Octane is a funny thing...
If your engine computer senses a knock (detonation/ping) it will retard the timing (and other changes) which will cost you some power & efficiency.
More octane increases the detonation resistance but so does increase in elevation and cooler ambient temperatures. Every 1000 feet of elevation at 70 degrees F would allow you to lower the octane rating by one point. Every 10 degree drop in temperature does the same.
If you live at sea level and its hot, odds are you should be running the premium to get the most out of your car.
Pay close attention to your actual fuel milage (using your odometer and fuel receipts) running premium for a month while driving normally then do the math for MPG, make the switch to regular and do the same. If your fuel milage increases with one Vs the other odds are it is making more power. Now compare the cost difference of the fuel and decide if its worth it.
Note: Some PCM's learn where the knock threshold is and adjust the programming accordingly, however they may not immediately adjust back the other way just because you put the premium gas in. PCM's will test themselves and make adjustments when certain drive cycles are met like only if it is between 65-75 degrees ambient temperature when the engine is started and the intake air temperature is within 2 degrees of ambient after 5 minutes and the moon is full, and you are traveling west at 52 MPH for exactly 3 minutes. Some drive cycles are ridiculous...
But there is probably a way to get you PCM to reset before you start each test I don't know what Jeep requires but my Acura just had to have the battery disconnected for 5 minutes to reset. The Acura would change tunes if sensed a knock and seemed like it would never go back until the battery was disconnected.