Mean Squared Error

Mean squared error is the default way to score a regression: how far off were you, on average, with the misses squared before averaging.

Task: write mse(y_true, y_pred) returning that average, rounded to 4 decimal places.

• The two lists are the same length and line up example by example.
• Square each error, then take the mean — divide by n, the number of examples.
• Squaring handles the signs: being 3 too high and 3 too low are equally wrong, and without the square they would cancel to zero.
• A perfect prediction gives exactly 0.0.

Squaring does something else too, and it's the reason MSE is sometimes the wrong choice. Being off by 10 costs a hundred times as much as being off by 1, so a single outlier can dominate the whole score — and a model trained to minimise MSE will contort itself to accommodate that one point. When that's not what you want, the usual answers are mean absolute error or Huber loss.