Evaluate Every Parameter Candidate

Task

Write evaluate_parameter_candidates(inputs, targets, candidates). inputs and targets are finite one-dimensional numeric NumPy arrays with the same non-zero length. candidates is a non-empty one-dimensional array of finite numeric candidate slopes. The arrays are observations in their existing order; do not reorder them. The supplied model has a fixed zero intercept.

For each candidate slope p, use the supplied complete rules:

prediction = p * input
error = prediction - target
score = mean(error ** 2)

Evaluate every candidate and retain the complete table. Return a dictionary with exactly these keys:

• "candidates": an independent float64 copy in the supplied order;
• "predictions": an independent float64 array of shape (number_of_candidates, number_of_observations);
• "scores": an independent float64 array with one mean-squared-error score per candidate;
• "best_index": the zero-based index of the smallest score;
• "best_candidate": the candidate at that index as a float;
• "best_score": its score as a float.

If two scores are exactly equal, choose the first candidate in the supplied order. This is the only tie rule; do not use a tolerance to change it. Raise ValueError("inputs and targets must be non-empty and have equal length") for an empty or unequal observation pair and ValueError("candidates must be non-empty") for no candidates. Keep every input unchanged.

Example

For inputs=[0,1,2], targets=[0,2,4], and candidates=[1,2], candidate 2 predicts [0,2,4] and has score 0; candidate 1 predicts [0,1,2] and has score 5/3. The complete prediction table has shape (2,3) and the best index is 1.

Your implementation

You may import NumPy as np. Do not modify an input, print, or ask for input.