Following on from #17853

I'm interested in the mean distribution of the error which i'm calling bias (over or under predicting).
I can do this as a one liner in numpy (np.average(y_pred - y_true)) but I would prefer to stay in scikit-learn.

Describe the workflow you want to enable

bias(y_true, y_pred)

Describe your proposed solution

It has mostly been implemented in https://github.com/scikit-learn/scikit-learn/blob/fd237278e/sklearn/metrics/_regression.py#L181

Would just have to adjust

    output_errors = np.average(np.abs(y_pred - y_true),
                               weights=sample_weight, axis=0)

to

    output_errors = np.average(y_pred - y_true,
                               weights=sample_weight, axis=0)

Describe alternatives you've considered, if relevant

Additional context

Discussion of whether this is an error metric or not at #17853 (comment)