sklearn.feature_selection.f_regression(X, y, *, center=True)[source]

Univariate linear regression tests returning F-statistic and p-values.

Quick linear model for testing the effect of a single regressor, sequentially for many regressors.

This is done in 2 steps:

  1. The cross correlation between each regressor and the target is computed, that is, ((X[:, i] - mean(X[:, i])) * (y - mean_y)) / (std(X[:, i]) * std(y)) using r_regression function.

  2. It is converted to an F score and then to a p-value.

f_regression is derived from r_regression and will rank features in the same order if all the features are positively correlated with the target.

Note however that contrary to f_regression, r_regression values lie in [-1, 1] and can thus be negative. f_regression is therefore recommended as a feature selection criterion to identify potentially predictive feature for a downstream classifier, irrespective of the sign of the association with the target variable.

Furthermore f_regression returns p-values while r_regression does not.

Read more in the User Guide.

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data matrix.

yarray-like of shape (n_samples,)

The target vector.

centerbool, default=True

Whether or not to center the data matrix X and the target vector y. By default, X and y will be centered.

f_statisticndarray of shape (n_features,)

F-statistic for each feature.

p_valuesndarray of shape (n_features,)

P-values associated with the F-statistic.

See also


Pearson’s R between label/feature for regression tasks.


ANOVA F-value between label/feature for classification tasks.


Chi-squared stats of non-negative features for classification tasks.


Select features based on the k highest scores.


Select features based on a false positive rate test.


Select features based on an estimated false discovery rate.


Select features based on family-wise error rate.


Select features based on percentile of the highest scores.

Examples using sklearn.feature_selection.f_regression