r2_score: Coefficient of Determination (R²) Metric

The r2_score function computes the coefficient of determination (R²) for regression tasks. This metric measures the proportion of variance in the target variable that is explained by the model.

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Overview

R² is a standard metric for evaluating regression models: - R² = 1 indicates perfect prediction. - R² = 0 indicates the model does no better than the mean. - R² < 0 indicates the model performs worse than the mean.

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Parameters

Parameter	Type	Description	Default
y_true	array-like	True values (targets).	Required
y_pred	array-like	Predicted values.	Required
verbose	bool	If True, enables detailed logging for debugging.	False

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Returns

• float
  Proportion of variance explained (1 is perfect prediction).

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Raises

• TypeError
  If inputs are not array-like.
• ValueError
  If shapes do not match or inputs are empty.

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Example Usage

import numpy as np
from machinegnostics.metrics import r2_score

y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
score = r2_score(y_true, y_pred)
print(score)

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adjusted_r2_score: Adjusted R² Metric

The adjusted_r2_score function computes the adjusted R² score, which accounts for the number of predictors in the model. This metric penalizes the addition of unnecessary features.

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Overview

Adjusted R² is useful for comparing models with different numbers of predictors: - Adjusted R² increases only if the new predictor improves the model more than would be expected by chance.

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Parameters

Parameter	Type	Description	Default
y_true	array-like	True values (targets).	Required
y_pred	array-like	Predicted values.	Required
n_features	int	Number of features (independent variables) in the model.	Required
verbose	bool	If True, enables detailed logging for debugging.	False

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Returns

• float
  Adjusted R² accounting for number of predictors.

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Raises

• TypeError
  If inputs are not array-like or n_features is not a non-negative integer.
• ValueError
  If shapes do not match, inputs are empty, or n_features is invalid.

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Example Usage

import numpy as np
from machinegnostics.metrics import adjusted_r2_score

y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
n_features = 2
score_adj = adjusted_r2_score(y_true, y_pred, n_features)
print(score_adj)

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Notes

• Both functions support input as lists, numpy arrays, or pandas Series.
• Inputs must be 1D, have the same shape, and must not be empty or contain NaN/Inf.
• Adjusted R² is undefined if the number of samples is less than or equal to the number of features plus one.

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Author: Nirmal Parmar
Date: 2025-09-24

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