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• Linear_least_squares_(mathematics) abstract "In statistics and mathematics, linear least squares is an approach fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. The resulting fitted model can be used to summarize the data, to predict unobserved values from the same system, and to understand the mechanisms that may underlie the system.Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations, where the best approximation is defined as that which minimizes the sum of squared differences between the data values and their corresponding modeled values. The approach is called linear least squares since the assumed function is linear in the parameters to be estimated. Linear least squares problems are convex and have a closed-form solution that is unique, provided that the number of data points used for fitting equals or exceeds the number of unknown parameters, except in special degenerate situations. In contrast, non-linear least squares problems generally must be solved by an iterative procedure, and the problems can be non-convex with multiple optima for the objective function. If prior distributions are available, then even an underdetermined system can be solved using the Bayesian MMSE estimator.In statistics, linear least squares problems correspond to a particularly important type of statistical model called linear regression which arises as a particular form of regression analysis. One basic form of such a model is an ordinary least squares model. The present article concentrates on the mathematical aspects of linear least squares problems, with discussion of the formulation and interpretation of statistical regression models and statistical inferences related to these being dealt with in the articles just mentioned. See outline of regression analysis for an outline of the topic.".
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• Linear_least_squares_(mathematics) wikiPageExternalLink LeastSquaresFitting.html.
• Linear_least_squares_(mathematics) wikiPageExternalLink LeastSquaresFittingPolynomial.html.
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• Linear_least_squares_(mathematics) wikiPageWikiLink Argument_(complex_analysis).
• Linear_least_squares_(mathematics) wikiPageWikiLink Arithmetic_mean.
• Linear_least_squares_(mathematics) wikiPageWikiLink B-spline.
• Linear_least_squares_(mathematics) wikiPageWikiLink Beer–Lambert_law.
• Linear_least_squares_(mathematics) wikiPageWikiLink Calibration_curve.
• Linear_least_squares_(mathematics) wikiPageWikiLink Octave_code.
• Linear_least_squares_(mathematics) wikiPageWikiLink Category:Articles_with_example_Python_code.
• Linear_least_squares_(mathematics) wikiPageWikiLink Category:Computational_statistics.
• Linear_least_squares_(mathematics) wikiPageWikiLink Category:Least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink Category:Numerical_linear_algebra.
• Linear_least_squares_(mathematics) wikiPageWikiLink Category:Regression_analysis.
• Linear_least_squares_(mathematics) wikiPageWikiLink Central_limit_theorem.
• Linear_least_squares_(mathematics) wikiPageWikiLink Chebyshevs_inequality.
• Linear_least_squares_(mathematics) wikiPageWikiLink Chemometrics.
• Linear_least_squares_(mathematics) wikiPageWikiLink Chi-squared_distribution.
• Linear_least_squares_(mathematics) wikiPageWikiLink Cholesky_decomposition.
• Linear_least_squares_(mathematics) wikiPageWikiLink Closed-form_expression.
• Linear_least_squares_(mathematics) wikiPageWikiLink Coefficient.
• Linear_least_squares_(mathematics) wikiPageWikiLink Comparison_of_statistical_packages.
• Linear_least_squares_(mathematics) wikiPageWikiLink Complex_number.
• Linear_least_squares_(mathematics) wikiPageWikiLink Condition_number.
• Linear_least_squares_(mathematics) wikiPageWikiLink Constrained_generalized_inverse.
• Linear_least_squares_(mathematics) wikiPageWikiLink Convex_function.
• Linear_least_squares_(mathematics) wikiPageWikiLink Covariance.
• Linear_least_squares_(mathematics) wikiPageWikiLink Covariance_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Curve_fitting.
• Linear_least_squares_(mathematics) wikiPageWikiLink Data.
• Linear_least_squares_(mathematics) wikiPageWikiLink Degrees_of_freedom_(statistics).
• Linear_least_squares_(mathematics) wikiPageWikiLink Dependent_and_independent_variables.
• Linear_least_squares_(mathematics) wikiPageWikiLink Descriptive_statistics.
• Linear_least_squares_(mathematics) wikiPageWikiLink Diagonal_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Distribution_function.
• Linear_least_squares_(mathematics) wikiPageWikiLink Dominating_decision_rule.
• Linear_least_squares_(mathematics) wikiPageWikiLink Dot_product.
• Linear_least_squares_(mathematics) wikiPageWikiLink Errors-in-variables_models.
• Linear_least_squares_(mathematics) wikiPageWikiLink Errors_and_residuals.
