“method of least squares”的概念、定义、翻译、参考文献-科学参考

method of least squares

Mathematics

Statistics

A method originated by Legendre, which refers to the process of estimating the unknown parameters of a model by minimizing the sum of squared differences between the observed values of a random variable and the values predicted by the model. If every observation is given equal weight then this is ordinary least squares (OLS).
For example, with n pairs of observations (x₁, y₁), …, (x_n, y_n) and the linear regression model $method of least squares$
where α and β are unknown parameters, ε_j is an error of observation, and E(Y_j) denotes the expected value of Y_j, the ordinary least squares estimates are the values for α and β that minimize $method of least squares$ See also generalized least squares; weighted least squares.

单词	method of least squares
释义	method of least squares Mathematics See least squares. Statistics A method originated by Legendre, which refers to the process of estimating the unknown parameters of a model by minimizing the sum of squared differences between the observed values of a random variable and the values predicted by the model. If every observation is given equal weight then this is ordinary least squares (OLS). For example, with n pairs of observations (x₁, y₁), …, (x_n, y_n) and the linear regression model $method of least squares$ where α and β are unknown parameters, ε_j is an error of observation, and E(Y_j) denotes the expected value of Y_j, the ordinary least squares estimates are the values for α and β that minimize $method of least squares$ See also generalized least squares; weighted least squares.
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