A statistical analysis of the relationship between solar energetic particles (SEPs) and properties of solar flares and coronal mass ejections (CMEs) is presented. SEP events during Solar Cycle 23 are selected that are associated with solar flares originating in the visible hemisphere of the Sun and that are at least of magnitude M1. Taking into account all flares and CMEs that occurred during this period, the probability for the occurrence of an SEP event near Earth is determined. A strong rise of this probability is observed for increasing flare intensities, more western locations, higher CME speeds, and halo CMEs. The correlations between the proton peak flux and these solar parameters are derived for a low (> 10 MeV) and high (> 60 MeV) energy range excluding any flux enhancement due to the passage of fast interplanetary shocks. The obtained correlation coefficients are 0.55±0.07 (0.63±0.06) with flare intensity, and 0.56±0.08 (0.40±0.09) with CME speed for E>10 MeV (E>60 MeV). For both energy ranges, the correlations with flare longitude and CME width are very weak or non-existent. Furthermore, the occurrence probabilities, correlation coefficients, and mean peak fluxes are derived in multi-dimensional bins combining the aforementioned solar parameters. The correlation coefficients are also determined in different proton energy channels ranging from 5 to 200 MeV. The results show that the correlation between the proton peak flux and the CME speed decreases with energy, while the correlation with the flare intensity shows the opposite behaviour. Furthermore, the correlation with the CME speed is stronger than the correlation with the flare intensity below 15 MeV and becomes weaker above 20 MeV. When the enhancements in the flux profiles due to interplanetary shocks are not excluded, only a small but not very significant change is observed in the correlation coefficients between the proton peak flux below 7 MeV and the CME speed.