Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

62Jxx Linear inference and regression

This subtopic introduces the core ideas in linear inference and regression, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

62J05 Linear regression; mixed models

Overview

Linear regression; mixed models. This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks

62J07 Ridge regression; shrinkage estimators (Lasso)

Overview

Ridge regression; shrinkage estimators (Lasso). This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks

62J10 Analysis of variance and covariance

Overview

Analysis of variance and covariance. This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks

62J12 Generalized linear models (logistic models)

Overview

Generalized linear models (logistic models). This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks

62J15 Paired and multiple comparisons

Overview

Paired and multiple comparisons. This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks

62J20 Diagnostics, and influence diagnostics

Overview

Diagnostics, and influence diagnostics. This topic addresses linear inference and regression, including estimation, diagnostics, model selection, and linear-model geometry.

Related Wikipedia Page

Wikipedia: Regression analysis

Useful Links

Key Ideas

  • linear model specification and estimation
  • hypothesis testing and confidence procedures
  • diagnostics and model adequacy

Typical Uses

Used to infer associations and effects under linear modeling assumptions.

Applications

  • Experimental and observational studies
  • Forecasting and trend analysis
  • Econometric and biomedical modeling

References

Recommended Textbooks