COV - Covariance

\[\text{COV}(y, \hat{y}) = \frac{\sum_{i=1}^{N} (y_i - mean(Y)) (\hat{y}_i - mean(\hat{Y}))}{N}\]

• There is no best value, bigger value is better. Range = [-inf, +inf)

• Positive covariance: Indicates that two variables tend to move in the same direction.

• Negative covariance: Reveals that two variables tend to move in inverse directions.

Latex equation code for covariance of population:

\text{COV}(y, \hat{y}) = \frac{\sum_{i=1}^{N} (y_i - mean(Y)) (\hat{y}_i - mean(\hat{Y}))}{N}

Latex equation code for covariance of sample:

\text{COV}(y, \hat{y}) = \frac{\sum_{i=1}^{N} (y_i - mean(Y)) (\hat{y}_i - mean(\hat{Y}))}{N - 1}

• COV is a measure of the relationship between two random variables.

• evaluates how much – to what extent – the variables change together.

• does not assess the dependency between variables.

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

Example to use COV 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.covariance())

## 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.COV(multi_output="raw_values"))