Is it possible to conduct a regression if all dependent and independent variables are categorical variables?
We need to be clear on our terms here, but in general, yes:
- If your dependent variable is continuous (and the residuals are normally distributed—see here), but all of your independent variables are categorical, this is just an ANOVA.
- If your dependent variable is categorical and your independent variables are continuous, this would be logistic regression (possibly binary, ordinal, or multinomial, depending).
- If both your dependent variable and your independent variables are categorical variables, you can still use logistic regression—it's kind of the ANOVA-ish version of LR.