In developing models of the radiation belt energetic electron flux, it is important to include the states of the interplanetary medium and the magnetosphere, as well as the solar activity. In this study we choose the log flux je(t;L;E) at 2--6 MeV, as measured by the Proton-Electron Telescope (PET) on SAMPEX in the period 1993--2002, as a representative flux variable and evaluate the usefulness of 17 interplanetary and magnetospheric (IP/MS) parameters in its specification. The reference parameter is the solar wind velocity, chosen because of its known high geoeffectiveness. We use finite impulse response filters to represent the effective coupling of the individual parameters to the log flux. We measure the temporal and spatial scales of the coupling using the impulse response function and the input's geoeffectiveness using the data-model correlation. The correlation profile as a function of L is complex, and we identify its peaks in reference to the radial regions P0 (L = 3.1--4.0, inner edge of the outer belt), P1 (4.1--7.5, main outer belt), and P2 (>7.5, quasi-trapped population), whose boundaries are determined from a radial correlative analysis (Vassiliadis et al., 2003b). Using the profiles, we classify the IP/MS parameters in four categories: (1) For the solar wind velocity and pressure the correlation is high and largely independent of L across P0 and P1, reaching its maximum in L = 4.8--6.1, or the central part of P1. (2) The IMF BSouth component and related IP/MS parameters have a bimodal correlation function, with peaks in region P0 (L = 3.0--4.1) and the geosynchronous orbit region within P1. (3) The IMF BNorth and four other interplanetary or solar irradiance parameters have a minimum correlation in P1, while the highest correlation is in the slot--outer belt boundary (L = 2.5). (4) Finally, the solar wind density has a unique correlation profile, which is anticorrelated with that of the solar wind velocity for certain L shells. We verify this classification using more complex filtering methods as well as standard correlation analysis. The categories correspond to four types of solar-terrestrial interactions, namely, viscous interaction, magnetic reconnection, effects of ionospheric heating, and effects of high solar wind density. The response to these interactions produces the observed inner magnetospheric coherence. In each category the L dependence of the correlation profile helps explain why geoeffective solar wind structures are followed by electron acceleration in some L ranges but not in others.