Please note that the official course website is on Canvas (log in with CNetID), NOT here. This webpage is for those who are interested in STAT 22400 to get an idea of what the course is like.
STAT 22000 or 23400 with a grade of at least C; or 24500, 24510, or PBHS 32100, or AP Statistics credit, or equivalent. and two-quarters of calculus (MATH 13200, 15200, or 16200 or above).
STAT 22400/PBHS32400 introduces the methods and applications of fitting and interpreting multiple regression models. The primary emphasis is on the method of least squares and its many varieties. Topics include the examination of residuals, the transformation of data, strategies, and criteria for the selection of a regression equation, the use of dummy variables, tests of fit, nonlinear models, multi-collinearity, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The techniques discussed are illustrated by many real examples involving data from both the natural and social sciences. Matrix notation is introduced as needed.
Chatterjee & Hadi. Regression Analysis by Example, 5th edition 2005, Wiley
| Week/Date | Slides | Content | Textbook Coverage |
|---|---|---|---|
| Before CLass | L00.pdf | Brief Intro to R and RStudio | – |
| Week 1 – 9/27 | L01.pdf | Intro to the ggplot2 library |
– |
| Week 1 – 9/29 | LA0928_demo1.Rmd, LA0928_demo2.Rmd LA0928_demo3.Rmd LA0928slides.pdf |
Intro to R Markdown | – |
| Week 1 – 10/1 | LA1001slides.pdf LA1001.Rmd LA1001.pdf |
Example: NC Birth Data | – |
| Week 2 – 10/4 | L02.pdf | What are multiple linear regression models? Least-square estimation; Fitted values; residuals and their properties; Interpretation of regression coefficients as effects of Xi on Y after adjusting for other covariates | Section 3.1-3.5 |
| Week 2 – 10/6 | L03.pdf | Standard errors and distributions of least-square estimators; Confidence intervals and hypothesis tests of individual regression coefficients | Section 3.7, 3.9 |
| Week 2 – 10/8 | L04.pdf (p.1-25) | Confidence intervals and prediction intervals for predictions; Sum of squares and their degrees of freedom; Mean squares; Multiple R-squared, Adjusted R-Squared |
Section 3.11, 3.8 |
| Week 3 – 10/11 | L04.pdf (p.26-end) | F-Tests of multiple coefficients (all coefficients, a subset of coefficients, the equality of coefficients, estimation and tests of coefficients under constraints) | Section 3.10 |
| Week 3 – 10/13 | L05.pdf | Models with categorical predictors/dummy variables; Interactions of two categorical predictors |
Section 5.1-5.3 |
| Week 3 – 10/15 | L06.pdf | Interactions of categorical and numerical predictors | Section 5.4 |
| Week 4 – 10/18 | L07.pdf | Interactions of three or more predictors | Section 5.4 |
| Week 4 – 10/20 | L08.pdf L09.pdf |
Polynomial Models Ordinal Categorical Predictors |
– |
| Week 4 – 10/22 | L10.pdf | Model Diagnostics; Assumptions of MLR; Leverage; Standardized and Studentized residuals; Residual Plots |
Section 4.1-4.4 |
| Week 5 – 10/25 | L11.pdf qqnorm.pdf |
Checking assumptions; Pairwise scatterplots and better tools; Checking interactions of two numerical predictors; Residual-plus-component plot; Normal Probability Plots |
Section 4.5-4.7, 4.12.2 |
| Week 5 – 10/27,10/29 | L12.pdf | Influential points and outliers; Hat matrix, leverages, high leverage points; Cook’s distance; Added-Variable Plot |
Section 4.8-4.11, 4.12.1 |
| Week 6 – 11/1 | L13.pdf | Transformation of variables | Chapter 6 |
| Week 6 – 11/3 | – | Midterm Exam. No lecture | – |
| Week 6 – 11/5 Week 7 – 11/8 |
L14.pdf | Weighted least-squares | Section 7.1-7.2 |
| Week 7 – 11/10, 11/12 | L15.pdf | The problem of correlated errors; Detection (time plot, runs test, Durbin-Watson test, lag plots, autocorrelation function and plots Remedies (by removing AR(1) dependence, by including missing predictors, by removing seasonality) |
Chapter 8 |
| Week 8 – 11/15, 11/17 | L16.pdf | Multicollinearity | Chapter 9 |
| Week 8 – 11/19 Week 9 – 11/29, 12/1 |
L17.pdf L17_example.pdf |
Variable Selection Procedures | Chapter 11 |
| Week 9 – 12/3 | L18.pdf | Ridge and Lasso Regression | Chapter 9 |
| Week 10 – 12/8, 12/9 | – | Online Final Exam | – |
Last Update: 08/14/2022