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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.


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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 $$ \frac{\partial y}{\partial x_1}=a_1+a_{12}x_2 $$

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