The Error the Model Cannot Explain

A linear model $\hat{y} = \beta_0 x_0 + \beta_1 x_1$ is fitted by least squares to four observations. The design matrix columns are a bias column $x_0$ and a single centred binary feature $x_1$ :

observation	bias $x_0$	feature $x_1$	target $y$
1	$1$	$+1$	$3$
2	$1$	$-1$	$1$
3	$1$	$+1$	$5$
4	$1$	$-1$	$3$

Least squares picks $\boldsymbol{\beta}$ to minimise $\|\mathbf{y} - X\boldsymbol{\beta}\|^2$ . What is the residual sum of squares $\|\mathbf{y} - \hat{\mathbf{y}}\|^2$ at the fitted solution?

The Error the Model Cannot Explain

Hints