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, generalized linear models, and causal inference will be covered if time permits.
Syllabus
Lectures and Assignments
| Week | Date | Topics | References | Assignments | Notes |
| 1 | 2/20 | Introduction | Seber & Lee Secs. 1.1–1.3 | | |
| 2/22 | Random vectors, quadratic forms, moment generating functions | Seber & Lee Secs. 1.4–1.6 | | |
| 2 | 2/27 | Multivariate normal distribution | Seber & Lee Secs. 2.1–2.3 | | |
| 3 | 3/5 | Distribution of quadratic forms, least squares | Seber & Lee Secs. 2.4, 3.1 | | |
| 3/7 | Generalized inverse, properties of least squares | Seber & Lee App. A.10, Secs. 3.2, 3.3 | Seber & Lee 1a.1; 1b.2, 5; 1c.2; 1m.3, 5; 2a.1; 2b.8; 2c.2; 2d.2, 4; 2m.5, 8, 12; 3a.1, 6, 8; 3b.1, 4 | Homework 1 due 3/19 |
| 4 | 3/12 | Distribution theory, maximum likelihood, generalized least squares | Seber & Lee Secs. 3.4, 3.5, 3.10 | | |
| 5 | 3/19 | Adding predictors and cases | Seber & Lee Secs. 3.7, 11.6 | Seber & Lee 3c.1, 2; 3d.2; 3f.1, 4; 3g.1, 3; 3k.4, 5; 3misc.4, 9 | |
| 3/21 | F-tests in linear regression | Seber & Lee Secs. 3.8, 4.1, 4.3 | | |
| 6 | 3/26 | Likelihood ratio tests, multiple correlation coefficient | Seber & Lee Secs. 4.2, 4.4 | Seber & Lee 4a.5; 4b.3; 4c.1; 4m.1, 2, 4 | Homework 2 due 4/2 |
| 7 | 4/2 | Goodness-of-fit tests, simultaneous confidence intervals | Seber & Lee Secs. 4.6, 5.1 | | |
| 4/4 | No class | | | |
| 8 | 4/9 | Prediction intervals and bands | Seber & Lee Secs. 5.2, 5.3 | Seber & Lee 5m.4, 5, 6 | |
| 9 | 4/16 | More examples on straight lines | Seber & Lee Secs. 6.1, 6.4 | | |
| 4/18 | Midterm exam | | | Mean = 52, median = 57, Q1 = 36, Q3 = 70, high score = 89 |
| 10 | 4/23 | Two-phase regression, one-way ANOVA | Seber & Lee Secs. 6.5, 8.1, 8.2 | Seber & Lee 6a.3, 4; 6c.3; 6m.3 | |
| 11 | 4/30 | No class | | | |
| 5/2 | No class | | | |
| 12 | 5/7 | Two-way ANOVA | Seber & Lee Secs. 8.3–8.5 | | |
| 13 | 5/14 | ANCOVA, model misspecification, bias–variance trade-off | Seber & Lee Secs. 8.8, 9.1–9.3 | Seber & Lee 8a.4, 5; 8b.2; 8c.1; 8e.3; 8m.3, 5 | Homework 3 due 5/21 |
| 5/16 | Outliers, asymptotic F-tests, random predictors | Seber & Lee Secs. 9.4–9.6.1 | | |
| 14 | 5/21 | Measurement error, collinearity | Seber & Lee Secs. 9.6.2–9.7 | Seber & Lee 9a.3; 9b.2; 9d.2; 9m.2, 3 | |
| 15 | 5/28 | Diagnostics for regression surfaces | Seber & Lee Secs. 10.1–10.3 | | |
| 5/30 | Diagnostics for variance functions, outlier dectection | Seber & Lee Secs. 10.4, 10.6, 10.7 | Seber & Lee 10a.3; 10b.2, 3, 4; 10c.4; 10e.3; 10m.2, 3 | Homework 4 due 6/11 |
| 16 | 6/4 | Principal component regression, Lasso | Seber & Lee Secs. 10.7.3, 12.5.3 | | |
| 18 | 6/18 | Final exam | | | Mean = 49, median = 50, Q1 = 38, Q3 = 61, high score = 78
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