Build the first working regression loss workbench

Now implement the shortest complete path for the artifact. The working mechanism is: compute per-example residuals, transform them with square or absolute value, then average without hiding the individual contributions. Keep every intermediate value available for inspection; hiding it behind a framework would make this lesson harder to reason about. The output should be deterministic for this fixture. Only after this path works should you generalize the data source or user interface.

The artifact's user-facing goal is specific: compare mean squared error and mean absolute error on ordinary predictions and one costly outlier. Its accepted input is equal-length finite numeric target and prediction lists. Those statements are intentionally narrower than “build an AI system.” Narrow scope lets us inspect every input and expected result, and it prevents a toy result from being presented as a production claim. This is the chapter's first end-to-end implementation. Run it twice and verify identical output.

Save this as lesson.py and run python3 lesson.py. It uses only the language standard library, so the example is reproducible offline.

truth=[2,4,6,8]; pred=[2.5,3.5,6.5,12]
mse=sum((p-y)**2 for y,p in zip(truth,pred))/len(truth)
mae=sum(abs(p-y) for y,p in zip(truth,pred))/len(truth)
print(round(mse,3), round(mae,3))

Expected output: MSE 4.188 and MAE 1.375. Exact floating-point formatting may vary slightly, but the asserted behavior must not. Read the output as evidence about this stage, not merely proof that the interpreter started.

Print every residual and transformed contribution before averaging. A single large squared term should visibly dominate MSE; if it does not, verify operand order, exponent placement, and the denominator. Reject unequal lengths because Python's zip silently drops extras. Reject NaN and infinity before aggregation, and keep target units visible so a mathematically correct score is not interpreted in the wrong scale.

At the implementation stage, save the smallest failing fixture beside the expected result. Change one cause at a time and rerun the exact command printed above; that makes the repair reviewable and keeps this chapter's progressive artifact reproducible.

Compare MAE and MSE on the same holdout rows and show the largest contributor to each. Then translate the error into the product unit, such as minutes, dollars, or degrees. If underprediction costs more than overprediction, evaluate an asymmetric business cost separately; do not claim that minimizing a convenient textbook loss automatically minimizes operational harm.

For this implementation page, preserve the fixture and result as evidence for the next page. Label observations separately from conclusions: a passing assertion establishes the behavior it names, while broader usefulness requires the chapter's full evaluation set and stated operating limits.