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.

General regression analysis concepts

Overview articles

• Regression analysis
• Linear regression

Non-statistical articles related to regression

• Least squares
• Linear least squares (mathematics)
• Non-linear least squares
• Least absolute deviations
• Curve fitting
• Smoothing
• Cross-sectional study

Basic statistical ideas related to regression

• Conditional expectation
• Correlation
• Correlation coefficient
• Mean square error
• Residual sum of squares
• Explained sum of squares
• Total sum of squares

Visualization

• Scatterplot

Linear regression based on least squares

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

Generalized linear models

• Generalized linear models
• Logistic regression
• Ordered logit
• Probit model
• Ordered probit
• Poisson regression
• Maximum likelihood
• Cochrane–Orcutt estimation

Computation

• Numerical methods for linear least squares

Inference for regression models

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

Challenges to regression modeling

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

Diagnostics for regression models

• Regression model validation
• Studentized residual
• Cook's distance
• Variance inflation factor
• DFFITS
• Partial residual plot
• Partial regression plot
• Leverage
• Durbin–Watson statistic

Formal aids to model selection

• Model selection
• Mallows' Cp
• Akaike information criterion
• Bayesian information criterion
• Hannan–Quinn information criterion
• Cross validation

Robust regression

• Robust regression

Terminology

• Linear model — relates to meaning of "linear"
• Dependent and independent variables
• Errors and residuals in statistics
• Hat matrix
• Trend stationary
• Cross-sectional data
• Time series

Methods for dependent data

• 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
• Deming regression
• Errors-in-variables model
• Instrumental variables regression
• Quantile regression
• Generalized additive model
• Autoregressive model
• Moving average model
• Autoregressive moving average model
• Autoregressive integrated moving average
• Autoregressive conditional heteroskedasticity

See also

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