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Predicts a continuous dependent variable based on one or more independent variables.
Equation:
y = β₀ + β₁x₁ + β₂x₂ + ... + βₙxₙ + ϵ
Types:
- Simple Linear Regression: Single independent variable
- Multiple Linear Regression: Multiple independent variables
Used for binary classification (e.g., yes/no). Outputs a probability (between 0 and 1).
Equation:
P(y=1) = 1/(1 + e^-(β₀ + β₁x))
Models nonlinear relationships by adding polynomial terms.
Equation:
y = β₀ + β₁x + β₂x² + ... + βₙxⁿ + ϵ
Prevents overfitting by adding an L2 penalty term.
Equation:
Minimize Σ(yᵢ - ŷᵢ)² + λΣβⱼ²
Performs feature selection by shrinking some coefficients to zero.
Equation:
Minimize Σ(yᵢ - ŷᵢ)² + λΣ|βⱼ|
Combines L1 and L2 penalties (Ridge + Lasso).
For count data (e.g., number of events in a fixed interval).
Predicts specific quantiles (e.g., median) instead of the mean.
Uses Bayesian inference for parameter estimation.
Models complex nonlinear relationships.
Multiple dependent variables.
Works well with high-dimensional data.
Uses tree structures to predict values.
Ensemble of decision trees.
Boosts weak learners sequentially.
| Regression Type | Use Case | Key Feature |
|---|---|---|
| Linear | Continuous output | Simple, interpretable |
| Logistic | Binary classification | Probability output |
| Polynomial | Nonlinear relationships | Flexible curve fitting |
| Ridge/Lasso/Elastic Net | Regularization | Prevents overfitting |
| Poisson | Count data | Discrete outcomes |
| Quantile | Non-mean predictions | Robust to outliers |
| SVR | High-dimensional data | Kernel-based |
| Tree-based | Complex patterns | Handles non-linearity |