We have used scanning tunneling spectroscopy to investigate short-length electronic correlations in three-layer Bi2Sr2Ca2Cu3O10+δ (Bi-2223). We show that the superconducting gap and the energy Ωdip, defined as the difference between the dip minimum and the gap, are both modulated in space following the lattice superstructure and are locally anticorrelated. Based on fits of our data to a microscopic strong-coupling model, we show that Ωdip is an accurate measure of the collective-mode energy in Bi-2223. We conclude that the collective mode responsible for the dip is a local excitation with a doping dependent energy and is most likely the (π, π) spin resonance.