Statistics 312/612: Linear models (fall 1997)
Instructor: David Pollard
Office: 24 Hillhouse Avenue
Office hours: Thursday 4:00 -- 5:00
Email:
David.pollard@yale.edu
Classes: Tuesday, Thursday 10:30--11:45.
Grading
- Problem sets every second week
- Lab exercises using Splus (Stat 200 recommended for those who are
not
familiar with Splus)
- Take-home exam at end of semester
Texts and references
No single text.
-
J. M. Chambers (1977) Computational Methods for Data Analysis
- Good explanation of why X(X'X)^{-1}X' is not the way to go.
- Golub and Van Loan (1983 first ed., 1989 second ed.)
Matrix computations
- Good discussion of SVD and least squares
- A. C. Atkinson Plots, Transformations and Regression
- Nice discussion of diagnostic plots.
- Box, Hunter and Hunter (1978) Statistics for Experimenters: An
Introduction to Design, Data Analysis, and Model Building
- Excellent reference. Not too heavy on the mathematics. Clear.
-
R. A. Fisher (1935 first ed., eight editions) The Design of Experiments
- A classic.
- H. Scheffé (1959)
The Analysis of Variance
- Thorough for its time. Not for bedtime reading.
- J. M.Chambers, W. S. Cleveland, B. Kleiner, and P. A. Tukey (1983)
Graphical Method for Data Analysis
- Very clear explanations about standard diagnostic plots.
-
W. N. Venables and B. D. Ripley (1997?)
Modern Applied Statistics with S-Plus
- You might find it useful for Splus. It also has very terse
accounts of
several topics in this course.
- P. McCullagh and J. A. Nelder (1983 first ed., 1989 second ed.)
Generalized Linear Models
- The standard reference. Big second edition.
- LINPACK Users' Guide (1986).
- General descriptions of algorithms. Clear. (Splus uses some
LINPACK ideas. MatLab grew out of LINPACK, I think.)
- K. V. Mardia, J. T. Kent, and J. M. Bibby (1979)
Multivariate Analysis
- Good source for mathematics of principal components, etc.
- D. A. Belsley, E. Kuh, and R. E. Welsch (1980)
Regression Diagnostics: Identifying Influential Data and Sources
of Collinearity
- Discussion of SVD as a tool for sensitivity analysis.
Tentative list of topics
- least squares theory:
- orthonormal bases; projections; Q-R decompositions
- iterative least squares fitting
- variances and covariances of random vectors
- Gauss-Markov theorem
- estimation of variance using residual sum of squares
- variance minimization; principal components
- singular value decomposition; canonical correlations
- ridge regression
- overparametrized models; estimable functions;
- sensitivity analysis of least squares; near-collinearity
- specific models
- regression
- analysis of variance
- random effects and mixed models
- model fitting in Splus
- normal distribution theory
- multivariate normal and rotation of axes
- chi-square, t, and F distributions
- hypothesis testing
- noncentral chi-square and power of tests
- ANOVA tables
- diagnostics and plots
- experimental design
- orthogonal and unbalanced designs
- latin squares (and maybe balanced incomplete block
designs)
- factorial designs
- (maybe) Yates's algorithm and the FFT
- confounding and partial fractional designs
- analysis of transformations and departures from additivity
- categorical models and log-linear models
- generalized linear models
- least absolute deviations regression
Link to the boxcox data set in Splus
dump format.
Some solutions to Sheet 5.