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First, regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Second, in some situations regression analysis can be used to show causal relationships between the independent and dependent variables. Importantly, regressions by themselves only reveal ...
A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. [1] This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. [2]
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]
Regression analysis – use of statistical techniques for learning about the relationship between one or more dependent variables (Y) and one or more independent variables (X). Overview articles [ edit ]
In statistics, path analysis is used to describe the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, as well as more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA).
Certain types of problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.
In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). PCR is a form of reduced rank regression . [ 1 ] More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model .
A regression model may be represented via matrix multiplication as y = X β + e , {\displaystyle y=X\beta +e,} where X is the design matrix, β {\displaystyle \beta } is a vector of the model's coefficients (one for each variable), e {\displaystyle e} is a vector of random errors with mean zero, and y is the vector of predicted outputs for each ...