Linear models: fall 2002

Statistics 312/612: Linear models (fall 2002)

The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms (with particular reference to S-plus); alternatives to least squares. Generalized linear models. After Statistics 242b and Mathematics 222 or equivalents.


Instructor:	David Pollard
Email:	david.pollard@yale.edu
Office hours:	Thurs 12:00–1:15 or immediately after lectures
Time:	Tuesday, Thursday 9:00–10:15.
Place:	24 Hillhouse (Dana House), room 107
TA:	Peter Radchenko

Grading

approximately nine homework sheets, with lab exercises using Splus or R (two very similar implementations of the S language)

final grade based on homework

Texts and references

No single text.
Material drawn from many sources.
See also the Handouts and references for specific topics.

Tentative list of topics

brief introduction to the S language:
- matrices and data frames; lm(); lm.object; summary(); etc
- interpretation of output from S
fitting by least squares:
- orthonormal bases; Q-R decompositions
- hat matrices (projections)
- singular value decompositions
- possible singularity of design matrix; near collinearity; stability of the fit
variances and covariances
- Gauss-Markov theorem
- estimation of variance using residual sum of squares
- weighted least squares
- instrumental variables and two-stage least squares
- variance minimization; principal components
- ridge regression
- overparametrized models; estimable functions; contrasts
- sensitivity analysis of least squares; near-collinearity
statistical theory for normal errors:
- multivariate normal and rotation of axes
- chi-square, t, and F distributions
- hypothesis testing
- noncentral chi-square and power of tests
- ANOVA tables
randomization and permutation distributions:
- Fisher's justification of normal approximation via randomization
- experimental design: orthogonal and unbalanced designs; blocking; factorial designs
- choice of contrasts for analysis of variance
random effects and mixed models
causality and the interpretation of fitted models; ecological regression
diagnostics and plots
analysis of transformations and departures from additivity
categorical models and log-linear models

DP: 3 Oct 2002