# Does stand-alone dummy variables in linear regression models make sense?

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.

• A regression with one response and a one binary predictor is in essence equivalent to Student's t test comparing two means. This is often regarded as too puzzling to be mentioned in introductory texts and too obvious to be underlined in more advanced texts. (In practice, not everything in your favourite software to do either procedure may match exactly.) – Nick Cox Oct 25 '13 at 13:54