# Why is the p-value changing and what does it mean [duplicate]

I have a simple question about regression.

The situation:
I have three variables $$X_1,X_2,X_3$$ and a variable I try to estimate $$Y$$. (In practice I have a list of participants for which the values of all of these variables are known)

Using regression I obtain $$Y= a_0 + a_1X_1 +a_2 X_2 +a_3 X_3 +a_{1,2}X_1\cdot X_2 + a_{1,3} X_1\cdot X_3 + a_{2,3} X_2\cdot X_3 + a_{1,2,3}X_1\cdot X_2\cdot X_3$$

and I get $$p$$-values for each of these coefficients.

I decreased all the values of $$Y$$ by $$10$$ (because I wanted the values to start at zero). Then I replaced $$X_1$$ with $$X_1-1$$ ($$X_1$$ was the gender, and instead of $$1,2$$ I wanted it to be $$0,1$$). Finally I divided $$X_2,X_3$$ by $$40$$ to get values between $$0$$ to $$1$$.
All these changes also changed the coefficieints $$a_0,a_1,...$$ (I understand why this is). Positive coefficients stay positive and negative stay negative. But the $$p$$-value changed and I do not understand why.
Does the $$p$$-value suppose to change by making these changes? What does it mean?
Basically I lack the understanding myself and I need your help to decide whether I can use the new data (for which the $$p$$ value is better) to conclude what I want.
• Ask yourself what the p-values are testing. For instance, in the original model the p-value for $a_1$ was testing $H_0: a_1=0.$ In the second model what is the null hypothesis in terms of the new coefficient? What is it in terms of the original coefficient?