The dominant theoretical uncertainties in both the anomalous magnetic moment of the muon and the value of the electromagnetic coupling at the Z scale, M(Z), arise from their hadronic contributions. Since these will ultimately dominate the experimental errors, we study the correlation between them, as well as with other fundamental parameters. To this end we present analytical formulas for the QCD contribution from higher energies and from heavy quarks. Including these correlations affects the Higgs boson mass extracted from precision data.