Standard syllabus
Linear models · Graduate · Math
Learning objectives from the Linear models syllabus, grouped by unit. Click an objective for study materials.
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
Learning objectives
Click an objective for study materials.
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
Definitions and structure
- 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
Proofs and reasoning
- Analysis of variance as linear models — Analysis of variance as linear models
- Multicollinearity — Multicollinearity
- Variance inflation — Variance inflation
- F and t tests in matrix notation — F and t tests in matrix notation
- Confidence ellipsoids for coefficients — Confidence ellipsoids for coefficients
Abstraction and generalization
- 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
Modeling and computation
- Apply gauss–markov theorem and blue in engineering contexts — Apply gauss–markov theorem and blue in engineering contexts
- Apply weighted in engineering contexts — Apply weighted in engineering contexts
- Apply generalized least squares in engineering contexts — Apply generalized least squares in engineering contexts
- Apply partitioned regression in engineering contexts — Apply partitioned regression in engineering contexts
- Apply frisch–waugh in engineering contexts — Apply frisch–waugh in engineering contexts
Data and technology
- Use software to explore linear models problems numerically — Use software to explore linear models problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Analysis of variance as linear models — Analysis of variance as linear models
- Multicollinearity — Multicollinearity
- Variance inflation — Variance inflation
- F and t tests in matrix notation — F and t tests in matrix notation
- Confidence ellipsoids for coefficients — Confidence ellipsoids for coefficients
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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