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- Least_squares abstract "The method of least squares is a standard approach in regression analysis to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.The most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model. When the problem has substantial uncertainties in the independent variable (the x variable), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.Least squares problems fall into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. The non-linear problem is usually solved by iterative refinement; at each iteration the system is approximated by a linear one, and thus the core calculation is similar in both cases.Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.When the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator.The following discussion is mostly presented in terms of linear functions but the use of least-squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least-squares method may be used to fit a generalized linear model.For the topic of approximating a function by a sum of others using an objective function based on squared distances, see least squares (function approximation).The least-squares method is usually credited to Carl Friedrich Gauss (1795), but it was first published by Adrien-Marie Legendre.".
- Least_squares thumbnail Linear_least_squares2.png?width=300.
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- Least_squares wikiPageWikiLink Adjustment_of_observations.
- Least_squares wikiPageWikiLink Adrien-Marie_Legendre.
- Least_squares wikiPageWikiLink Age_of_Discovery.
- Least_squares wikiPageWikiLink Age_of_Exploration.
- Least_squares wikiPageWikiLink Alexander_Aitken.
- Least_squares wikiPageWikiLink Astronomy.
- Least_squares wikiPageWikiLink Bayesian_statistics.
- Least_squares wikiPageWikiLink Best_linear_unbiased_estimator.
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- Least_squares wikiPageWikiLink Bias.
- Least_squares wikiPageWikiLink Carl_Friedrich_Gauss.
- Least_squares wikiPageWikiLink Category:Least_squares.
- Least_squares wikiPageWikiLink Category:Mathematical_and_quantitative_methods_(economics).
- Least_squares wikiPageWikiLink Category:Mathematical_optimization.
- Least_squares wikiPageWikiLink Category:Regression_analysis.
- Least_squares wikiPageWikiLink Category:Single-equation_methods_(econometrics).
- Least_squares wikiPageWikiLink Central_limit_theorem.
- Least_squares wikiPageWikiLink Ceres_(dwarf_planet).
- Least_squares wikiPageWikiLink Closed-form_expression.
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- Least_squares wikiPageWikiLink Compressed_sensing.
- Least_squares wikiPageWikiLink Confidence_interval.
- Least_squares wikiPageWikiLink Confidence_limits.
- Least_squares wikiPageWikiLink Convex_optimization.
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- Least_squares wikiPageWikiLink Covariance_matrix.
- Least_squares wikiPageWikiLink Curve_fitting.
- Least_squares wikiPageWikiLink Degrees_of_freedom_(statistics).
- Least_squares wikiPageWikiLink Dependent_and_independent_variables.
- Least_squares wikiPageWikiLink Dependent_variable.
- Least_squares wikiPageWikiLink Elastic_net_regularization.
- Least_squares wikiPageWikiLink Errors-in-variables_models.
- Least_squares wikiPageWikiLink Errors_and_residuals.
- Least_squares wikiPageWikiLink Errors_and_residuals_in_statistics.
- Least_squares wikiPageWikiLink Estimation_theory.
- Least_squares wikiPageWikiLink Expected_value.
- Least_squares wikiPageWikiLink Exponential_family.
- Least_squares wikiPageWikiLink Feasible_generalized_least_squares.
- Least_squares wikiPageWikiLink Fisher_information.
- Least_squares wikiPageWikiLink Force_constant.
- Least_squares wikiPageWikiLink Franz_Xaver_von_Zach.
- Least_squares wikiPageWikiLink Gauss_Method.
- Least_squares wikiPageWikiLink Gauss–Markov_theorem.
- Least_squares wikiPageWikiLink Gauss–Newton_algorithm.
- Least_squares wikiPageWikiLink Gauss–Seidel.
- Least_squares wikiPageWikiLink Gauss–Seidel_method.
- Least_squares wikiPageWikiLink Generalized_least_squares.
- Least_squares wikiPageWikiLink Generalized_linear_model.
- Least_squares wikiPageWikiLink Geodesy.
- Least_squares wikiPageWikiLink Giuseppe_Piazzi.
- Least_squares wikiPageWikiLink Gradient.
- Least_squares wikiPageWikiLink Heteroscedasticity.
- Least_squares wikiPageWikiLink Heteroskedasticity.
- Least_squares wikiPageWikiLink Hookes_law.
- Least_squares wikiPageWikiLink Hypothesis_testing.
- Least_squares wikiPageWikiLink Independent_variable.
- Least_squares wikiPageWikiLink Jacobian_matrix_and_determinant.
- Least_squares wikiPageWikiLink Jupiter.
- Least_squares wikiPageWikiLink Keplers_laws_of_planetary_motion.
- Least_squares wikiPageWikiLink L1-norm.
- Least_squares wikiPageWikiLink L2-norm.
- Least_squares wikiPageWikiLink L2_norm.
- Least_squares wikiPageWikiLink Lagrange_multiplier.
- Least_squares wikiPageWikiLink Lagrange_multipliers.
- Least_squares wikiPageWikiLink Laplace_distribution.
- Least_squares wikiPageWikiLink Least-angle_regression.
- Least_squares wikiPageWikiLink Least-squares_function_approximation.
- Least_squares wikiPageWikiLink Least_absolute_deviation.
- Least_squares wikiPageWikiLink Least_absolute_deviations.
- Least_squares wikiPageWikiLink Least_angle_regression.
- Least_squares wikiPageWikiLink Least_squares_(function_approximation).
- Least_squares wikiPageWikiLink Least_squares_adjustment.
- Least_squares wikiPageWikiLink Libration.
- Least_squares wikiPageWikiLink Linear.
- Least_squares wikiPageWikiLink Linear_combination.
- Least_squares wikiPageWikiLink Linear_least_squares_(mathematics).
- Least_squares wikiPageWikiLink Linearity.
- Least_squares wikiPageWikiLink Loss_function.
- Least_squares wikiPageWikiLink Maxima_and_minima.
- Least_squares wikiPageWikiLink Maximum_likelihood.
- Least_squares wikiPageWikiLink Maximum_likelihood_estimator.
- Least_squares wikiPageWikiLink Measurement_uncertainty.
- Least_squares wikiPageWikiLink Method_of_moments_(statistics).
- Least_squares wikiPageWikiLink Minimum_mean_square_error.
- Least_squares wikiPageWikiLink Non-linear_least_squares.
- Least_squares wikiPageWikiLink Norm_(mathematics).
- Least_squares wikiPageWikiLink Normal_distribution.
- Least_squares wikiPageWikiLink Ordinary_least_squares.
- Least_squares wikiPageWikiLink Overdetermined_system.
- Least_squares wikiPageWikiLink Parameter_estimation.
- Least_squares wikiPageWikiLink Pierre-Simon_Laplace.