What kind of regression can I run for categorical independent variables and continuous dependent variable? So I am currently trying to analyse the relationship between 3 categorical variables and their impact on the continuous/quantitative independent variable in R.
Basically, I want to analyse the impact that credit scores have on the remaining balance a customer has when they default and stop paying their loan.
Could someone tell me what kind of regression or test I could do to obtain explanatory results?
My linear regression only gives me an r squared of .27 with about 8700 observations in the initial data set.

You can use ANOVA as jzTUD indicates in which case you may have to use a post-hoc test such as Duncan or Bonferroni to determine which variables are significant. Alternatively, you can use multiple regression with indicator variables that although it requires a little more analysis after you get the results, it will tell you immediately which dependent variables are relevant to your model. See Ways of comparing linear regression interepts and slopes?.
