The inversion of regolith thickness over the nearside hemisphere of the Moon from newly acquired Earth-based 70-cm Arecibo radar data is investigated using a quantitative radar scattering model. The radar scattering model takes into account scattering from both the lunar surface and buried rocks in the lunar regolith, and three parameters are critically important in predicting the radar backscattering coefficient: the dielectric constant of the lunar regolith, the surface roughness, and the size and abundance of subsurface rocks. The measured dielectric properties of the Apollo regolith samples at 450 MHz are re-analyzed, and an improved relation among the complex dielectric constant, bulk density and regolith composition is obtained. The complex dielectric constant of the lunar regolith is estimated globally from this relation using the regolith composition derived from Lunar Prospector gamma-ray spectrometer data. To constrain the lunar surface roughness and abundance of subsurface rocks from radar data, nine regions are selected as calibration sites where the regolith thickness has been estimated using independent analysis techniques. For these sites, scattering from the lunar surface and buried rocks cannot be perfectly distinguished, and a tradeoff relationship exists between the size and abundance of buried rocks and surface roughness. Using these tradeoff relations as guidelines for globally representative parameters, the regolith thickness of four regions over the lunar nearside is inverted, and the inversion uncertainties caused by calibration errors of the radar data and model input parameters are analyzed. The regolith thickness of the maria is generally smaller than that of highlands, and older surfaces have thicker regolith thicknesses. Our approach cannot be applied to regions where the surface roughness is very high, such as with young rocky craters and regions in the highly rugged highlands.