Motivated by the back-reaction debate, and some unexplained characteristics of the CMB, we investigate the possibility of some anisotropy in the universe observed around us. To this aim, we build up a novel prediction for the Hubble law for the late universe from a Bianchi type I model, taken as proof of concept, transcribing the departure of such model from a ΛCDM model. We dicussed the redshift measurement in this universe, and finally formalized the Hubble diagram.