I have spent a significant amount of time on this, but my knowledge in Matrix Algebra is still limited. So, I am not sure ...
I have a linear regression model based on $n$ observations. The dependent variable is $y$.
As predictors, there are 10 independent continuous variables + 9 dummy variables (based on a 10-category scale) + 5 dummy variables (based on a 6-category response). The model looks like: $$ y = \beta_0+\beta_1 \text{C}_1+\beta_2 \text{C}_2+ ...+\beta_{11}\text{dummy}_1+\beta_{12}\text{dummy}_2+ ...+\beta_{19}\text{dummy}_9+\beta_{20}\text{dummy}_{10}+...\beta_{24}\text{dummy}_{14}+\epsilon $$
Would this be an accurate matrix notation of the above model? $$ \textbf{y} = \textbf{C}{\beta}+\textbf{S} \gamma + \mathbf{R}\lambda + \textbf{e} $$
where $\textbf{C}$ is n $\times$ 10+1 design matrix with 1s in the first column and 10 other columns containing the continuous predictors , $\textbf{S}$ is the n $\times$ 9 matrix containing dummy variables for the 10-category scale, $\textbf{R}$ is the n $\times$ 5 matrix containing dummy variables for the 6-category response, ${\beta}$, ${\gamma}$ and ${\lambda}$ are the vectors of parameters, and $\textbf{e}$ is the error vector.
Is this notation sufficiently accurate? Any references on matrix notation for dummy variables are also very much appreciated.
Sincerely,
Jacob