Re: +25 bhp resistor
The theory is they go in the air temperature sensor circuit to make the ecu think the air coming in is colder with more oxygen in, so you can add more fuel to get more power.
Thing is, most of the time the lambda sensor is just gonna report back to the ecu and say "It's a bit rich down here, back off a bit - there's a good chap" so negating any effect.
In some circumstances like flat out when the ecu ignores the lambda sensor, it will make the engine run a smidge richer, but that won't really give you any more power.
Best let the sensors do what they are designed to. If you want more power that way, the only effective method is a remap of the ecu.
Make something idiot proof and someone will only go and build a better idiot...