We present the analysis of a decaying active region observed by the EUV Imaging Spectrometer on Hinode during 2009 December 7-11. We investigated the temporal evolution of its structure exhibited by plasma at temperatures from 300,000 to 2.8 million degrees, and derived the electron density, differential emission measure, effective electron temperature, and elemental abundance ratios of Si/S and Fe/S (as a measure of the First Ionization Potential (FIP) Effect). We compared these coronal properties to the temporal evolution of the photospheric magnetic field strength obtained from the Solar and Heliospheric Observatory Michelson Doppler Imager magnetograms. We find that, while these coronal properties all decreased with time during this decay phase, the largest change was at plasma above 1.5 million degrees. The photospheric magnetic field strength also decreased with time but mainly for field strengths lower than about 70 Gauss. The effective electron temperature and the FIP bias seem to reach a “basal” state (at 1.5 × 106 K and 1.5, respectively) into the quiet Sun when the mean photospheric magnetic field (excluding all areas <10 G) weakened to below 35 G, while the electron density continued to decrease with the weakening field. These physical properties are all positively correlated with each other and the correlation is the strongest in the high-temperature plasma. Such correlation properties should be considered in the quest for our understanding of how the corona is heated. The variations in the elemental abundance should especially be considered together with the electron temperature and density.