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

regression analysis

Physics

A method for calculating the best straight line for a linear equation with two variables x and y, for which x can be measured accurately and y has a random error associated with its measurement. The linear equation is written in the form y=α+β‎x, where α‎ and β‎ are constants. The error is associated with a mean and variance. For a given x_i, the true value of y_i is given by y_i=α+β‎x_i. The measured value Y_i of y_i is given by Y_i=y_i+ε‎_i, where ε‎_i is a random error. The relation between x and y is a straight line together with a random error. If the line y=a+bx is considered then the quantity d_i=a+bx_i−Y_i is the difference between the value of y_i on the line at x_i and Y_i. The method of least squares is used to find a and b, which minimize S, defined by

$S = Σ_{i = 1}^{n} d_{i}^{2} .$

This is done using partial derivatives. b is given by:

$(Σ_{i = 1}^{n} x_{i} Y_{i} - n \bar{x} \bar{Y}) / (Σ_{i = 1}^{n} x_{i}^{2} - n \bar{x} 2),$

where $\bar{x}$ and $\bar{Y}$ denote the mean values. a can be worked out from b by $a = \bar{Y} - b \bar{x}$ . The line y=a+bx, with the values of a and b obtained by the method of least squares, is called the regression line.

Chemical Engineering

The statistical analysis and measure of the association between a dependent variable (y) and an independent variable (x) that involves calculating the best straight line for a linear equation between x and y as $y = a + b x$ where a and b are constants. While x can be measured accurately, there is a statistical random error associated with y. The least squares method aims to minimize the sum of the square of the difference between all (n) values of y on the line at x:
$\begin{array}{l} a n + b Σ x = Σ y \\ a Σ x + b Σ x^{2} = Σ x y \end{array}$

The regression line is the calculated line of best fit.

Computer

A statistical technique that is concerned with fitting relationships between a dependent variable, y, and one or more independent variables, x₁, x₂,…, usually by the method of least squares.
A linear regression model is one in which the theoretical mean value, μ‎_i, of the observation y_i is a linear combination of independent variables,
$μ = β_{0} + β_{1} x_{1} + \dots + β_{k} x_{k}$
when k x-variables are included in the model. The multiples β‎₀, β‎₁,… β‎_k are parameters of the model and are the quantities to be estimated; they are known as regression coefficients, β‎₀ being the intercept or constant term. A model with more than one x-variable is known as a multiple regression model.
Nonlinear regression models express μ‎ as a general function of the independent variables. The general functions include curves such as exponentials and ratios of polynomials, in which there are parameters to be estimated.
Various procedures have been devised to detect variables that make a significant contribution to the regression equation, and to find the combination of variables that best fits the data using as few variables as possible. Analysis of variance is used to assess the significance of the regression model. See also generalized linear model, influence.

Geography

A technique for identifying the relationship between a dependent variable y, and one or more independent variables x. While correlation ‘makes no assumption as to which is the dependent and which the independent variable, it simply assesses the degree of association between the variables. Regression attempts to describe the dependence of a variable on one or more explanatory variables. It assumes that there is a one-way causal effect from the explanatory variable(s) to the response variable. Principal components analysis is a regression technique.

单词	regression analysis
释义	regression analysis Physics A method for calculating the best straight line for a linear equation with two variables x and y, for which x can be measured accurately and y has a random error associated with its measurement. The linear equation is written in the form y=α+β‎x, where α‎ and β‎ are constants. The error is associated with a mean and variance. For a given x_i, the true value of y_i is given by y_i=α+β‎x_i. The measured value Y_i of y_i is given by Y_i=y_i+ε‎_i, where ε‎_i is a random error. The relation between x and y is a straight line together with a random error. If the line y=a+bx is considered then the quantity d_i=a+bx_i−Y_i is the difference between the value of y_i on the line at x_i and Y_i. The method of least squares is used to find a and b, which minimize S, defined by $S = Σ_{i = 1}^{n} d_{i}^{2} .$ This is done using partial derivatives. b is given by: $(Σ_{i = 1}^{n} x_{i} Y_{i} - n \bar{x} \bar{Y}) / (Σ_{i = 1}^{n} x_{i}^{2} - n \bar{x} 2),$ where $\bar{x}$ and $\bar{Y}$ denote the mean values. a can be worked out from b by $a = \bar{Y} - b \bar{x}$ . The line y=a+bx, with the values of a and b obtained by the method of least squares, is called the regression line. Chemical Engineering The statistical analysis and measure of the association between a dependent variable (y) and an independent variable (x) that involves calculating the best straight line for a linear equation between x and y as $y = a + b x$ where a and b are constants. While x can be measured accurately, there is a statistical random error associated with y. The least squares method aims to minimize the sum of the square of the difference between all (n) values of y on the line at x: $\begin{array}{l} a n + b Σ x = Σ y \\ a Σ x + b Σ x^{2} = Σ x y \end{array}$ The regression line is the calculated line of best fit. Computer A statistical technique that is concerned with fitting relationships between a dependent variable, y, and one or more independent variables, x₁, x₂,…, usually by the method of least squares. A linear regression model is one in which the theoretical mean value, μ‎_i, of the observation y_i is a linear combination of independent variables, $μ = β_{0} + β_{1} x_{1} + \dots + β_{k} x_{k}$ when k x-variables are included in the model. The multiples β‎₀, β‎₁,… β‎_k are parameters of the model and are the quantities to be estimated; they are known as regression coefficients, β‎₀ being the intercept or constant term. A model with more than one x-variable is known as a multiple regression model. Nonlinear regression models express μ‎ as a general function of the independent variables. The general functions include curves such as exponentials and ratios of polynomials, in which there are parameters to be estimated. Various procedures have been devised to detect variables that make a significant contribution to the regression equation, and to find the combination of variables that best fits the data using as few variables as possible. Analysis of variance is used to assess the significance of the regression model. See also generalized linear model, influence. Geography A technique for identifying the relationship between a dependent variable y, and one or more independent variables x. While correlation ‘makes no assumption as to which is the dependent and which the independent variable, it simply assesses the degree of association between the variables. Regression attempts to describe the dependence of a variable on one or more explanatory variables. It assumes that there is a one-way causal effect from the explanatory variable(s) to the response variable. Principal components analysis is a regression technique.
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