Consider a linear model:
$$y_{ij} = \alpha_i +\beta_i(x_{ij} − \bar x_i) + e_{ij}$$ , where $j \in \{1, \ldots , n\}$ and $i \in \{1, 2, 3\}$.
Suppose $H_0 : \alpha_1 = \alpha_2 = \alpha_3$ against the null that $H_0$ is not true.
I believe that I would use the F distribution, but how many degrees of freedom? Under the null hypothesis, I have 3 restricted parameters, so would the degrees of freedom under the null be 3?