The prediction of reactor antineutrino spectra will play a crucial role as reactor experiments enter the precision era. The positron energy spectrum of 3.5 million antineutrino inverse beta decay reactions observed by the Daya Bay experiment, in combination with the fission rates of fissile isotopes in the reactor, is used to extract the positron energy spectra resulting from the fission of specific isotopes. This information can be used to produce a precise, data-based prediction of the antineutrino energy spectrum in other reactor antineutrino experiments with different fission fractions than Daya Bay. The positron energy spectra are unfolded to obtain the antineutrino energy spectra by removing the contribution from detector response with the Wiener-SVD unfolding method. Consistent results are obtained with other unfolding methods. A technique to construct a data-based prediction of the reactor antineutrino energy spectrum is proposed and investigated. Given the reactor fission fractions, the technique can predict the energy spectrum to a 2% precision. In addition, we illustrate how to perform a rigorous comparison between the unfolded antineutrino spectrum and a theoretical model prediction that avoids the input model bias of the unfolding method.