Outline of regression analysis explained

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).

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
  • Multinomial logit
  • Ordered logit
• Probit model
  • Multinomial probit
  • 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
• Condition number

Formal aids to model selection

• Model selection
• Mallows's C_p
• 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 process
• 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