“linear regression”的概念、定义、翻译、参考文献-科学参考

linear regression

Mathematics

See regression.

Statistics

The simplest and most used of all statistical regression models. The model states that the random variable Y is related to the variable x by $linear regression$ where the parameters α and β correspond to the intercept and the slope of the line, respectively, and ε denotes a random error. With observations (x₁, y₁), (x₂, y₂),…, (x_n, y_n) the usual assumption is that the random errors are independent observations from a normal distribution with mean 0 and variance σ². In this case the parameters are usually estimated using ordinary least squares (see method of least squares). The estimates, denoted by α̂ and β̂, are given by $linear regression$ where x̄ and y¯ are the means of x₁, x₂,…, x_n and y₁, y₂,…, y_n, respectively, and where $linear regression$ The variance σ² is estimated by $linear regression$ where .
A 100(1−2θ)% confidence interval for β is provided by $linear regression$ where t_ν(θ) is the upper 100θ% point (see percentage point) of a t-distribution with ν degrees of freedom. A 100(1−2θ)% confidence interval for the expected value of Y when x=x₀ is $linear regression$ A 100(1−2θ)% prediction interval for the value y₀ of Y when x=x₀ is $linear regression$ See also multiple regression model; regression diagnostics; regression through the origin.
http://onlinestatbook.com/stat_sim/reg_by_eye/index.html Applet.

Geology and Earth Sciences

In statistics, a comparison of two sets of data to see if there is a linear relationship.

Economics

A method in numerical data analysis that models the relationship among variables as a linear function of the unknown parameters. One of the most popular methods of analysing linear regression in econometrics is ordinary least squares; other commonly used methods include least absolute deviation, orthogonal regression, and least median of squares, or robust regression.

单词	linear regression
释义	linear regression Mathematics See regression. Statistics The simplest and most used of all statistical regression models. The model states that the random variable Y is related to the variable x by $linear regression$ where the parameters α and β correspond to the intercept and the slope of the line, respectively, and ε denotes a random error. With observations (x₁, y₁), (x₂, y₂),…, (x_n, y_n) the usual assumption is that the random errors are independent observations from a normal distribution with mean 0 and variance σ². In this case the parameters are usually estimated using ordinary least squares (see method of least squares). The estimates, denoted by α̂ and β̂, are given by $linear regression$ where x̄ and y¯ are the means of x₁, x₂,…, x_n and y₁, y₂,…, y_n, respectively, and where $linear regression$ The variance σ² is estimated by $linear regression$ where . A 100(1−2θ)% confidence interval for β is provided by $linear regression$ where t_ν(θ) is the upper 100θ% point (see percentage point) of a t-distribution with ν degrees of freedom. A 100(1−2θ)% confidence interval for the expected value of Y when x=x₀ is $linear regression$ A 100(1−2θ)% prediction interval for the value y₀ of Y when x=x₀ is $linear regression$ See also multiple regression model; regression diagnostics; regression through the origin. http://onlinestatbook.com/stat_sim/reg_by_eye/index.html Applet. Geology and Earth Sciences In statistics, a comparison of two sets of data to see if there is a linear relationship. Economics A method in numerical data analysis that models the relationship among variables as a linear function of the unknown parameters. One of the most popular methods of analysing linear regression in econometrics is ordinary least squares; other commonly used methods include least absolute deviation, orthogonal regression, and least median of squares, or robust regression.
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