We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability

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... tion, the variance of the conductance, and the shot noise power by varying b (the effective bandwidth of the PBRM model) from small (b≪ 1) to large (b>1) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit b→∞. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with b ∈ [0.2,0.4] reproduces well the scattering and transport properties of the 3D Anderson model.