Moderating variable in Regression

#1
I'm running a regression with a Moderating variable (M) and an independent variable (X).

Its my understanding that I need to run the following regs:
1) Y = aX +bM
(2) Y = a'X +b'M+ c(XM)


My questions are:
(1) do a a' b b' and c all have to be significant?
(2) a' < a, then M is a moderating variable?

Thanks
 

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Ninja say what!?!
#2
1) no.
2) no.

I would answer in more detail. However, I don't know enough about what you're trying to do. Good luck though.