COR - Correlation

\[\text{COR}(y, \hat{y}) = \frac{ COV(y, \hat{y}) }{ std(y) * std(\hat{y})}\]

• Best possible value = 1, bigger value is better. Range = [-1, +1)

Latex equation code:

\text{COR}(y, \hat{y}) = \frac{ COV(y, \hat{y}) }{ std(y) * std(\hat{y})}

• Measures the strength of the relationship between variables, is the scaled measure of covariance. It is dimensionless.

• the correlation coefficient is always a pure value and not measured in any units.

• https://corporatefinanceinstitute.com/resources/data-science/covariance/

Example to use COR metric:

from numpy import array
from permetrics.regression import RegressionMetric

## For 1-D array
y_true = array([3, -0.5, 2, 7])
y_pred = array([2.5, 0.0, 2, 8])

evaluator = RegressionMetric(y_true, y_pred, decimal=5)
print(evaluator.correlation())

## For > 1-D array
y_true = array([[0.5, 1], [-1, 1], [7, -6]])
y_pred = array([[0, 2], [-1, 2], [8, -5]])

evaluator = RegressionMetric(y_true, y_pred, decimal=5)
print(evaluator.COR(multi_output="raw_values"))