What is Regression?
Regression is a statistical procedure used to analyze the relationship between variables, helping to determine how changes in one variable (the independent variable) influence another (the dependent variable).
Linear regression is the simplest form, modeling this relationship as a straight line. It's widely used in finance, investing, and other fields. The slope of the line shows how much the dependent variable changes for each unit increase in the independent variable. The y-intercept represents the dependent variable's value when the independent variable is zero.
While linear regression is common, more complex relationships often require nonlinear regression models.
Regression Explained
Regression analysis is a statistical method that specifies and quantifies relationships between variables within a dataset. It determines if these relationships are statistically significant.
There are two primary types: simple and multiple linear regression. Simple regression examines how one independent variable affects a dependent variable, while multiple regression considers multiple independent variables. For more complex patterns, nonlinear regression methods exist.
In finance and investment, regression is a powerful tool. For example, it can predict sales based on various factors or calculate an asset's expected return using the Capital Asset Pricing Model (CAPM).
Types of Regression
Regression analysis is a broad statistical method, and there are numerous types to suit different data structures and objectives. Here's an overview of the most common ones:
Linear Regression
-
Simple Linear Regression: Predicts a continuous outcome variable based on a single independent variable.
-
Multiple Linear Regression: Predicts a continuous outcome variable based on multiple independent variables.
Nonlinear Regression
-
Polynomial Regression: Models the connection between the dependent variable and independent variable as an nth-degree polynomial.
-
Logistic Regression: Predicts the possibility of a categorical outcome (e.g., yes/no, pass/fail).
Regularization Techniques
-
Ridge Regression: Addresses multicollinearity by adding a penalty term to the regression equation.
-
Lasso Regression: Performs feature selection by shrinking some coefficients to zero.
-
ElasticNet Regression: Combines the properties of Ridge and Lasso regression.
Other Types
-
Stepwise Regression: Selects independent variables for the model in a stepwise manner.
-
Time Series Regression: Analyzes data points collected over time.
-
Poisson Regression: Models count data (e.g., number of occurrences).