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Both the "multilevel regression" and "poststratification" ideas of MRP can be generalized. Multilevel regression can be replaced by nonparametric regression [15] or regularized prediction, and poststratification can be generalized to allow for non-census variables, i.e. poststratification totals that are estimated rather than being known. [16]
Ridge regression; Regularized; Least absolute deviations; Iteratively reweighted; Bayesian; Bayesian multivariate; Least-squares spectral analysis; Background; Regression validation; Mean and predicted response; Errors and residuals; Goodness of fit; Studentized residual; Gauss–Markov theorem; Mathematics portal
The following outline is provided as an overview of and topical guide to regression analysis: 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).
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 infer causal relationships between the independent and dependent variables. Importantly, regressions by themselves only reveal ...
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).
In other words, a simple linear regression model might, for example, predict that a given randomly sampled person in Seattle would have an average yearly income $10,000 higher than a similar person in Mobile, Alabama. However, it would also predict, for example, that a white person might have an average income $7,000 above a black person, and a ...
The design matrix has dimension n-by-p, where n is the number of samples observed, and p is the number of variables measured in all samples. [4] [5]In this representation different rows typically represent different repetitions of an experiment, while columns represent different types of data (say, the results from particular probes).
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