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 R^{2}, 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 entries. | SAS: estimation of linear combination of entries in , 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, C_{p}, , 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 |