Simple Linear Regression problem involving its design matrix

Question

Problem states: Consider the simple linear regression model without intercept, i.e. $y_i = \beta x_i + \epsilon_i, i = 1, 2, ..., n$

Write down your design matrix, $\mathbf X$.

So then $\mathbf X$ $=$ $\begin{bmatrix}x_1\\x_2\\...\\x_n \end{bmatrix}$ $_{nx1}$

I believe this to be too simple, am I doing something wrong? Any help appreciated.

Answer 1

You are right, for $n$ observations you can check that it results in the right model: $$ \begin{pmatrix} y_1\\ y_2\\ \vdots\\ y_n \end{pmatrix} = \begin{pmatrix} x_1\\ x_2\\ \vdots\\ x_n \end{pmatrix} \beta + \begin{pmatrix} \epsilon_1\\ \epsilon_2\\ \vdots\\ \epsilon_n \end{pmatrix}, $$ so the $i$th row is $$ y_i = x_i\beta + \epsilon_i, $$ as required.