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 10:3011:45.
Grading
 Problem sets every second week
 Lab exercises using Splus (Stat 200 recommended for those who are
not
familiar with Splus)
 Takehome 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 SPlus
 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; QR decompositions
 iterative least squares fitting
 variances and covariances of random vectors
 GaussMarkov 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; nearcollinearity
 specific models
 regression
 analysis of variance
 random effects and mixed models
 model fitting in Splus
 normal distribution theory
 multivariate normal and rotation of axes
 chisquare, t, and F distributions
 hypothesis testing
 noncentral chisquare 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 loglinear models
 generalized linear models
 least absolute deviations regression
Link to the boxcox data set in Splus
dump format.
Some solutions to Sheet 5.