# Achieve continuous predictions in linear regression with all categorical independent variables

I am working my way for the first time through predicting a continuous dependent variable in a problem where all independent variables are categorical. Say I need to predict a continuous variable starting from a single categorical independent variable that can take 4 values. After dummy-encoding the categorical variable, a simple linear regression would find the coefficients, and predict discrete values (in my case, predictions would be four values). Is there any way to smooth my predictions?

• Can you give more detail on what you mean by "smoothing" & its purpose? After all, with only four possible predictor patterns it seems natural enough that there should only be four possible predictions - would you really want to make different predictions for individuals with identical predictor patterns? Mar 13, 2017 at 10:02
• What's continuous is the distribution at any combination of the covariates. If you only predict the mean of that distribution (a single point) at such a combination, then naturally that's not continuous when you have discrete predictors. Mar 13, 2017 at 10:07
• Can you say why you want to make predictions? Mar 13, 2017 at 12:33