals.
+
+Returns
+-------
+stdError : float
+    This is the unbiased estimator :math:`\hat{\sigma}` of the standard deviation
+    of the Gaussian observation error of the observed output.
+"
+
+// ---------------------------------------------------------------------
+
 %feature("docstring") OT::LinearModelAnalysis::getNormalityTestResultChiSquared
 "Performs Chi-Square test.
-The statistical test checks the Gaussian assumption of the model (null hypothesis).
+The statistical test checks the Gaussian assumption of the residuals.
 
 Returns
 -------
@@ -124,7 +136,7 @@ the :meth:`~openturns.FittingTest.ChiSquared` to check the normality.
 %feature("docstring") OT::LinearModelAnalysis::getNormalityTestResultKolmogorovSmirnov
 "Performs Kolmogorov test.
 
-Performs Kolmogorov test to check Gaussian assumption of the model (null hypothesis).
+Performs Kolmogorov test to check Gaussian assumption of the residuals.
 
 Returns
 -------
@@ -140,7 +152,7 @@ We check that the residual is Gaussian thanks to :class:`~openturns.FittingTest:
 
 %feature("docstring") OT::LinearModelAnalysis::getNormalityTestResultAndersonDarling
 "Performs Anderson-Darling test.
-The statistical test checks the Gaussian assumption of the model (null hypothesis).
+The statistical test checks the Gaussian assumption of the residuals.
 
 Returns
 -------