Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

$y$=value, $x_1$=material, $x_2$=weight, $x_3$=color

$x_1$ and $x_2$ are interacting variables but $x_3$ is not. Right now I'm using something like: $$ y = a_0 + a_1x_1 + a_2x_2 + a_3x_3 + a_{12}x_1x_2 + u $$ I'm pretty new to regression analysis so I wonder if there is any way to convert this formula to something like $$ y = a_0 + a_1x_1 + a_2x_2 + a_3x_3 + u $$ so I can see how much effect $x_1$ and $x_2$ have simply by looking at $a_1$ and $a_2$? 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 $a_{12}$ and distributing the effect over $a_1$ and $a_2$ 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.

share|improve this question

2 Answers 2

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.

share|improve this answer

The effect of $x_1$ depends on the value of $x_2$. For a particular value of $x_2$, the effect of $x_1$ is $$ \frac{\partial y}{\partial x_1}=a_1+a_{12}x_2 $$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.