Outline of regression analysis

In statistics, regression analysis includes any technique for learning about the relationship between one or more dependent variables Y and one or more independent variables X.

The following outline is an overview and guide to the variety of topics included within the subject of regression analysis.

Overview articles

• Regression analysis
• Linear regression

Non-statistical articles related to regression

• Least squares
• Linear least squares
• Non-linear least squares
• Least absolute deviations
• Curve fitting
• Smoothing

Basic statistical ideas related to regression

• Conditional expectation
• Correlation
• Correlation coefficient
• Mean square error

Visualization

• Scatterplot

Linear regression based on least squares

• General linear model
• Ordinary least squares
• Generalized least squares
• Simple linear regression
• Ridge regression
• Polynomial regression
• Segmented regression
• Nonlinear regression

Generalized linear models

• Generalized linear models
• Logistic regression
• Poisson regression

Inference for regression models

• F-test
• t-test
• Lack-of-fit sum of squares
• Confidence band
• Coefficient of determination
• Scheffé's method

Diagnostics for regression models

• Studentized residual
• Cook's distance
• Variance inflation factor
• DFFITS
• Partial residual plot
• Partial regression plot
• Leverage

Formal aids to model selection

• Mallows' Cp
• Akaike information criterion
• Bayesian information criterion
• Hannan-Quinn information criterion
• Cross validation

Robust regression

• Robust regression

Challenges to regression modeling

• Autocorrelation
• Multicollinearity
• Homoscedasticity and heteroscedasticity
• Lack of fit
• Non-normality of errors
• Outliers

Terminology

• Linear model — relates to meaning of "linear"
• Dependent and independent variables
• Errors and residuals in statistics
• Hat matrix

Methods for dependent data

• Generalized least squares
• Mixed model
• Random effects model
• Hierarchical linear models

Nonparametric regression

• Nonparametric regression
• Isotonic regression

Semiparametric regression

• Semiparametric regression
• Local regression

Other forms of regression

• Total least squares regression
• Errors-in-variables model
• Instrumental variables regression
• Quantile regression
• Generalized additive model
• Probit model

See also

• Prediction
• Design of experiments
• Data transformation
• Box-Cox transformation
• Machine learning
• Analysis of variance
• Causal inference