Applied linear models with a focus on practical applications. Topics include least squares estimation, model diagnostics, variable selection, regularization, mixed-effect models, splines, additive models, an introduction to GLMs, and missing data. Matrix formulations are used. Data analysis in R and Python and effective written communication is emphasized.
Athena Title
Applied Linear Models
Pre or Corequisite
STAT 4800/6800 or permission of department
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Student Learning Outcomes
Students will build and make inferences from linear models to analyze relationships between variables in real-world datasets. This includes assessing model assumptions, performing model remediation, performing variable selection, assessing model fit and performance, and drawing inferences regarding the data-generating mechanism. Emphasis will be on linear regression, but students will also learn the basic principles of experimental design and the analysis of variance.
Students will analyze high-dimensional data using shrinkage methods such as ridge regression and LASSO while balancing the bias-variance tradeoff.
Students will recognize the various purposes of statistical models and how this influences decisions about estimation, inference and model-building. In particular, they will understand that suitable methods depend on whether the purpose of the model is prediction versus estimation and inference, and whether the application is to observational versus experimental data.
Students will differentiate between fixed and random effects in linear mixed models and estimate model parameters using likelihood-based methods for hierarchical and longitudinal data.
Students will construct flexible models using splines and generalized additive models to capture complex nonlinear relationships in data.
Students will develop and interpret generalized linear models for non-Gaussian response variables and understand when to use these models.
Students will understand and apply methods for handling missing data. This includes differentiating between missingness mechanisms, recognizing the main approaches to analyzing data subject to missingness understanding their pros and cons.
Students will analyze real-world datasets in R or Python and communicate findings effectively through written reports using professional typesetting system (e.g. LaTeX).
Topical Outline
Introduction to linear models and least squares estimation, statistical inference, hypothesis testing, Gauss-Markov theorem
