Galactic cosmic rays are modulated in the heliosphere primarily by the global merged interaction regions with intense magnetic fields, which leads to a decrease in galactic cosmic rays throughout the heliosphere. Using long-term averages of solar wind (SW) component parameters in addition to cosmic ray count rates of four neutron monitors with different rigidity cutoffs, we analyzed the effect of these SW components on the count rates under different interplanetary magnetic field (IMF) disturbance levels. From first-order partial correlation, we found that the IMF-B was the most dominant modulating parameter, especially during quiet conditions and the SW dynamic pressure was more effective during disturbed conditions. The influence of more subtle parameters like wind speed, Bz component, and proton density were masked by these dominant parameters: IMF total B, and SW dynamic pressure.