Linear model analysis

In [1]:
# import relevant module
import openturns as ot
import otpod
# enable display figure in notebook
try:
    %matplotlib inline
except:
    pass
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/sklearn/ensemble/weight_boosting.py:29: DeprecationWarning: numpy.core.umath_tests is an internal NumPy module and should not be imported. It will be removed in a future NumPy release.
  from numpy.core.umath_tests import inner1d

Generate data

In [2]:
N = 100
ot.RandomGenerator.SetSeed(123456)
defectDist = ot.Uniform(0.1, 0.6)
# normal epsilon distribution
epsilon = ot.Normal(0, 1.9)
defects = defectDist.getSample(N)
signalsInvBoxCox = defects * 43. + epsilon.getSample(N) + 2.5
# Inverse Box Cox transformation
invBoxCox = ot.InverseBoxCoxTransform(0.3)
signals = invBoxCox(signalsInvBoxCox)

Run analysis without Box Cox

In [3]:
analysis = otpod.UnivariateLinearModelAnalysis(defects, signals)
WARNING:root:Some hypothesis tests failed : you may consider to use the Box Cox transformation.

Get some particular results

In [4]:
print(analysis.getIntercept())
print(analysis.getR2())
print(analysis.getKolmogorovPValue())
[Intercept for uncensored case : -604.758]
[R2 for uncensored case : 0.780469]
[Kolmogorov p-value for uncensored case : 0.803087]

Show graphs

The linear model is not correct

In [6]:
fig, ax = analysis.drawLinearModel()
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_11_1.png

The residuals are not homoskedastic

In [7]:
fig, ax = analysis.drawResiduals()
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_13_1.png

Run analysis with Box Cox

In [8]:
analysis = otpod.UnivariateLinearModelAnalysis(defects, signals, boxCox=True)

Save all results in a csv file

In [10]:
analysis.saveResults('results.csv')

Show graphs

The linear regression model with data

In [11]:
fig, ax = analysis.drawLinearModel(name='figure/linearModel.png')
# The figure is saved as png file
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_21_1.png

The residuals with respect to the defects

In [12]:
fig, ax = analysis.drawResiduals(name='figure/residuals.eps')
# The figure is saved as eps file
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_23_1.png

The fitted residuals distribution with the histogram

In [13]:
fig, ax = analysis.drawResidualsDistribution()
ax.set_ylim(ymax=0.45)
fig.show()
# The figure is saved after the changes
fig.savefig('figure/residualsDistribution.png', bbox_inches='tight')
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_25_1.png

The residuals QQ plot

In [14]:
fig, ax = analysis.drawResidualsQQplot()
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_27_1.png

The Box Cox likelihood with respect to the defect

In [15]:
fig, ax = analysis.drawBoxCoxLikelihood(name='figure/BoxCoxlikelihood.png')
fig.show()
/calcul/home/dumas/anaconda/lib/python3.6/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "
../_images/examples_linearAnalysis_29_1.png
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