OLS estimator (matrix form)

Question

I got the statistical model: $y = β_1x_1 + β_2x_2 + u$.
Then I have to write this as matrix problem and find the OLS estimator $\beta$^. I know that $\beta^=(X^tX)^{-1}X^ty$. So I think it's possible for me to find if I know the matrices. Can someone help me to write down the matrices?

Answer 1

If you have $m$ data points then

$$X=\begin{pmatrix} x_{11} & x_{12} \\ x_{21} & x_{22} \\ x_{31} & x_{32} \\ \vdots & \vdots \\ x_{m1} & x_{m2}\end{pmatrix}, \ y=\begin{pmatrix} y_1 \\ y_2 \\ y_3 \\ \vdots \\y_m \end{pmatrix}$$

Can you proceed?

Answer 2

$$y = \begin{pmatrix} \beta_1 & \beta_2 \end{pmatrix}\cdot \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}+u $$