Regression

Regression is a type of supervised learning that predicts continuous numerical values based on input features. Unlike classification, which predicts discrete categories, regression estimates quantities along a continuous range.

Core Concept

The fundamental goal is to find a mathematical function that best describes the relationship between input variables (features) and a continuous output variable (target). This function can then predict values for new, unseen data points.

Common Types of Regression

Linear Regression finds the best-fitting straight line (or hyperplane in multiple dimensions) through data points. It assumes a linear relationship between inputs and output. Simple to interpret but limited to linear patterns.

Polynomial Regression extends linear regression by adding polynomial terms, allowing it to fit curved relationships. More flexible but can overfit with high-degree polynomials.

Ridge and Lasso Regression are regularized versions of linear regression that add penalties to prevent overfitting. Ridge shrinks coefficients uniformly, while Lasso can reduce some coefficients to zero, effectively performing feature selection.

Decision Tree Regression uses a tree-like model of decisions to predict values. It splits data recursively based on feature values, with predictions made at leaf nodes.

Random Forest and Gradient Boosting are ensemble methods that combine multiple decision trees for more robust predictions.

Key Concepts

Loss Functions measure prediction errors. Mean Squared Error (MSE) and Mean Absolute Error (MAE) are most common. The algorithm minimizes these during training using optimisation algorithms like Gradient Descent.

Overfitting vs. Underfitting - Models can memorize training data too closely (overfitting) or fail to capture important patterns (underfitting). Techniques like cross-validation, regularization, and proper train-test splits help find the right balance.

Feature Engineering often significantly impacts performance. This includes scaling features, handling missing values, creating interaction terms, or transforming variables.

Evaluation Metrics

• R-squared (R²): Proportion of variance explained by the model (0 to 1, higher is better)
• Mean Squared Error (MSE): Average of squared differences between predictions and actual values
• Root Mean Squared Error (RMSE): Square root of MSE, in same units as target variable
• Mean Absolute Error (MAE): Average of absolute differences, less sensitive to outliers than MSE

Real-World Applications

Regression appears everywhere in practice: predicting house prices based on size and location, forecasting sales from advertising spend, estimating patient recovery time from medical data, predicting energy consumption from weather patterns, or determining optimal pricing strategies.

The key to successful regression modeling is understanding your data’s relationships, choosing appropriate algorithms, and carefully validating that your model generalizes well to new situations rather than just memorizing training examples.