The linear interrelationship between the Dst, AE, ap, and the IMF-Bz were presently investigated in pairs and multiples during magnetic quiet (), disturbed (), and combined activities, as well as for different storm phases using data obtained from 1996-2006. The results from the study indicate the highest correlation percentage (%corr) between pairs of indices was for the AE/ap (73%) occurring during the storm onset phase. The %corr was 21-57%, (50-73%), (23-52%), (5-40%), Bz/ap (24-60%), and (7-37%) across various levels of activities. The results for the multiple correlation relationships of the and showed that the magnitudes of the coefficients of best fit are smallest during quiet magnetic activity in comparison to other activities, suggesting that ap and Bz are well explained by the independent variables carrying the coefficient during the quiet condition and can be better inferred during the same period of magnetic activity. The present results suggest that the ap index is well correlated with the Dst as an intermediate index regarding the ap index and can describe the general state of planetary geomagnetic activity. It contains at least two or more major sources, the auroral electrojet () and the ring current; also, by means of a multiple correlation program, a linear fit can be performed for ap in terms of AE and Dst. Furthermore, only the pair has a %corr of above 50% for any activity class. For the entire data span, the AE/ap pair performed best at 67%, followed by the pair with 59%, and the least was the pair with 37%. Additionally, the results r.evealed that the AE/ap relationship presents the highest values of 73.25%, 62.16% and 68.56% during the storm onset, main, and recovery phases, respectively.