Linear models
Graduate · Statistics
Syllabus focus
Standard syllabus · Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Standard syllabus
Matrix linear models
- Gauss–Markov theorem and BLUE
- Weighted and generalized least squares
- Partitioned regression and Frisch–Waugh
- Analysis of variance as linear models
- Multicollinearity and variance inflation
Inference and diagnostics
- F and t tests in matrix notation
- Confidence ellipsoids for coefficients
- Influence diagnostics: hat matrix and Cook's distance
- Residual analysis and assumption checking
- Variable selection criteria: AIC, BIC, Mallows Cp
Extensions
- Polynomial and spline regression
- Robust regression (introduction)
- Mixed models preview
- Regularized regression at graduate level
Theoretical / proof-based
Proof-based linear model theory
- Proof of Gauss–Markov theorem
- Distribution theory for normal linear models
- Cochran's theorem and ANOVA decomposition
- Best invariant estimation
- Asymptotics for linear models under misspecification
- Geometric interpretation in Hilbert space
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Graduate-level treatment of regression. Theoretical sections include matrix proofs; standard sections cover computation and diagnostics at scale.