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Actually, there is quite a strong relationship between the F-4, F-15 and F-16.

The first relationship is that the F-15 only exists because the Air Force did not want to suffer the same commonality fate as they did when having to accept the Navy's F-4. The AirForce had originally failed to produce an effective replacement for their F-4E for long range interception. They were counting on using their "Eagle" long range missile, carried first by the A-12(SR-71 interceptor variant)which was being redesigned to be used on the F-111. They came very close to having to accept the Navy's F-14, upon the failure of the F-111 fighter variant for both services.

The F-15's performance(specifically time-to-climb) was what kept the Air Force from having to live with the AWG-9 Radar and Eagle(Phoenix)missile as an Intercept solution. Had the F-14 started life with better engines, there never would have been an F-15 as we know it.

The engines are also the reason for the relationship between the F-15 and F-16. The YF-16 won the AirForce's Lightweight Fighter Program over the YF-17 largely because it incorporated the F-100 engine used in the F-15, resulting in much lower procurement and operating costs for the Air Force.

The other relationship between the F-15 and F-16 is that they were both the product of fighter design specifications that took advantage of the Energy-Manuverability doctrine of one Col. John Boyd, who is now considered the "father" of both aircraft, although he was unhappy about the final versions of each airplane. Boyd felt that they had been loaded down or "gold-plated" with attack-version hardpoints and unnessesary complexity.