Mathematics / core
Linear models and statistical geometry
Interpret regression as projection, then analyze uncertainty, design, diagnostics, and extensions for dependent data.
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Module 01 core
Linear models and statistical geometry
Interpret regression as projection, then analyze uncertainty, design, diagnostics, and extensions for dependent data.
- 01
Least squares as orthogonal projection
Derive fitted values from a projection and separate deterministic geometry from statistical assumptions.
24 min - 02
Estimability and rank-deficient designs
Identify the parameter combinations a design can actually distinguish, including overparameterized group models.
25 min - 03
The Gauss–Markov theorem and efficiency
Prove the covariance comparison behind BLUE and identify exactly which competing estimators it covers.
27 min - 04
Gaussian regression and exact inference
Use independent orthogonal Gaussian components to derive exact coefficient t statistics and distinguish mean from future-response uncertainty.
27 min - 05
Contrasts, ANOVA, and nested models
Compare nested mean spaces using extra sums of squares and interpret group contrasts without treating significance as an effect size.
27 min - 06
Leverage, influence, and residual diagnostics
Distinguish unusual predictor geometry, unusual responses, and sensitivity to deleting an observation.
27 min - 07
Generalized least squares
Whiten a known error covariance and understand what changes when weights must be estimated from the same data.
27 min - 08
Ridge regression and bias–variance tradeoffs
Analyze shrinkage in singular-vector coordinates and assess bias, variance, scaling, and validation separately.
28 min - 09
Generalized linear models and link functions
Connect response distributions, linear predictors, and mean links without confusing a transformed mean with a transformed observation.
29 min - 10
Experimental design and optimal information
Choose informative predictor settings for a stated model, while preserving randomization, replication, and checks against misspecification.
28 min