Summary

DummyProbaRegressor._predict_var returns the standard deviation (σ) of the training labels instead of the variance (σ²). This is a unit-mismatch bug — variance ≠ std dev — so any downstream usage of predict_var on this estimator produces numerically incorrect results.

Steps to Reproduce

import numpy as np
import pandas as pd
from sklearn.datasets import load_diabetes
from sklearn.model_selection import train_test_split
from skpro.regression.dummy import DummyProbaRegressor

X, y = load_diabetes(return_X_y=True, as_frame=True)
X = X.iloc[:50]
y = pd.DataFrame(y.iloc[:50])
X_train, X_test, y_train, _ = train_test_split(X, y, random_state=42)

reg = DummyProbaRegressor(strategy="empirical")
reg.fit(X_train, y_train)

y_pred_var = reg.predict_var(X_test)

expected_variance = np.var(y_train.values)
std_dev            = np.std(y_train.values)

print(f"predict_var returned: {y_pred_var.values[0, 0]:.4f}")
print(f"std dev (wrong):      {std_dev:.4f}")
print(f"variance (correct):   {expected_variance:.4f}")

Expected output:

predict_var returned: 3057.xxxx   # matches variance
std dev (wrong):      55.xxxx
variance (correct):   3057.xxxx

Actual output (buggy):

predict_var returned: 55.xxxx    # matches std dev — WRONG
std dev (wrong):      55.xxxx
variance (correct):   3057.xxxx

Root Cause

In skpro/regression/dummy.py:

# _fit — self._sigma stores std dev, not variance
self._sigma = np.std(y.values)   # ← σ

# _predict_var — BUG: fills with self._sigma (std dev) instead of variance
y_pred = pd.DataFrame(
    np.ones(X_n_rows) * self._sigma,   # ← should be self._sigma**2 or self._var
    index=X_ind, columns=self._y_columns
)

The method _predict_var is documented to return variance, but uses self._sigma which stores the standard deviation. The same bug affects both 'empirical' and 'normal' strategies.

Expected Behaviour

predict_var should return values equal to np.var(y_train.values) — the variance of the training labels — matching the definition in BaseProbaRegressor.

Fix Direction

1. In _fit, store self._var = np.var(y.values) alongside the existing self._sigma.
2. In _predict_var, replace self._sigma with self._var.

This is a 2-line fix in a single file (skpro/regression/dummy.py, 182 lines total).

Environment

• skpro version: current main (commit c83950a)
• Python 3.12

Good First Issue?

Yes — this is a straightforward, beginner-friendly fix:

• Single file, 2-line change
• No algorithmic complexity
• Needs 1 new test to verify correctness
• Good entry point for understanding the skpro regressor API (_fit/_predict_var pattern)