# How to properly conduct regression analysis with correlated variables

I am trying to assess the impact of a policy change using multiple market variables which are all correlated to some degree. In essence, there are domino effects in response to one policy. I have a model that I am putting hypothetical values in for the coefficients, but in trying to determine these values I realize that they too would be impacted by a change in the other independent variables.

How would I go about constructing a model where I can change values of one independent variable (the policy change) and get corresponding estimates for the effects of multiple variables? I could run the regression for each market variable independently, but I want to see how they all interact in the same system simultaneously.

Update: I Included a screenshot that shows how I am trying to use interaction variables. Again, I am primarily concerned with changes in independent variable A. However, the different values of A are going to impact B, C, D, E, and F. Likewise, when B changes, this will impact C, D, E, and F. Moreover, C will change and impact B, D, E, and F, etc. Is there a way to approach this efficiently? One way I thought is to have each value be a function that ultimately comes out to a regression, but then I would run into circular logic I think, and I'm not sure if this is correct.

## 1 Answer

I don't know if I've correctly understood your question, but could the thing you're searching for be the inclusion of interaction terms?

A normal bivariate regression is expressed as:

$y=w_1x+w_2z+\epsilon$

Including an interaction term to model the influence of $x$ in $z$ (and viceversa), you would add a third term like this:

$y=w_1x+w_2z+w_3xz+\epsilon$

I don't recall how interaction terms worked for continuous variables, but they certainly work like this for binary variables.

• This would definitely be worth exploring. I am trying to recall methods learned about in econometrics 18 months ago now. Sad how fast we can forget things, but yes interaction terms would seem to me to be a tool for addressing what I need I think. Nov 6, 2014 at 16:34
• I'm glad I helped :) Just ensure to check if and how they work for continuous variables, just to be sure. Nov 6, 2014 at 16:35
• The interaction variables help slightly, but they are hard to interpret. After centering them, they result in arbitrarily large numbers. When I go to predict the y value, I am not sure the models are doing what I hoped they would. Yes, they yield reasonable predictions but I am still faced with the issue of having to go variable-by-variable and make arbitrary estimates on an individual independent variable basis, where each estimate is sort of useless unless it factors in how the other variables affect it. Nov 6, 2014 at 18:38