## Statistics 312a/612a, Fall 1996

## Linear Models

**Instructor: ** Marten Wegkamp

**Office: ** 24 Hillhouse Ave., room 208

**Phone:** 432-0638

**Email: **wegkamp@stat.yale.edu

**Teaching assistant: **Brendan Murphy

** Class times and locations: **
Tuesdays and Thursdays, both at 2.30 - 3.45 WLH 114

**Prerequisites: **
basic knowledge of both linear algebra and probability theory.
Splus will be needed for some exercises to illustrate the theory; those
who're not familiar with this computer package are strongly recommended
to follow the crash course (the first four weeks) of Stat200 on the Friday
afternoons.

#### Topics

I shall treat most of the topics of Chapters 3,4,5,6 in ``Linear
statistical models'' by J. Stapleton, Wiley (1995).
- The geometry of the least squares.
- Statistical properties of the least squares estimator
- the Gausz-Markov theorem
- distribution theory
- confidence intervals/ ellipsoids

- Model choice: shrinking the number of regression variables
- Multicollinearity:
- identifiability constraints
- principal components regression
- ridge estimation

- Linear hypothesis testing:
- F-test (general case)
- regression
- analysis of variance

- Generalized linear regression
- Aitken estimator
- heteroscedasticity
- autoregression

- Restricted least squares
- Sensitivity analysis:
- prediction (hat) matrix
- effect of a single observation
- measures based on residuals/ confidence ellipsoids
- diagnostic plots

- Robust regression
- Boostrapping linear regression models.