Regression analysis information

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis^[1]) or estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression).

Regression analysis is primarily used for two conceptually distinct purposes. 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 relationships between a dependent variable and a collection of independent variables in a fixed dataset. To use regressions for prediction or to infer causal relationships, respectively, a researcher must carefully justify why existing relationships have predictive power for a new context or why a relationship between two variables has a causal interpretation. The latter is especially important when researchers hope to estimate causal relationships using observational data.^[2]^[3]

^ Necessary Condition Analysis
^ David A. Freedman (27 April 2009). Statistical Models: Theory and Practice. Cambridge University Press. ISBN 978-1-139-47731-4.
^ R. Dennis Cook; Sanford Weisberg Criticism and Influence Analysis in Regression, Sociological Methodology, Vol. 13. (1982), pp. 313–361

[1] Necessary Condition Analysis

[Freedman2009-2] David A. Freedman (27 April 2009). Statistical Models: Theory and Practice. Cambridge University Press. ISBN 978-1-139-47731-4.

[3] R. Dennis Cook; Sanford Weisberg Criticism and Influence Analysis in Regression, Sociological Methodology, Vol. 13. (1982), pp. 313–361

Regression analysis information

and 28 Related for: Regression analysis information

Regression analysis

Linear regression

Logistic regression

Polynomial regression

Time series

Nonlinear regression

Quantile regression

Poisson regression

Segmented regression

Regression testing

Regression discontinuity design

Regression toward the mean

Analysis of covariance

Ridge regression

Robust regression

Ordinal regression

Bivariate analysis

Least squares

Multivariate statistics

Regression validation

Isotonic regression

Survival analysis

Nonparametric regression

Stepwise regression

Local regression

Partial least squares regression

General linear model

Binary regression

Regression analysis
Part of a series on
Models
Linear regression Simple regression Polynomial regression General linear model
Generalized linear model Vector generalized linear model Discrete choice Binomial regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson
Multilevel model Fixed effects Random effects Linear mixed-effects model Nonlinear mixed-effects model
Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal components Least angle Local Segmented
Errors-in-variables
Estimation
Least squares Linear Non-linear
Ordinary Weighted Generalized Generalized estimating equation
Partial Total Non-negative 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
v t e

Machine learning and data mining
Part of a series on
Paradigms Supervised learning Unsupervised learning Online learning Batch learning Meta-learning Semi-supervised learning Self-supervised learning Reinforcement learning Curriculum learning Rule-based learning Quantum machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association rules Semantic analysis Structured prediction Feature engineering Feature learning Learning to rank Grammar induction Ontology learning Multimodal learning
Supervised learning (classification • regression) Apprenticeship learning Decision trees Ensembles Bagging Boosting Random forest k-NN Linear regression Naive Bayes Artificial neural networks Logistic regression Perceptron Relevance vector machine (RVM) Support vector machine (SVM)
Clustering BIRCH CURE Hierarchical k-means Fuzzy Expectation–maximization (EM) DBSCAN OPTICS Mean shift
Dimensionality reduction Factor analysis CCA ICA LDA NMF PCA PGD t-SNE SDL
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov
Anomaly detection RANSAC k-NN Local outlier factor Isolation forest
Artificial neural network Autoencoder Cognitive computing Deep learning DeepDream Feedforward neural network Kolmogorov–Arnold Network Recurrent neural network LSTM GRU ESN reservoir computing Restricted Boltzmann machine GAN Diffusion model SOM Convolutional neural network U-Net Transformer Vision Mamba Spiking neural network Memtransistor Electrochemical RAM (ECRAM)
Reinforcement learning Q-learning SARSA Temporal difference (TD) Multi-agent Self-play
Learning with humans Active learning Crowdsourcing Human-in-the-loop RLHF
Model diagnostics Coefficient of determination Confusion matrix Learning curve ROC curve
Mathematical foundations Kernel machines Bias–variance tradeoff Computational learning theory Empirical risk minimization Occam learning PAC learning Statistical learning VC theory
Machine-learning venues ECML PKDD NeurIPS ICML ICLR IJCAI ML JMLR
Related articles Glossary of artificial intelligence List of datasets for machine-learning research List of datasets in computer vision and image processing Outline of machine learning
v t e