Multiple Linear Regression in Matrix Form

Question

I am currently studying for my exams and came across the following question:

State the multiple linear regression equation in matrix form. Write down the order of each matrix and explain what the elements of each matrix and vector stand for. Write down the standard assumptions for the multiple linear regression.

I understand how order in a matrix normally depending on the amount of rows and columns of the matrix, but don't understand when I am talking in terms of the multiple linear regression equation. If you could include what the elements of each matrix and vector standard for as well that would be much appreciated.

I am perfectly fine with the assumptions.

Thank you

Answer 1

Let $n$ be the sample size and $q$ be the number of parameters. The multiple regression equation in matrix form is

$$Y=X\beta+\epsilon$$

where $Y$ and $\epsilon$ are $n\times 1$ vactors; $X$ is a $n\times q$ matrix; $\beta$ is a $q\times 1$ vector of parameters. The model is usually written in vector form as

$$Y_i=X_i'\beta+\epsilon_i$$