When recording in mp4 format would you expect both resolution and bit rate to affect the files size?

I'm not seeing any change when changing resolution but I do when changing bit rate.

Guess I thought I read somewhere that file size is related to (resolution W x resolution H x bit rate). Any truth to that?

File size = Bit-rate x duration

If you think about it, the file size is measured in bits or bytes (where 8bits = 1 byte), or in KB or MB, and the bit-rate is bits per second, so what you're defining is effectively size/time, and duration equals time, so the overall formula is "size/time x time = size".

Resolution doesn't come into this particular equation, but there is a bigger equation in which you could include it, along the lines of:-
"resolution x frame rate x quality = bit-rate" so that if you want to increase the resolution or frame rate AND maintain the quality (using the same codec), then you must also increase the bit-rate, and by implication also the file size (for a given duration).