Regression analysis is fundamental in the field of machine learning and statistics, serving as a predictive modeling technique that analyzes the relationship between a dependent (target) variable and one or more independent (predictor) variables. The goal is to model the expected value of the dependent variable as a function of the independent variables, allowing for the prediction of outcomes based on new, unseen data. Regression techniques are varied, including linear regression, which assumes a linear relationship between variables, and non-linear regression, which can model more complex relationships. These methods are crucial in fields like finance for predicting stock prices, in meteorology for weather forecasting, and in marketing for sales forecasting.

The method of least squares, which is the foundation of linear regression, was first published by Adrien-Marie Legendre in 1805. Regression, as a concept, gained prominence in the 19th century, notably used by Francis Galton in the 1880s in the context of genetics, examining the relationship between parents and their offspring's heights, thereby introducing the term "regression" to statistics.

- Adrien-Marie Legendre and Carl Friedrich Gauss are credited with the development of the least squares method, crucial for linear regression.
- Francis Galton introduced the term "regression" and applied it in a statistical study, marking a significant milestone in its conceptual evolution.