Definition

1. Noun:
   • A method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curve: "Least squares" is a statistical and mathematical technique used to find the best-fitting line or curve through a set of data points. The "best fit" is defined as the model for which the sum of the squared differences (the squares) between the observed values and the values predicted by the model is the smallest (the least).

Usage Examples

• Noun:
  • The researcher used the least squares method to determine the linear relationship between the two variables.
  • Least squares is a fundamental technique in regression analysis.
  • The algorithm calculates the parameters by applying least squares.

Advanced Usage

• "Ordinary least squares (OLS)": The most common form of least squares, used in linear regression, which minimizes the sum of squared vertical distances (residuals) between the observed and predicted values.
  • The assumptions of ordinary least squares must be checked before interpreting the model results.
• "Method of least squares": A synonymous phrase often used in formal or instructional contexts.
  • The method of least squares was developed independently by Legendre and Gauss.

Variants and Related Words

• Least-squares (adjective): Used to describe an estimator, solution, or fit obtained by this method.
  • The least-squares estimator is known for its desirable properties under certain conditions.
• Weighted least squares: A variation of the method where data points are given different weights, often used when the variance of the errors is not constant.
• Non-linear least squares: An application of the principle to fit models that are non-linear in their parameters.

Synonyms

• Least squares estimation
• Least squares fitting
• Method of least squares

Related Phrases

• "Least squares regression": A very common application of the least squares principle to estimate the parameters of a regression model.
  • The trend line was generated using least squares regression.
• "Minimize the sum of squared errors/residuals": A descriptive phrase that defines the objective of the least squares method.
  • The goal is to minimize the sum of squared residuals.

Noun

1. a method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curve