Summaries of individual lectures

Lecture	Contents	Software examples
1	Course outline, assumed background, definition of linear model.
2	The linear model in matrix form, Examples of linear models.
3	Least squares, the normal equations, matrix form of these equations.	Splus for simple linear regression and matrix manipulation
4	The geometry of least squares, orthogonality of fitted vector and residual vector, ANOVA tables and Pythagoras theorem.
5	Polynomial regression example, ANOVA decomposition	SAS: polynomial regression, recoding.
6	Polynomial regression continued.	SAS: ANOVA tables for polynomial regression.
7	Multiple R2, model order selection introduction, distribution theory, the normal distribution.
8	Multivariate normal distribution, matrix-vector formulation.
9	Distribution Theory for Least Squares, the Hat matrix, idempotent matrices, trace.
10	Quadratic forms, applications of trace, inference (confidence intervals and tests) for linear combinations of $\beta$ entries.	SAS: estimation of linear combination of entries in $\beta$, polynomial regression.
11	F tests and the extra sum of squares, multiple regression.	SAS: Multiple regression, interactions, ANOVA.
12	Extra Sum of Squares and ANOVA tables
13	Model assessment, residual plots.	SAS: residual analysis.
14	Standardized, case deleted, PRESS and Studentized residuals, leverage.
15	A more general extra sum of squares principal
16	Densities, joint densities, normal and multivariate normal densities
17	Distribution theory of linear and quadratic forms in normals, eigenvalue and eigenvector calculations.
18	Course outline, assumed background, definition of linear model
19	SCENIC data examined via multiple regression; variable selection.	SPlus: multiple regression.
20	SCENIC data set: variable selection	SPlus: multiple regression.
21	Regression Diagnostics: DFFITS, DFBETAS, Cook's distance, leverage.	SAS: Regression diagnostics
22	Goodness-of-fit, pure error sum of squares.	SAS Pure error Sum of squares.
23	Goodness-of-fit, pure error sum of squares, added variables plots, categorical covariates, analysis of covariance	SAS: Categorical independent variables
24	Categorical independent variables	SAS: Categorical independent variables
25	Analysis of covariance, interaction terms	SAS: adding interaction terms
26	Two way ANOVA	SAS: Two way ANOVA.
27	Variable selection: forward, backward, stepwise, all subsets	SAS: variable selection
28	Variable selection with categorical variates, Cp, $R^2_{\rm adj}$, power and sample size calculations	SAS: Variable selection with categorical variates
29	Power and sample size, non-centrality parameters
30	Power, sample size, heteroscedastic errors: weighted least squares, transformation, generalized linear models	SAS: weighted least squares
31	Heteroscedastic Errors: weighted least squares	SAS: weighted least squares
32	Logistic and Poisson regression; generalized linear models	SPlus: fitting generalized linear models, logistic and Poisson regression
33	Generalized Linear Models: theory. Non-linear least squares
34	Non-linear least squares	SPlus: fitting non-linear models, initial estimates. SAS: proc nlin.
35	Estimating equations, large sample, introduction to further courses
36	Course review