Calculating an LOOCV MSE by hand

Last week, we had an "mid-term" exam, for our introduction to statistical learning course. The question is simple: consider three points, [latex](x_i,y_i)[/latex], here [latex display="true"]\\{(0,2),(2,2),(3,1)\\}[/latex]Consider here some linear models, estimated using least square techniques, what would be the leave-one-out cross-validation MSE ? I like this exercise since we can compute everything easily, by hand. Since at each step we remove one single observation, only two observations ...