Dummy (or binary) variables ($X_2$) can be used in linear regression models to help explaining a possible group effect that a continuous predictor variable ($X_1$) might present in explaining the response variable ($Y$).
Now, I am wondering if it makes sense to have only dummy variables as predictors in a linear regression model with a continuous response variable. Does it?
Example:
% of population with instruction = influenced by politics A + influenced by politics B.
Both politics A and B can assume values 1 or 0.
Best Answer
Because linear regression does not assume any distribution of predictors, as long as
Your example is just like using regression as an ANOVA sans interaction (aka, not a full-factorial design.) If additional effect due to co-influence by A & B is of your interest, compute an interaction term (by multiplying your two dummy variables) and include it as a predictor as well.