Suppose we have a linear regression model where the response $Y$ is continuous and have $X_1, X_2$ as continuous predictor variables and $I_1, I_2, I_3, I_4$ as categorical predictors that refer to the seasons, i.e., $I_1$ is fall, $I_2$ is winter, etc.
Suppose we have:
$$ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3I_1 + \beta_4I_2 + \beta_5I_3 + \epsilon $$
where $I_4$ was dropped to prevent multicollinearity.
Normally, the interpretation of $\beta_3$ in a model where there are ONLY categorical predictors is that it is the difference in effects between $I_4$ and $I_1$, and that the intercept is the case where $\beta_0$ is the effect of $I_4$.
However, in this model, how do we interpret $\beta_0$ and $\beta_3$? Do we set the continuous predictors to zero? Thanks.