# How to identify coefficients for all levels of categorical variables when you have multiple of them

I have an equation like y ~ x1 + x2 + x3 + x4 where the first 3 variables are categorical and the last one is continues. I want to identify the coefficients for all levels of these categorical variables. As you know, fitting OLS, I get one level for each variable as the base and the coefficients for the other levels are deviations from that base. I tried fitting 3 different specifications where I drop the intercept and estimate a coefficient for all of the levels in one of the categorical variables. I was hoping to use the results to solve the system of equations implied by those fits but it failed. Any suggestions for this problem?

## 1 Answer

The left-out level has an implied coefficient of 0, with an implied standard deviation of 0. How can I compute the standard error and confidence intervals for the base level on a variable? is a similar question with more details. Also Interpreting coefficient in GLM with categorical explanatory variables