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All major statistical software packages perform least squares regression analysis and inference. Simple linear regression and multiple regression using least squares can be done in some spreadsheet applications and on some calculators. While many statistical software packages can perform various types of nonparametric and robust regression ...
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 ...
Commonality analysis is a statistical technique within multiple linear regression that decomposes a model's R 2 statistic (i.e., explained variance) by all independent variables on a dependent variable in a multiple linear regression model into commonality coefficients.
The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable.
The multilevel regression with poststratification model involves the following pair of steps: MRP step 1 (multilevel regression) : The multilevel regression model specifies a linear predictor for the mean μ Y {\displaystyle \mu _{Y}} , or the logit transform of the mean in the case of a binary outcome, in poststratification cell j ...
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 ...
The main approaches for stepwise regression are: Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant ...
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]