• Linear_least_squares_(mathematics) wikiPageWikiLink Expected_value.
• Linear_least_squares_(mathematics) wikiPageWikiLink Factor_analysis.
• Linear_least_squares_(mathematics) wikiPageWikiLink Gauss–Markov_theorem.
• Linear_least_squares_(mathematics) wikiPageWikiLink Generalized_inverse.
• Linear_least_squares_(mathematics) wikiPageWikiLink Goodness_of_fit.
• Linear_least_squares_(mathematics) wikiPageWikiLink Gramian_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Gran_plot.
• Linear_least_squares_(mathematics) wikiPageWikiLink Hat_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Idempotent_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Identity_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Integer.
• Linear_least_squares_(mathematics) wikiPageWikiLink Iterative_method.
• Linear_least_squares_(mathematics) wikiPageWikiLink Iteratively_reweighted_least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink James–Stein_estimator.
• Linear_least_squares_(mathematics) wikiPageWikiLink Least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink Linear_equation.
• Linear_least_squares_(mathematics) wikiPageWikiLink Linear_independence.
• Linear_least_squares_(mathematics) wikiPageWikiLink Linear_least_squares_(mathematics).
• Linear_least_squares_(mathematics) wikiPageWikiLink Linear_regression.
• Linear_least_squares_(mathematics) wikiPageWikiLink Line–line_intersection.
• Linear_least_squares_(mathematics) wikiPageWikiLink MATLAB.
• Linear_least_squares_(mathematics) wikiPageWikiLink Mathematical_model.
• Linear_least_squares_(mathematics) wikiPageWikiLink Mathematical_optimization.
• Linear_least_squares_(mathematics) wikiPageWikiLink Mathematics.
• Linear_least_squares_(mathematics) wikiPageWikiLink Matrix_(mathematics).
• Linear_least_squares_(mathematics) wikiPageWikiLink Matrix_calculus.
• Linear_least_squares_(mathematics) wikiPageWikiLink Maxima_and_minima.
• Linear_least_squares_(mathematics) wikiPageWikiLink Maximum_likelihood.
• Linear_least_squares_(mathematics) wikiPageWikiLink Mean_squared_error.
• Linear_least_squares_(mathematics) wikiPageWikiLink Minimum_mean_square_error.
• Linear_least_squares_(mathematics) wikiPageWikiLink Moore–Penrose_pseudoinverse.
• Linear_least_squares_(mathematics) wikiPageWikiLink Multiplicative_inverse.
• Linear_least_squares_(mathematics) wikiPageWikiLink Non-linear_least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink Non-negative_least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink Normal_distribution.
• Linear_least_squares_(mathematics) wikiPageWikiLink Numerical_stability.
• Linear_least_squares_(mathematics) wikiPageWikiLink Observational_error.
• Linear_least_squares_(mathematics) wikiPageWikiLink Ordered_vector_space.
• Linear_least_squares_(mathematics) wikiPageWikiLink Ordinary_least_squares.
• Linear_least_squares_(mathematics) wikiPageWikiLink Orthogonal_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Orthogonal_polynomials.
• Linear_least_squares_(mathematics) wikiPageWikiLink Outlier.
• Linear_least_squares_(mathematics) wikiPageWikiLink Outline_of_regression_analysis.
• Linear_least_squares_(mathematics) wikiPageWikiLink Overdetermined_system.
• Linear_least_squares_(mathematics) wikiPageWikiLink Parameter.
• Linear_least_squares_(mathematics) wikiPageWikiLink Partial_derivative.
• Linear_least_squares_(mathematics) wikiPageWikiLink Pearson_product-moment_correlation_coefficient.
• Linear_least_squares_(mathematics) wikiPageWikiLink Polynomial.
• Linear_least_squares_(mathematics) wikiPageWikiLink Polynomial_regression.
• Linear_least_squares_(mathematics) wikiPageWikiLink Positive-definite_matrix.
• Linear_least_squares_(mathematics) wikiPageWikiLink Prediction.
• Linear_least_squares_(mathematics) wikiPageWikiLink Prior_probability.
• Linear_least_squares_(mathematics) wikiPageWikiLink Projection_(linear_algebra).
• Linear_least_squares_(mathematics) wikiPageWikiLink Propagation_of_uncertainty.
• Linear_least_squares_(mathematics) wikiPageWikiLink Python_(programming_language).
• Linear_least_squares_(mathematics) wikiPageWikiLink QR_decomposition.

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