Estimating error variance in a five-point line fit

Bob fits $Y=\beta_0+\beta_1x+\epsilon$, with $\mathbb{E}\epsilon=0$ and $\operatorname{Var}\epsilon=\sigma^2$, by least squares to these five points: $(2,3)$, $(1,1)$, $(0,1)$, $(-1,0)$, $(-2,0)$. Give the usual unbiased estimate of $\sigma^2$.

$11/30$. The fitted line is $\hat y=1+0.7x$, leaving residuals $0.4,-0.3,0,-0.7,0.6$ (ordered by increasing $x$). Their squares sum to $1.1$, and dividing by $n-2=3$ degrees of freedom gives $\tfrac{11}{30}$.