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The classical, frequentists linear least squares solution is to simply estimate the matrix of regression coefficients ^ using the Moore-Penrose pseudoinverse: ^ = (). To obtain the Bayesian solution, we need to specify the conditional likelihood and then find the appropriate conjugate prior.
It is particularly useful in analysis of variance (a special case of regression analysis), and in constructing simultaneous confidence bands for regressions involving basis functions. Scheffé's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not ...
In statistics, particularly regression analysis, the Working–Hotelling procedure, named after Holbrook Working and Harold Hotelling, is a method of simultaneous estimation in linear regression models. One of the first developments in simultaneous inference, it was devised by Working and Hotelling for the simple linear regression model in 1929 ...
The extension to multiple and/or vector-valued predictor variables (denoted with a capital X) is known as multiple linear regression, also known as multivariable linear regression (not to be confused with multivariate linear regression). [10] Multiple linear regression is a generalization of simple linear regression to the case of more than one ...
The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable. If Y , B , and U were column vectors , the matrix equation above would represent multiple linear regression.
Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. [1]
It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection. In general, total sum of squares = explained sum of squares + residual sum of squares.
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals.