coincidence or ??

Ds1 had issues with milk based formula when he was an infant -- he is now 16, so when ds2 started giving me vague reminders of ds1 I decided to change him from milk based to Prosobee -- the same formula that worked with ds1. (I am pumping and bottle feeding and supplementing with formula as needed since I am not able to pump enough for every feeding)

Ds2 (now 5weeks) was not eating well (1-1.5 ounces every 2-3 hours at 2-3 weeks).  He had lost almost half of a pound between birth and his 4th day when he was hospitalized due to jaundice, dehydration, and low body temp (in hypothermia range).  It took him almost a week to regain his birth weight even with the ng tube.  He was released from the hospital weighing 6lbs1oz on 3/18/13.  On 3/29/13 his weight was still only at 6lbs4oz.  On 3/30/13 I made the decision to switch his formula to Prosobee and we feed him formula only on 3/31/13 and 4/1/13.  On 4/2/13 he weighed in at almost 6lbs10oz.  We resumed his previous feedings (part breastmilk part formula) with me eliminating dairy and as of 4/12/13 he was at almost 7.5lbs.  His intake also went from the 1-1.5oz to 3 oz. Now he is up to 3.5-4.5 oz every 2-3 hours.

Is it just a coincidence that he started eating and gaining weight when milk was removed or is that in indication that he doesn't tolerate milk like his older brother?  How would I prove the correlation, assuming one does exist?

Thanks.