Multiple linear regression with interaction

Question

I'm doing a multiple linear regression with interacting variables. I'll give you an example:

y=value a1=material a2=weight a3=color

a1 and a2 are interacting variables but a3 is not. Right now I'm using something like:

y = a0 + a1x1 + a2x2 + a3x3 + a12x1x2

I'm pretty new to regression analysis so I wonder if there is any way to convert this formula to something like

y = a0 + a1x1 + a2x2 + a3x3

so I can see how much effect a1 and a2 have simply by looking at a1 and a2? What I want to do is to just be able to look at the equation and understand how much 1 kg of extra weight adds in value without needing to calculate y. Splitting up the interaction term a12 and distributing the effect over a1 and a2 if you guys understand what I mean. Maybe it's not possible or maybe there is a better regression method that is more suited for this, I don't know. I'd love to get some pointers from you guys.

Thanks.

Answer 1

If interaction is significant then model $y=\alpha_0+\alpha_1x_1+\alpha_2x_2+\alpha_3x_3+\alpha_{12}x_1x_2$ is pretty good, however, interaction term $x_1x_2$ is non-distributable - this is the reason it is called interaction term. If $\alpha_{12}=4$, we can not know whether we should add 1 to $\alpha_1$ and 3 to $\alpha_2$ or vice versa - they affect $y$ together.