Linear models
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Linear models — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Matrix linear models
- Gauss–Markov theorem and BLUE — Gauss–Markov theorem and BLUE
- Weighted — Weighted
- Generalized least squares — Generalized least squares
- Partitioned regression — Partitioned regression
- Frisch–Waugh — Frisch–Waugh
- Analysis of variance as linear models — Analysis of variance as linear models
- Multicollinearity — Multicollinearity
- Variance inflation — Variance inflation
Inference and diagnostics
- F and t tests in matrix notation — F and t tests in matrix notation
- Confidence ellipsoids for coefficients — Confidence ellipsoids for coefficients
- Influence diagnostics: hat matrix — Influence diagnostics: hat matrix
- Cook's distance — Cook's distance
- Residual analysis — Residual analysis
- Assumption checking — Assumption checking
- Variable selection criteria: AIC, BIC, Mallows Cp — Variable selection criteria: AIC, BIC, Mallows Cp
Extensions
- Polynomial and spline regression — Polynomial and spline regression
- Robust regression (introduction) — Robust regression (introduction)
- Mixed models preview — Mixed models preview
- Regularized regression at graduate level — Regularized regression at graduate level
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Matrix linear models
Gauss–Markov theorem and BLUE
Coming soon - Inference and diagnostics
F and t tests in matrix notation
Coming soon - Extensions
Polynomial and spline regression
Coming soon
Notes
Graduate Linear models — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/linear_models.json`.