The simplest kind of correlation: proportionality.
Which would mean in an ideal world that if the I-797 reads that you should be getting the IL within 100 days, it would come in 100 days. And if it reads 425 days the IL would be coming within 425 days.
The point is that it is not quite the case - some letters mention 900 days and the IL comes after a matter of months. Other letters mention 100 days and a VERY long time elapses before the IL comes.
Granted, by nature the USCIS does not own the whole process, in particular the time required by different agencies to perform the security checks.
To summarize, the number of days on the I-797 is a kind of "best guesstimate", i.e. it somehow indicates what the initial assessment by the USCIS of the time it *should* take to process the application in the best case.
On a positive note, my I-797 mentioned 120 days and... guess what... I got the IL after 115 days from the Priority Date. Quite good "guesstimate" indeed!!! And another good point to the credit of the USCIS is that the Interview is 6 months minus one day from the Priority Date - very much in line with the congressional view that the Naturalization process should require six months.
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Detroit DO - NSC
03/16/07 N-400 sent to NSC
03/20/07 Priority Date
03/23/07 Notice of Action letter received
03/23/07 FP letter received
04/12/07 FP done
09/19/07 Interview Appointment
(Notice date July 13)