Refactor Linear Regression to Fully Vectorized Version

[ARES2525]

Describe your change:

Refactored linear_regression.py to be fully vectorized using NumPy.

• Replaced manual loops with NumPy operations in mean_absolute_error and other helper functions.
• Cleaned up redundant calculations in gradient descent.
• Improved code clarity, maintainability, and performance.

This helps learners understand vectorization and efficient numerical computing.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: Fixes #<issue-number>.