What Is Least Squares?

Least squares is a statistical method used to determine a line of best fit by minimizing the sum of squares created by a mathematical function. A "square" is determined by squaring the distance between a data point and the regression line or mean value of the data set.

The least squares approach limits the distance between a function and the data points that a function is trying to explain. It is used in regression analysis, often in nonlinear regression modeling in which a curve is fit into a set of data.

What Does Least Squares Tell You?

The least squares approach is a popular method for determining regression equations, and it tells you about the relationship between response variables and predictor variables. Instead of trying to solve an equation exactly, mathematicians use the least squares method to make a close approximation (referred to as a maximum-likelihood estimate).

Modeling methods that are often used when fitting a function to a curve include the straight-line method, polynomial method, logarithmic method, and Gaussian method.

Linear or ordinary least squares is the most simple and commonly used linear regression estimator for analyzing observational and experimental data. It finds a straight line of best fit through a set of given data points.

Key Takeaways

  • Least squares results can be used to summarize data and make predictions about related but unobserved values from the same group or system.
  • Linear least squares regression is the simplest and most commonly used form of least squares regression.

How to Use Least Squares

Advances in computing power coupled with new financial engineering techniques have increased the use of the least square methods, including extensions of its basic principles. Throughout finance, economics, and investing disciplines, least squares and related statistical methods are commonplace, even if beneficiaries are unknowing.

For instance, the rise in so-called Robo-advisors utilizes Monte Carlo simulation techniques to manage portfolios, much of which is done behind the scenes out of sight of the account holders.

Other applications include time-series analysis of return distributions, economic forecasting and policy strategy, and advanced option modeling.