Multiple linear regression

One day before your Statistics exam, you want to practice fitting a linear regression model by hand. You see the following toy dataset in your textbook:

Based on this data, you want to fit a model as follows:

$\hat{y} = w_0 + w_1x_1 + w_2x_2$.

Estimate the optimal values of the model coefficients $w_0, \ w_1$ and $w_2$ based on the least-squares method.

Enter the obtained values of $w_0, \ w_1$ and $w_2$ divided by space. For example, if you get

$w_0^* = 0.2, \ w_1^* = -3, \ w_2^* = 12$

your answer should be 0.2 -3 12.

You can use one of the online matrix calculators, for example https://matrixcalc.org, or your favorite programming language for matrix calculations.

Tip: The exact formula to compute the optimal values of a linear regression model is as follows: $w=(X^\top X)^{-1}X^\top Y$