Finding regression intervals

It's not always guaranteed that we have accurate models. Sometimes, our data is inherently noisy and we cannot model it using a regressor. In these cases, it is important to be able to quantify how certain we arein our estimations. Usually, regressors make point predictions. These are the expected values (typically the mean) of the target (y) at each value of x. A Bayesian ridge regressor is capable of returning the expected values as usual, yet it also returns the standard deviation of the target (y) at each value of x.

To demonstrate how this works, let's create a noisy dataset, where :

import numpy as np
import pandas as pd

df_noisy = pd.DataFrame(
    {
        'x': np.random.random_integers(0, 30, size=150),
        'noise': np.random.normal(loc=0.0, scale=5.0, size=150)
    }
)

df_noisy['y'...