EC - Efficiency Coefficient

\[\text{EC}(y, \hat{y}) = 1 - \frac{ \sum_{i=1}^n (y_i - \hat{y_i})^2 }{ \sum_{i=1}^n (y_i - mean(Y))^2 }\]

Latex equation code:

\text{EC}(y, \hat{y}) = 1 - \frac{ \sum_{i=1}^n (y_i - \hat{y_i})^2 }{ \sum_{i=1}^n (y_i - mean(Y))^2 }

Efficiency Coefficient (EC) [18] is a metric used to evaluate the accuracy of a regression model in predicting continuous values.

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

• The EC ranges from negative infinity to 1, where a value of 1 indicates a perfect match between the model predictions and the observed data, and a value

of 0 indicates that the model predictions are no better than the benchmark prediction. + A negative value indicates that the model predictions are worse than the benchmark prediction. + Link to equation

Example to use EC 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)
print(evaluator.efficiency_coefficient())

## 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)
print(evaluator.EC(multi_output="raw_values"))