Multiple Linear Regression with Feature Selection

HardRegressionFeature SelectionModel FittingStatistical Testing

Implement multiple linear regression from scratch and explore feature selection techniques.

Problem:

Implement multiple linear regression from scratch and explore feature selection techniques.

Examples:

Input: X, y = make_regression(n_samples=100, n_features=3)
coefficients = calculate_coefficients(X, y)
Output: R-squared: 0.85
Adjusted R-squared: 0.84
Multiple regression on synthetic data
Input: X, y = fetch_california_housing(return_X_y=True)
selected = forward_selection(X, y)
Output: Selected features: [0, 4, 7]
R-squared improved from 0.54 to 0.61
Feature selection on California housing dataset

Constraints:

  • Must handle multicollinearity
  • Must calculate adjusted R-squared
  • Must implement statistical tests

Code Editorpython

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Output

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