Seven Classic Regression Models for Machine Learning

What is Regression Analysis?

Regression analysis is a predictive modeling technique that studies the relationship between a dependent variable (target) and one or more independent variables (predictors). It is commonly used for forecasting, time‑series modeling, and uncovering causal links such as the correlation between reckless driving and traffic accidents.

Why Use Regression Analysis?

Regression quantifies the significance of relationships, shows the strength of multiple predictors on a single outcome, and enables comparison of variables measured on different scales, helping data analysts and scientists select the best set of variables for a predictive model.

How Many Regression Techniques Are There?

There are many regression techniques, primarily distinguished by the number of predictors, the type of dependent variable, and the shape of the regression line. The most common methods are described below.

1. Linear Regression

Linear regression models a continuous target as a linear combination of predictors. The basic equation is Y = a + b·X + e , where a is the intercept, b the slope, and e the error term. It can be extended to multiple predictors (multiple linear regression).

2. Logistic Regression

Logistic regression estimates the probability of a binary outcome (0/1). It uses the logit link function: logit(p) = ln(p/(1‑p)) = b0 + b1X1 + … + bkXk . Unlike linear regression, it does not require a linear relationship between predictors and the target.

3. Polynomial Regression

When the relationship between the predictor and target is non‑linear, polynomial regression fits a curve such as y = a + b·x² . It captures higher‑order effects while still using the least‑squares fitting principle.

4. Stepwise Regression

Stepwise regression automates variable selection by iteratively adding (forward selection) or removing (backward elimination) predictors based on criteria such as R‑square, AIC, or t‑statistics, aiming to achieve strong predictive power with a minimal set of variables.

5. Ridge Regression

Ridge regression addresses multicollinearity by adding an L2 penalty to the ordinary least‑squares loss: min‖y‑Xβ‖² + λ‖β‖² . The penalty shrinks coefficient magnitudes, reducing variance without performing variable selection.

6. Lasso Regression

Lasso adds an L1 penalty: min‖y‑Xβ‖² + λ‖β‖₁ . This can force some coefficients to exactly zero, performing both regularization and automatic feature selection.

7. Elastic‑Net Regression

Elastic‑Net combines L1 and L2 penalties: min‖y‑Xβ‖² + λ₁‖β‖₁ + λ₂‖β‖² . It retains the feature‑selection ability of Lasso while preserving the stability of Ridge, especially useful when predictors are highly correlated.

How to Choose the Right Regression Model

Selecting a model depends on data exploration, the type of dependent variable, the number of predictors, and the intended purpose. Evaluate models using metrics such as R‑square, Adjusted R‑square, AIC, BIC, cross‑validation error, and consider regularization methods (Ridge, Lasso, Elastic‑Net) for high‑dimensional or collinear data.

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