Method of Least Squares

The Method of Least Squares is a statistical technique used to find the best-fitting line, curve, or surface to a given set of data points. It is commonly used in regression analysis to minimize the sum of the squared residuals between the observed data points and the predicted values based on the model. The method was first developed by Carl Friedrich Gauss and Adrien-Marie Legendre in the early 19th century.

In linear regression, the Method of Least Squares finds the coefficients of a linear equation that best approximates the relationship between a dependent variable and one or more independent variables. The best-fitting line minimizes the sum of the squared differences between the observed data points and the predictions made by the model. This technique can be extended to non-linear models, as well, such as polynomial regression and exponential regression.

The Method of Least Squares has applications in various fields, including economics, physics, engineering, and data analysis. It is an essential tool for analyzing data and making predictions based on historical trends.