Note

Click here to download the full example code

# Estimate correlation coefficients¶

In this example we are going to estimate the correlation between an output sample Y and the corresponding inputs using various estimators:

Pearson coefficients

Spearman coefficients

PCC: Partial Correlation Coefficients

PRCC: Partial Rank Correlation Coefficient

SRC: Standard Regression Coefficients

SRRC: Standard Rank Regression Coefficient

```
from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
```

To illustrate the usage of the method mentionned above, we define a set of X/Y data using the Ishigami model. This classical model is defined in a data class :

```
from openturns.usecases import ishigami_function as ishigami_function
im = ishigami_function.IshigamiModel()
```

Create X/Y data We get the input variables description :

```
input_names = im.distributionX.getDescription()
size = 100
inputDesign = ot.SobolIndicesExperiment(im.distributionX, size, True).generate()
outputDesign = im.model(inputDesign)
```

## PCC coefficients¶

We compute here PCC coefficients using the CorrelationAnalysis

```
pcc_indices = ot.CorrelationAnalysis.PCC(inputDesign, outputDesign)
print(pcc_indices)
```

Out:

```
[0.48083,0.0118573,-0.0399335]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(pcc_indices, input_names, "PCC coefficients")
view = viewer.View(graph)
```

## PRCC coefficients¶

We compute here PRCC coefficients using the CorrelationAnalysis

```
prcc_indices = ot.CorrelationAnalysis.PRCC(inputDesign, outputDesign)
print(prcc_indices)
```

Out:

```
[0.48438,-0.00850357,-0.0310585]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(prcc_indices, input_names, "PRCC coefficients")
view = viewer.View(graph)
```

## SRC coefficients¶

We compute here SRC coefficients using the CorrelationAnalysis

```
src_indices = ot.CorrelationAnalysis.SRC(inputDesign, outputDesign)
print(src_indices)
```

Out:

```
[0.231036,0.000107773,0.00122827]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(src_indices, input_names, 'SRC coefficients')
view = viewer.View(graph)
```

Case where coefficients sum to 1 :

```
scale_src_indices = ot.CorrelationAnalysis.SRC(inputDesign, outputDesign, True)
print(scale_src_indices)
```

Out:

```
[0.99425,0.000463796,0.00528582]
```

And its associated graph:

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(scale_src_indices, input_names, 'Scaled SRC coefficients')
view = viewer.View(graph)
```

Finally, using signed src: we get the trend importance :

```
signed_src_indices = ot.CorrelationAnalysis.SignedSRC(inputDesign, outputDesign)
print(signed_src_indices)
```

Out:

```
[0.480662,0.0103814,-0.0350468]
```

and its graph :

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(signed_src_indices, input_names, 'Signed SRC coefficients')
view = viewer.View(graph)
```

## SRRC coefficients¶

We compute here SRRC coefficients using the CorrelationAnalysis

```
srrc_indices = ot.CorrelationAnalysis.SRRC(inputDesign, outputDesign)
print(srrc_indices)
```

Out:

```
[0.234826,5.52475e-05,0.00074076]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(srrc_indices, input_names, 'SRRC coefficients')
view = viewer.View(graph)
```

## Pearson coefficients¶

We compute here the Pearson coefficients using the CorrelationAnalysis

```
pearson_correlation = ot.CorrelationAnalysis.PearsonCorrelation(inputDesign, outputDesign)
print(pearson_correlation)
```

Out:

```
[0.482871,0.0178456,-0.0638373]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(pearson_correlation,
input_names,
"Pearson correlation coefficients")
view = viewer.View(graph)
```

## Spearman coefficients¶

We compute here the Pearson coefficients using the CorrelationAnalysis

```
spearman_correlation = ot.CorrelationAnalysis.SpearmanCorrelation(inputDesign, outputDesign)
print(spearman_correlation)
```

Out:

```
[0.486298,-0.00194796,-0.0585667]
```

```
graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(spearman_correlation,
input_names,
"Spearman correlation coefficients")
view = viewer.View(graph)
plt.show()
```

**Total running time of the script:** ( 0 minutes 0.590 seconds)