I have 4 independent variables, and I want to check their combined and interrelated effects on 1 dependent variable (thus 1 y and 4 -xs).

(My study is into the effects of certain portfolio configurations, thus involving a lot of interactions)

I understand that this can be done via the creation of a 4-way interaction variable. However, this has the disadvantage of having to implement a whole lot of other terms aswell (for possible interaction, one term), or am I wrong?

The (second) question is, can this be done in a linear regression model?

Thanks in advance

Paul de Boer