Linear Regression

Linear Regression #

Linear regression is one of the most fundamental methods in machine learning and statistics. It approximates the relationship between inputs (features) and an output (target) with a “line” or “plane” to predict values and understand variable relationships.

Why learn linear regression? #

  • Mathematically simple and interpretable
  • Easy to implement and compute
  • Useful for both prediction and interpretation
  • Foundation for many advanced methods (Ridge/Lasso, GLMs, neural nets, etc.)

What can it do? #

  • Prediction: e.g., predict sales from advertising, exam score from study time
  • Relationship analysis: coefficients show how outputs change per unit change in inputs
  • Feature importance: identify which variables matter for prediction

What you’ll learn in this section #

  1. Least squares — how to fit the best line to data
  2. Ridge and Lasso — regularization to combat overfitting
  3. Robust regression (e.g., Huber) — handling messy data with outliers

Summary #

  • Linear regression is “simple yet widely applicable”.
  • Despite its simplicity, it’s heavily used in practice.
  • The concepts here carry over to more advanced models (trees, SVMs, neural nets).