Milestone 2 of 8

Implement and hand-check line prediction and score

Keep prediction and mean squared difference independent, validate their arrays, and reproduce one small calculation by hand.

Keep the two supplied numerical rules independent. A search is easier to trust when prediction and scoring can be checked without running the whole project.

Goal

Implement predict_line and mean_squared_difference, verify their inputs and outputs, and reproduce one supplied calculation by hand before adding search.

Inputs

Use the line contract:

prediction = slope * x + intercept

Use the score contract:

mean((prediction - observed) ** 2)

Work with one three-value input, prediction, and observed example whose values are small enough to expand on paper. Arrays must be one-dimensional, finite, equal in length, and non-empty wherever the function requires both arrays.

Deliverables

Implement the two independent functions in src/line.py. The prediction function returns one value per input. The score function returns one finite number and does not change either input array.

Record the three-value expansion and its result in report.md. Keep the name mean_squared_difference in the public boundary; do not replace it with a statistical interpretation that the project does not teach.

Checks

Check a scalar or one-element prediction, a three-value hand calculation, and a larger finite array. Reject empty score inputs, mismatched lengths, non-one-dimensional arrays, and non-finite values with a clear result or exception.

Check that prediction and observed inputs remain unchanged, that the score is non-negative, and that a zero difference gives zero. Verify the compact NumPy calculation against the expanded three-value calculation.

Workspace

Put both functions in src/line.py and keep configuration loading in src/config.py. The later search module should call these functions rather than copy their formulas into a loop. Keep the hand-check in report.md.

Hints

HintExpand before reducing

Write each prediction, each difference, each squared difference, and the final mean for the small example.

HintShape is part of the contract

Two arrays can have the same number of stored values while still having different dimensions. Check the one-dimensional boundary explicitly.

Review

Compare the hand calculation with the function result. Explain why the score is a supplied comparison value for this project, not a claim about how well a line will work on future data.

How to check your work

Checks compare the functions and edge-case behavior with the supplied fixture. The supplied fixture makes the numerical boundary visible without requiring a particular NumPy expression.