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  

Richard Lockhart