The specification that led to the F-15 was created before the MiG-25 scare. It was originally intended to be a 60,000 lb Mach 3 interceptor, but the "fighter mafia" got the weight trimmed down to 40,000 lbs. In the LBJ/McNamara years, getting money for an aircraft with only a single mission ("not a pound for air to ground") was almost impossible, so the MiG-25 was used as a justification for funding the F-15 program. The Mach 3 specification was eventually reduced to Mach 2.8 (which the original F-15 can supposedly do if only for a moment) to help cut costs and permit a large bubble canopy.
The MiG-25 blew the Phantom away in time to climb records and supposedly achieved Mach 3.2 (later information indicates that it was an unmanned drone being tracked on radar, not a MiG-25 or that it was a MiG-25 with an engine overspeed problem... the MiG-25 starts suffering thermal damage to its wings at Mach 3). The US experts assumed the Soviets achieved this speed and climb performance with high-bypass turbofans much like the ones used in the F-15 and F-111/F-14. In fact they had used an ingenius arrangement involving turbojets centered in large pipes that get bypassed by supersonic airflow to become ramjets. They also assumed the MiG-25 used titanium extensively like the SR-71, but it was only stainless steel and aluminum (hence the speed limit of Mach 2.8 to 3 regardless of engine power). Since turbofans are even more powerful at lower speeds and titanium construction would permit a lighter airframe weight and higher g-limits, they grossly overestimated the subsonic thrust to weight ratio and agility of the MiG-25.
The F-15 pushed the limits of Western technology at the time and could not even begin to match the intell estimates. Of course, announcing this to the public secured funding for the F-15. The 1976 defection of Victor Belenko occurred 3 years after the first F-15 flight and 1 year after the F-15 entered service. It lifted the veil of secrecy over the MiG-25 and left the F-14/F-15 fighters standing far above all others as the best interceptors in the world.
I have to say that it is a fact that the F-15 was being planned and developed 2 to 5 years before the existence of the MiG-25 was even publicly announced, so it was not a response to that aircraft Experience in Vietnam had more influence on the design changes than the MiG-25 threat: bubble canopy rather than top speed, internal gun, and maneuverabililty over speed.
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TAC, the F-4 was originally bought by the Navy for "Fleet Air Defense"-- a missile interceptor. The Air Force was never happy having been forced to buy the F-4 since their pride was hurt when a Navy multi-role aircraft with the weight penalties associated with carrier borne aircraft smoked all the the Air Force's single mission types (the F-4 climbed faster than an F-104, it was outright faster than anything else at altitude, and had better radar than the F-106). So the F-15 was meant to be a true Air Force design to replace the F-4 in the air-to-air roles, of course Vietnam taught them that a 60,000 lb Mach 3 fighter with no gun and no maneuverability was not a good replacement, so the specification was radically modified.
