英语词汇“principle of least squares”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

method (also principle) of least squares n. a method of finding an equation that best fits some experimental or observed data, in which the sum of the squares of the differences between the data and the corresponding values of the equation are minimized. [In method of least squares n. after French méthode des moindres carrés ( A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1805) 74).]

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1819 Philos. Mag. 53 435 The only use to which two or three results thus obtained by one observer can be legitimately applied, is to make them parts of a series obtained by different persons in different places, and reduce the whole to computation by the ‘method of least squares’.

1964 Math. Mag. 37 150 Let us apply the principle of least squares..to the consistent linear system.

2012 J. Stewart Single Variable Calculus (ed. 7) II. vi. 395 We use a graphing calculator with exponential regression capability to apply the method of least squares.

b. method (also principle) of least squares [translating French méthode des moindres quarrés (A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1806) 74)] , the technique of estimating a quantity, fitting a graph to a set of experimental values, etc., so as to minimize the sum of the squares of the differences between the observed data and their estimated true values; so least square(s) attributive, denoting estimates, regression lines, etc., obtained by this method, the method itself, and the processes which it involves.

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the world > relative properties > number > probability or statistics > [noun] > population > numerical characteristic of > method used to estimate

method (also principle) of least squares1825

estimator1939

1812 Philos. Mag. 39 242 M. Legendre had not in any way mentioned the method which he has denominated that of small squares, (moindres carrées,).

1812 Philos. Mag. 39 243 The principle of the small squares.]

1825 Philos. Mag. 65 10 The principle of least squares will hold good, whatever law of probability be adopted.

1829 tr. S. D. Poisson in Q. Jrnl. Sci. & Arts July 96 This embarrassment..remained to the period when M. Legendre proposed a direct and uniform method of forming the final equations, which was generally adopted under the name of Method of least squares of the errors, which was assigned to it by its author.

1872 W. Thomson & P. G. Tait Treat. Nat. Philos. i. iii. 115 A and B are to be found by the method of least squares from values of l observed for different given values of t.

1916 L. D. Weld Theory of Errors & Least Squares v. 87 If more [observations] are made, least-square reduction may be applied to their adjustment.

1939 A. E. Treloar Elem. Statistical Reasoning iv. 59 ‘Least squares’ solutions, or the minimizing of squared deviations to reach representative values, may be made with facility, whereas the minimizing of absolute deviations becomes so involved that the problems can rarely be solved that way.

1950 A. McF. Mood Introd. Theory Statistics xiii. 311 The primary reason that the method of least squares is commonly used for curve fitting is merely that it leads to a simple linear system of equations for determining the coefficients.

1957 G. E. Hutchinson Treat. Limnol. I. vii. 469 C is determined from the distribution of temperatures by the method of least squares.

1970 Jrnl. Gen. Psychol. July 127 The principle of the method is to rotate one matrix (usually a principal-components matrix) as close as possible to a hypothesized factor matrix, in a least-square solution.

1974 Encycl. Brit. Macropædia VII. 967/1 Gauss developed a technique for calculating its orbital components with such accuracy that several astronomers late in 1801 and early in 1802 were able to locate Ceres again without difficulty. As part of his technique, Gauss used his method of least squares, developed about 1794.

单词	principle of least squares
释义	> as lemmas method (also principle) of least squares method (also principle) of least squares n. a method of finding an equation that best fits some experimental or observed data, in which the sum of the squares of the differences between the data and the corresponding values of the equation are minimized. [In method of least squares n. after French méthode des moindres carrés ( A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1805) 74).] ΚΠ 1819 Philos. Mag. 53 435 The only use to which two or three results thus obtained by one observer can be legitimately applied, is to make them parts of a series obtained by different persons in different places, and reduce the whole to computation by the ‘method of least squares’. 1964 Math. Mag. 37 150 Let us apply the principle of least squares..to the consistent linear system. 2012 J. Stewart Single Variable Calculus (ed. 7) II. vi. 395 We use a graphing calculator with exponential regression capability to apply the method of least squares. extracted from leastadj.pron.n.adv. method (also principle) of least squares b. method (also principle) of least squares [translating French méthode des moindres quarrés (A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1806) 74)] , the technique of estimating a quantity, fitting a graph to a set of experimental values, etc., so as to minimize the sum of the squares of the differences between the observed data and their estimated true values; so least square(s) attributive, denoting estimates, regression lines, etc., obtained by this method, the method itself, and the processes which it involves. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > population > numerical characteristic of > method used to estimate method (also principle) of least squares1825 estimator1939 1812 Philos. Mag. 39 242 M. Legendre had not in any way mentioned the method which he has denominated that of small squares, (moindres carrées,). 1812 Philos. Mag. 39 243 The principle of the small squares.] 1825 Philos. Mag. 65 10 The principle of least squares will hold good, whatever law of probability be adopted. 1829 tr. S. D. Poisson in Q. Jrnl. Sci. & Arts July 96 This embarrassment..remained to the period when M. Legendre proposed a direct and uniform method of forming the final equations, which was generally adopted under the name of Method of least squares of the errors, which was assigned to it by its author. 1872 W. Thomson & P. G. Tait Treat. Nat. Philos. i. iii. 115 A and B are to be found by the method of least squares from values of l observed for different given values of t. 1916 L. D. Weld Theory of Errors & Least Squares v. 87 If more [observations] are made, least-square reduction may be applied to their adjustment. 1939 A. E. Treloar Elem. Statistical Reasoning iv. 59 ‘Least squares’ solutions, or the minimizing of squared deviations to reach representative values, may be made with facility, whereas the minimizing of absolute deviations becomes so involved that the problems can rarely be solved that way. 1950 A. McF. Mood Introd. Theory Statistics xiii. 311 The primary reason that the method of least squares is commonly used for curve fitting is merely that it leads to a simple linear system of equations for determining the coefficients. 1957 G. E. Hutchinson Treat. Limnol. I. vii. 469 C is determined from the distribution of temperatures by the method of least squares. 1970 Jrnl. Gen. Psychol. July 127 The principle of the method is to rotate one matrix (usually a principal-components matrix) as close as possible to a hypothesized factor matrix, in a least-square solution. 1974 Encycl. Brit. Macropædia VII. 967/1 Gauss developed a technique for calculating its orbital components with such accuracy that several astronomers late in 1801 and early in 1802 were able to locate Ceres again without difficulty. As part of his technique, Gauss used his method of least squares, developed about 1794. extracted from squaren. < as lemmas
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> as lemmas