Evaluation of linear regression model
The only difference is in your example is that you divide by an additional two, because you take the mean per vector instead of the sum. Correctness does not play here because for comparison between different models the only difference is a constant factor and for interpretability it depends on the problem you are solving.

The mean absolute error punishes mistakes linearly while the mean squared error punishes larger mistakes more heavily. This means this depends a bit on what you want to measure, based on the problem you are solving. Next to proper evaluation you could use this same measure to change the KPI you are optimizing directly with a different loss function.