# Fixed effect panel regression with categorical variable

I have a fixed effect panel regression model using 'plm' function in R along with its 'within' option. It has three dummy variables x1, x2, and x3 representing four categories for my binary variables. So if all x1, x2, and x3 are 0, the forth category is 1 automatically. All variables and data are time varying.

I use these in my fixed effect panel regression using 'plm' command with its 'within' option. It has one more numerical variable x4 which is not binary. However, the regression has no intercept when I run the fixed effect panel regression.

Y = ax1 + bx2 + cx3 + dx4

If I want to find the effect of forth category I need to set all x1, x2, x3 as zeros. If so, what should I set for x4 to find the effect of the fourth category?

$$y = \beta_1d_1 + \beta_2d_2 + \beta_3d_3 + \beta_4d_4 + \beta_5x +\epsilon$$ is the same as $$y = \beta_0 + \beta_1d_1 + \beta_2d_2 + \beta_3d_3 + \beta_5x +\epsilon$$ with $x$ being your continuous variable and $d$ your categories. You need either the intersect $\beta_0$ or a categorical variable $d_4$ to include the effect of your fourth category in the model.