I have a multiple linear regression model:
$$y= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5$$
where $x_1$ is a continuous variable and $x_2$, $x_3$, $x_4$ and $x_5$ are all dummy variables come from a 5 levels categorical variable. Now I found out the continuous variable and the categorical variable are dependent, so I have to add the interaction term into my model.
In this case, how many terms do I have to add? In other words, how many betas do I have to add to my model?
I don't think it is simply 4 or 5 betas, will it be something like 15 by combination?