00133110: Applied Regression Analysis
Course Description
This is an undergraduate-level course for students majoring in statistics, probability, or any other field where applied statistics plays an
essential role. Methodology and theory for linear regression will be introduced, illustrated by examples and applications. Extensions and advanced
topics, such as categorical predictors, polynomial regression, analysis of variance, weighted least squares, mixed models, transformations,
regression diagnostics, variable selection, nonlinear regression, and generalized linear models, will be covered if time permits.
Syllabus
Lectures and Assignments
| Week | Date | Topics | References | Assignments | Notes |
| 1 | 2/21 | Scatterplots and regression | Weisberg Chap. 1 | | |
| 2 | 2/28 | Random vectors, quadratic forms, moment generating functions | Seber & Lee Secs. 1.4–1.6 | | |
| 3/2 | Independence, multivariate normal distribution | Seber & Lee Secs. 1.6–2.2 | | |
| 3 | 3/7 | Independence and quadratic forms under the multivariate normal, linear regression | Seber & Lee Secs. 2.3–3.1 | Seber & Lee 1a.1, 4; 1b.2, 5; 1c.2; 1m.3, 5; 2a.1, 3; 2b.8; 2c.2; 2d.2, 4; 2m.5, 8, 12 (errata) | Homework 1 due 3/16 |
| 4 | 3/14 | Least squares | Seber & Lee Secs. 3.1 | | |
| 3/16 | Properties of least squares | Seber & Lee Secs. 3.2–3.5 | Seber & Lee 3a.1, 6, 8; 3b.1, 4; 3c.1, 2; 3d.2 | |
| 5 | 3/21 | Generalized least squares, adding predictors | Seber & Lee Secs. 3.10, 3.7 | | |
| 6 | 3/28 | Adding cases, F-tests in linear regression | Seber & Lee Secs. 11.6, 3.8, 4.1, 4.3 | Seber & Lee 3f.1, 4; 3g.1, 3; 3k.4, 5; 3misc.4, 9 | |
| 3/30 | Likelihood ratio tests, multiple correlation coefficient | Seber & Lee Secs. 4.2, 4.4 | | |
| 7 | 4/2 | Goodness-of-fit tests, simultaneous confidence intervals | Seber & Lee Secs. 4.6, 5.1 | Seber & Lee 4a.5; 4b.3; 4c.1; 4m.1, 2, 4 | Homework 2 due 4/11 |
| 8 | 4/11 | Scheffé's method, prediction intervals and bands | Seber & Lee Secs. 5.1–5.3 | | |
| 4/13 | More examples on straight lines | Seber & Lee Sec. 6.1 | Seber & Lee 5m.4, 5, 6; 6a.3, 4 | |
| 9 | 4/18 | Midterm exam | | | Mean = 63, median = 64.5, Q1 = 52, Q3 = 80, high score = 94 |
| 10 | 4/25 | Comparing straight lines, two-phase regression | Seber & Lee Secs. 6.4, 6.5 | Seber & Lee 6c.3; 6m.3 | |
| 4/27 | One-way ANOVA | Seber & Lee Secs. 8.1, 8.2 | | |
| 11 | 5/2 | No class | | | |
| 12 | 5/9 | Two-way ANOVA | Seber & Lee Secs. 8.3–8.5 | Seber & Lee 8a.4, 5; 8b.2; 8c.1; 8e.3; 8m.3, 5 | Homework 3 due 5/16 |
| 5/11 | Bias due to underfitting/overfitting, mispecified covariance matrix, outliers | Seber & Lee Secs. 9.1–9.4 | | |
| 13 | 5/16 | Robustness to nonnormality, random predictors | Seber & Lee Secs. 9.5, 9.6 | | |
| 14 | 5/23 | Measurement error, collinearity | Seber & Lee Secs. 9.6, 9.7 | Seber & Lee 9a.3; 9b.2; 9m.2, 3 | |
| 5/25 | Diagnostic quantities, diagnostics for regression surfaces | Seber & Lee Secs. 10.1–10.3 | | |
| 15 | 5/30 | Variable importance, diagnostics for variance functions, outliers, and collinearity | Seber & Lee Secs. 10.4, 10.6, 10.7 | Seber & Lee 10a.3; 10b.1; 10f.2; 10m.1, 2, 3; Lab | Homework 4 & Lab due 6/13 |
| 16 | 6/6 | Generalized linear models | Casella & Berger Sec. 12.3 | | |
| 6/8 | Robust regression | Seber & Lee Sec. 3.13 | | |
| 18 | 6/20 | Final exam | | | Mean = 45, median = 48, Q1 = 30.5, Q3 = 58.5, high score = 83
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