By assuming a simple dipole approximation for the plasmonic response of small metallic nanoparticles, we derive close-form analytical expressions for the overall absorption enhancement and Raman scattering enhancement expected in the material filling the space around them. Ohmic losses inside the nanoparticles as well as inter-nanoparticle plasmon coupling effects are incorporated in the model. A comparison with accurate numerical simulations shows excellent agreement for a wide range of nanoparticle volume filling ratios, core/shell geometries, and even in the case of mixing different types of metals. Even though a simplified geometry without interfaces has been adopted in these derivations, our expressions nevertheless are intuitive and can become great tools in understanding, designing and optimizing nanoparticle-based plasmonic devices.