How to calculate Mean Squared Error when there are multiple observed y values for a single x value? Given a data set where there exists multiple different observed y-values for a given x-value, how do I calculate Mean Squared Error? The formula implies that I subtract the predicted from a singular observed value, but what if there is multiple?

Just take the squared error multiple times.
If you have {...,(1,1),(1,2),(1,3),...} and you predict y=2 at x=1, the error sum of squares would be
$...+(1-2)^2+(2-2)^2+(3-1)^2+...$
Then, just divide it by the number of observations to get MSE.
